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      <text:p text:style-name="P2"><text:span text:style-name="T7">contexto de modelos lineales</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T7">Estimativa e avaliação computacional do coeficiente de competição intraespecífica em arestas no </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T7">contexto de modelos lineares</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T2">Department </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Agronomy, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Universidad </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Nacional </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">de </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Colombia, Bogotá, Colombia. Postal code: 111321</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Received: 24-09-2021 </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Accepted: <text:s/>13-11-2021 </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2">Published: 20-02-2022</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Abstract</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">In experimental trials, it is usually of interest to give special regard to </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the response of experimental units at the edges, since it is well known that </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>performance <text:s/>of <text:s/>these <text:s/>can <text:s/>be <text:s/>greater <text:s/>than <text:s/>that <text:s/>of <text:s/>the <text:s/>rest <text:s/>of <text:s/>the <text:s/>units </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">due <text:s/>to <text:s/>having <text:s/>less <text:s/>competition <text:s/>from <text:s/>neighboring <text:s/>units. <text:s/>When <text:s/>treatments </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">are available, it is possible that the differences in the mean crop response </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">are attributable to the edge effect. Therefore, it is important to consider the </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">edge or not in the modeling process. In this case, using the Kempton-Besag </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">model and the reparameterization of the model, the intraspecific competition </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">coefficient was estimated through least quadratic estimation that in this case </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">was <text:s/>associated <text:s/>with <text:s/>the <text:s/>edge <text:s/>effect. <text:s/>Its <text:s/>distributional <text:s/>pattern <text:s/>was <text:s/>studied </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="10.344cm" svg:height="0.369cm" svg:x="10.195cm" svg:y="18.654cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">using Monte Carlo simulation. Simulated variance analyses were carried out </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">to see the distributional effect of the F-statistic in the presence of the edge </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">effect as a form of spatial dependence that was evaluated with the Moran </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="10.357cm" svg:height="0.369cm" svg:x="10.195cm" svg:y="19.924cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">index. The coefficient associated with the edge effect showed a clear normal </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="10.209cm" svg:height="0.369cm" svg:x="10.195cm" svg:y="20.347cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">distribution in all the considered edge scenarios. The sign of the coefficient </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="10.107cm" svg:height="0.369cm" svg:x="10.195cm" svg:y="20.771cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and the confidence intervals generated made it possible to discriminate the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">presence/absence of edge effect. In addition, a method was proposed to allow </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="10.378cm" svg:height="0.369cm" svg:x="10.195cm" svg:y="21.617cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">a user to mitigate the fuzziness that may result from the point estimate of the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">coefficient. This procedure can be used in other neighborhood patterns and </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.927cm" svg:height="0.369cm" svg:x="10.195cm" svg:y="22.464cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">other design models of importance in agricultural research.</text:span></text:p>
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   </draw:page>
   <draw:page draw:name="page2" draw:style-name="dp2" draw:master-page-name="master-page40">
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      <text:p text:style-name="P2"><text:span text:style-name="T8">This scientific publication in digital format is a continuation of the Printed Review: Legal Deposit pp 196802ZU42, ISSN 0378-7818.</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr3" draw:text-style-name="P4" draw:layer="layout" svg:width="0.352cm" svg:height="0.412cm" svg:x="0.675cm" svg:y="0.462cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T9"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr3" draw:text-style-name="P4" draw:layer="layout" svg:width="16.174cm" svg:height="0.412cm" svg:x="1.945cm" svg:y="0.462cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T9"><text:s text:c="2"/></text:span><text:span text:style-name="T9">Rev. Fac. Agron. (LUZ). 2022, 39(1): e223916. January - March. ISSN 2477-9407.</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.726cm" svg:height="0.39cm" svg:x="1.175cm" svg:y="0.478cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T10">2-6 </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T9">|</text:span></text:p>
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    <draw:frame draw:style-name="gr5" draw:text-style-name="P6" draw:layer="layout" svg:width="2.199cm" svg:height="0.497cm" svg:x="1.2cm" svg:y="1.094cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Resumen</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">En los ensayos experimentales suele ser de interés prestar especial </text:span></text:p>
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    </draw:frame>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">atención a la respuesta de las unidades experimentales en los bordes, </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.26cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="2.826cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">ya que es bien sabido que el rendimiento de estas puede ser superior </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.696cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="3.239cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">al <text:s/>del <text:s/>resto <text:s/>de <text:s/>unidades <text:s/>por <text:s/>tener <text:s/>menor <text:s/>competencia de <text:s/>unidades </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.332cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="3.652cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">vecinas. En un experimento, donde se tienen tratamientos, es posible </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.751cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="4.065cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">que <text:s/>las <text:s/>diferencias <text:s/>en <text:s/>la <text:s/>respuesta <text:s/>media <text:s/>de <text:s/>las <text:s/>variables <text:s/>medidas </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.239cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="4.477cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">sean <text:s/>atribuibles <text:s/>al <text:s/>efecto <text:s/>de <text:s/>borde. <text:s/>Por <text:s/>lo <text:s/>tanto, <text:s/>es <text:s/>importante </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.922cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="4.89cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">considerar el borde o no en el proceso de modelado. En este caso, </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.188cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="5.303cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">utilizando <text:s/>el <text:s/>modelo <text:s/>de <text:s/>Kempton-Besag <text:s/>y <text:s/>la <text:s/>reparametrización </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.112cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="5.716cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">del modelo, se estimó el coeficiente de competencia intraespecífica </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.985cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="6.128cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">mediante estimación mínima cuadrática que en este caso se asoció </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.353cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="6.541cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">con el efecto de borde. Su patrón de distribución se estudió mediante </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.281cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="6.954cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">simulación <text:s/>Monte <text:s/>Carlo.De <text:s/>cada <text:s/>análisis <text:s/>de <text:s/>varianza <text:s/>con <text:s/>datos </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.616cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="7.367cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">simulados <text:s/>se <text:s/>extrajo <text:s/>el <text:s/>valor <text:s/>del <text:s/>estadístico <text:s/>F <text:s/>y <text:s/>se <text:s/>representó <text:s/>su </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.21cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="7.779cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">comportamiento <text:s/>distribucional <text:s/>para <text:s/>relacionarlo <text:s/>con <text:s/>la <text:s/>ausencia </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.646cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="8.192cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">o <text:s/>presencia <text:s/>del <text:s/>efecto <text:s/>del <text:s/>borde <text:s/>como <text:s/>una <text:s/>forma <text:s/>de <text:s/>dependencia </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.125cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="8.605cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">espacial, la cual se confirmó desde el punto de vista estadístico con </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.947cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="9.018cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">el índice de Moran. El coeficiente asociado con el efecto de borde </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.48cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="9.43cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">mostró una clara distribución normal en todos los escenarios de borde </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.108cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="9.843cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">considerados. El signo del coeficiente y los intervalos de confianza </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.337cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.256cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">generados permitieron discriminar la presencia/ausencia de efecto de </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.527cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.669cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">borde. Además, se propuso un método para permitir al usuario mitigar </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.977cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="11.081cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">la falta de claridad que puede resultar de la estimación puntual del </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.396cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="11.494cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">coeficiente. Este procedimiento se puede utilizar en otros patrones de </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.599cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="11.907cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">vecindad y otros modelos de diseño de importancia en la investigación </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.336cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="12.32cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">agrícola. <text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.759cm" svg:height="0.39cm" svg:x="1.2cm" svg:y="13.12cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Palabras </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.984cm" svg:height="0.39cm" svg:x="2.797cm" svg:y="13.12cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">clave</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="3.523cm" svg:y="13.132cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">: </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.904cm" svg:height="0.369cm" svg:x="3.947cm" svg:y="13.132cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">efecto </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.938cm" svg:height="0.369cm" svg:x="5.097cm" svg:y="13.132cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">borde, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.556cm" svg:height="0.369cm" svg:x="6.275cm" svg:y="13.132cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">coeficiente </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.404cm" svg:height="0.369cm" svg:x="8.057cm" svg:y="13.132cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">de </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.831cm" svg:height="0.369cm" svg:x="8.705cm" svg:y="13.132cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">competición, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.848cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="13.545cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">reparametrización,simulación Monte Carlo.</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr5" draw:text-style-name="P6" draw:layer="layout" svg:width="1.903cm" svg:height="0.497cm" svg:x="1.2cm" svg:y="14.264cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T4">Resumo</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.757cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="15.171cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Em ensaios experimentais, geralmente é de interesse dar atenção </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.176cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="15.583cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">especial à resposta das unidades experimentais nas bordas, uma vez </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.934cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="15.996cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">que é bem conhecido que o desempenho destas pode ser maior do </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.294cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="16.409cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">que o do resto das unidades devido à menor competição de unidades </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.293cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">vizinhas. </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.153cm" svg:height="0.369cm" svg:x="2.626cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Quando </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.387cm" svg:height="0.369cm" svg:x="3.912cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">os </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.649cm" svg:height="0.369cm" svg:x="4.435cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">tratamentos </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.777cm" svg:height="0.369cm" svg:x="6.223cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">estão </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.708cm" svg:height="0.369cm" svg:x="7.137cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">disponíveis, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="8.973cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">é </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.192cm" svg:height="0.369cm" svg:x="9.346cm" svg:y="16.822cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">possível </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.981cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="17.234cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">que as diferenças na resposta média da cultura sejam atribuídas ao </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.671cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="17.647cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">efeito <text:s/>de <text:s/>borda. <text:s/>Portanto, <text:s/>é <text:s/>importante <text:s/>considerar <text:s/>a <text:s/>borda <text:s/>ou <text:s/>não </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.413cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="18.06cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">no <text:s/>processo <text:s/>de <text:s/>modelagem. <text:s/>Nesse <text:s/>caso, <text:s/>utilizando <text:s/>o <text:s/>modelo <text:s/>de </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.603cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="18.473cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Kempton-Besag <text:s/>e <text:s/>a <text:s/>reparametrização <text:s/>do <text:s/>modelo, <text:s/>o <text:s/>coeficiente <text:s/>de </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.692cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="18.885cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">competição <text:s/>intraespecífico <text:s/>foi <text:s/>estimado <text:s/>por <text:s/>meio <text:s/>da <text:s/>estimativa <text:s/>do </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.243cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="19.298cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">mínimo quadrático que, neste caso, foi associada ao efeito de borda. </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.252cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="19.711cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Seu padrão de distribuição foi estudado usando simulação de Monte </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.476cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="20.124cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Carlo. Análises de variância simuladas foram realizadas para verificar </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.002cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="20.536cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">o efeito distributivo da estatística F na presença do efeito de borda </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.756cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="20.949cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">como uma forma de dependência espacial que foi avaliada com o índice </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.442cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="21.362cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">de Moran. O coeficiente associado ao efeito de borda apresentou uma </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.514cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="21.775cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">distribuição normal clara em todos os cenários de borda considerados. </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.54cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="22.187cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">O sinal do coeficiente e os intervalos de confiança gerados permitiram </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.273cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="22.6cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">discriminar a presença / ausência do efeito de borda. Além disso, foi </text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">proposto um método para permitir ao usuário mitigar a imprecisão </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">que </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">pode </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">resultar </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">da </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.463cm" svg:height="0.369cm" svg:x="4.636cm" svg:y="23.426cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">estimativa </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">pontual </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">do </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">coeficiente. </text:span></text:p>
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    </draw:frame>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Este </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">procedimento <text:s/>pode <text:s/>ser <text:s/>usado <text:s/>em <text:s/>outros <text:s/>padrões <text:s/>de <text:s/>vizinhança </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="24.251cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">e </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.929cm" svg:height="0.369cm" svg:x="1.554cm" svg:y="24.251cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">outros </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">modelos </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">de </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.039cm" svg:height="0.369cm" svg:x="4.459cm" svg:y="24.251cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">projeto </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">importantes </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">na </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">pesquisa </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">agrícola. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Palabras </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">chave: </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">efeito </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">de </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.938cm" svg:height="0.369cm" svg:x="5.462cm" svg:y="25.487cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">borda, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">coeficiente </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">de </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">competição, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">reparameterização,Simulação de Monte Carlo</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Introduction</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">It <text:s/>has <text:s/>been <text:s/>100 <text:s/>years <text:s/>since <text:s/>the <text:s/>publications <text:s/>of <text:s/>Arny <text:s/>(1922), </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.396cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="2.45cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">describing <text:s/>the <text:s/>edge <text:s/>effect <text:s/>in <text:s/>agricultural <text:s/>experiments <text:s/>and <text:s/>where </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">proposing <text:s/>ways <text:s/>to <text:s/>avoid <text:s/>it. <text:s/>Even <text:s/>the <text:s/>term <text:s/>competition <text:s/>was <text:s/>used </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.591cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="3.312cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">to <text:s/>associate <text:s/>it <text:s/>with <text:s/>the <text:s/>performance <text:s/>of <text:s/>off-edge <text:s/>row <text:s/>performance </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.108cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="3.744cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">with the rows at the edge, recognizing since then that removing the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">rows <text:s/>from <text:s/>the <text:s/>edge <text:s/>could <text:s/>in <text:s/>certain <text:s/>situations <text:s/>be <text:s/>an <text:s/>unnecessary </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">operation, <text:s/>something <text:s/>that <text:s/>recent <text:s/>studies <text:s/>endorse <text:s/>(Romani </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">et <text:s/>al</text:span></text:p>
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    </draw:frame>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">., </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">1993; Kuemmel, 2003). However, others recommend the elimination </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of edges depending on the crop, with the purpose of making a better </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">estimation of the yield (Gałęzewski </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">et al</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="4.045cm" svg:height="0.369cm" svg:x="16.515cm" svg:y="5.899cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">., 2013). According to Keddy </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">(2001). The definition presents a challenge since it is an example of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">a generalized phenomenon that can occur in quite diverse conditions. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Current <text:s/>research <text:s/>focuses <text:s/>on <text:s/>an <text:s/>autoregressive <text:s/>competition <text:s/>model </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.472cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="7.623cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">(Ord, 1975) used by several authors to consider such an effect and for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">which various proposals are put forth (Connolly </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">et al</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.356cm" svg:height="0.369cm" svg:x="18.169cm" svg:y="8.055cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">., 1993). But this </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">time, rather than estimating the parameters of the model associated </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">with the effects considered, computational analysis was done on the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">least-squared <text:s/>estimator <text:s/>of <text:s/>the <text:s/>Kempton-Besag <text:s/>competition <text:s/>model. </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.569cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="9.779cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">These <text:s/>generated <text:s/>scenarios <text:s/>associated <text:s/>with <text:s/>situations <text:s/>described <text:s/>for </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.506cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="10.21cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">performance when there is no edge effect and when it is perceived not </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.349cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="10.641cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">only at the most exposed edge but also at the two outermost edges of </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.171cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="11.072cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the batch, as well as in partial edge situations (Besag and Kempton, </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.349cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="11.503cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">1986; Shukla and Subrahmanyam, 1999). With the calculation of the </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.552cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="11.934cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Moran index, the spatial dependence of the residuals of the model was </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.315cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="12.365cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">studied. Computationally the effect obviating the spatial dependence </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.96cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="12.797cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of the residuals on the analysis of variance for the two-way model </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">was shown. Finally, with the simulated construction of the confidence </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">interval <text:s/>for <text:s/>the <text:s/>competition <text:s/>estimator, <text:s/>the <text:s/>presence/ <text:s/>absence <text:s/>of </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.248cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="14.09cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">competition could be inferred. This is something that many research </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.285cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="14.521cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">usually describe in their trials (Phillips </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.743cm" svg:height="0.39cm" svg:x="16.413cm" svg:y="14.509cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">et al</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.128cm" svg:height="0.369cm" svg:x="17cm" svg:y="14.521cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">., 2020).</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr5" draw:text-style-name="P6" draw:layer="layout" svg:width="5.501cm" svg:height="0.497cm" svg:x="11.145cm" svg:y="15.25cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T4">Materials and methods</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.702cm" svg:height="0.369cm" svg:x="11.645cm" svg:y="16.168cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">This section considers a two-way classification model including </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">its <text:s/>reparametrization <text:s/>from <text:s/>the <text:s/>perpendicular <text:s/>projection <text:s/>operators </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">approach </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.819cm" svg:height="0.369cm" svg:x="12.651cm" svg:y="17.014cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">using </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.497cm" svg:height="0.369cm" svg:x="13.656cm" svg:y="17.014cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.331cm" svg:height="0.369cm" svg:x="14.344cm" svg:y="17.014cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">estimator </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.247cm" svg:height="0.369cm" svg:x="15.869cm" svg:y="17.014cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">obtained </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.137cm" svg:height="0.369cm" svg:x="17.301cm" svg:y="17.014cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">through </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.856cm" svg:height="0.369cm" svg:x="18.622cm" svg:y="17.014cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">least-squared </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.273cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="17.438cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">estimation of the coefficient of competition associated with the edge </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.099cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="17.861cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">effect while considering a series of closed-edge scenarios as partial </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.286cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="18.284cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">edges and off-edge. This suggests a greater response in units located </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.919cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="18.708cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">in any edge modality.</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.897cm" svg:height="0.39cm" svg:x="11.645cm" svg:y="19.119cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Model Structure and estimation approach</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.939cm" svg:height="0.369cm" svg:x="11.645cm" svg:y="19.554cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">The Besag-Kempton autoregressive model based on the argument </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.273cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="19.978cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">that the random response of neighboring units affects or competes is </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.407cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="20.401cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">written as:</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="14.285cm" svg:y="20.812cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="14.285cm" svg:y="20.812cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.362cm" svg:height="0.369cm" svg:x="14.489cm" svg:y="20.824cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">= </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.502cm" svg:height="0.39cm" svg:x="14.846cm" svg:y="20.812cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Xβ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.532cm" svg:height="0.369cm" svg:x="15.241cm" svg:y="20.824cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">+ κ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.612cm" svg:height="0.39cm" svg:x="15.767cm" svg:y="20.812cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">WY</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.362cm" svg:height="0.369cm" svg:x="16.269cm" svg:y="20.824cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">+ </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="16.626cm" svg:y="20.812cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">ε</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="16.763cm" svg:y="20.824cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.391cm" svg:height="0.369cm" svg:x="20cm" svg:y="20.824cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(1)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.904cm" svg:height="0.369cm" svg:x="11.645cm" svg:y="21.671cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">where </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="12.547cm" svg:y="21.659cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.758cm" svg:height="0.369cm" svg:x="12.752cm" svg:y="21.671cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is a random vector of length and denotes the response of </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.497cm" svg:height="0.369cm" svg:x="11.145cm" svg:y="22.094cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="11.655cm" svg:y="22.082cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">n</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.913cm" svg:height="0.369cm" svg:x="11.822cm" svg:y="22.094cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">units, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="12.759cm" svg:y="22.082cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">X</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.404cm" svg:height="0.369cm" svg:x="12.983cm" svg:y="22.094cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is a known design matrix of dimension </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="18.496cm" svg:y="22.082cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">n </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="18.764cm" svg:y="22.094cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">x</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="18.932cm" svg:y="22.082cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11"><text:s/></text:span><text:span text:style-name="T11">p</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">, </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">vector of unknown parameters of length </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">p</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">and consists of the effects </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of the model (treatments and blocks), </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">κ</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is the unknown competition </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">coefficient that was associated with the edge effect, </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">W</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is the matrix </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of weights of dimension </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">n </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">x</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11"><text:s/></text:span><text:span text:style-name="T11">n</text:span></text:p>
     </draw:text-box>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">that in this case were associated with </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>inverses <text:s/>of <text:s/>the <text:s/>Euclidean <text:s/>distances <text:s/>between <text:s/>the <text:s/>units <text:s/>with <text:s/>the </text:span></text:p>
     </draw:text-box>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">assumption that the non zero weights of the neighbors on a particular </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">unit yield a Markov matrix, and the effect of unit on itself is zero, </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">yielding a square matrix of the Hollow type (In our case, the weights </text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">matrix was standardized). Finally, independence and identical normal </text:span></text:p>
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   </draw:page>
   <draw:page draw:name="page3" draw:style-name="dp2" draw:master-page-name="master-page55">
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T8">This scientific publication in digital format is a continuation of the Printed Review: Legal Deposit pp 196802ZU42, ISSN 0378-7818.</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T2"><text:s/></text:span></text:p>
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    <draw:frame draw:style-name="gr3" draw:text-style-name="P4" draw:layer="layout" svg:width="11.953cm" svg:height="0.412cm" svg:x="11.367cm" svg:y="0.467cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T9">Darghan </text:span><text:span text:style-name="T13">et al</text:span><text:span text:style-name="T14">.</text:span><text:span text:style-name="T15"> Rev. Fac. Agron. (LUZ). 2022, 39(1): e223916</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">3-6 </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T9">|</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">distribution <text:s/>with <text:s/>zero <text:s/>mean <text:s/>and <text:s/>variance </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="7.063cm" svg:y="1.122cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">σ</text:span></text:p>
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    <draw:frame draw:style-name="gr10" draw:text-style-name="P10" draw:layer="layout" svg:width="0.194cm" svg:height="0.217cm" svg:x="7.228cm" svg:y="1.147cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T16">2</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="7.326cm" svg:y="1.122cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">I</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="3.24cm" svg:height="0.369cm" svg:x="7.456cm" svg:y="1.134cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">was <text:s/>assumed <text:s/>for <text:s/>the </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">vector of errors, </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="3.492cm" svg:y="1.545cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">I</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.243cm" svg:height="0.369cm" svg:x="3.62cm" svg:y="1.557cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">being an identity matrix of dimension </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="8.989cm" svg:y="1.545cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">n </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="9.274cm" svg:y="1.557cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">x</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="9.438cm" svg:y="1.545cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11"><text:s/></text:span><text:span text:style-name="T11">n</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.777cm" svg:height="0.369cm" svg:x="9.723cm" svg:y="1.557cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">. The </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.345cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="1.981cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">design matrix was associated with a two-way model, to which lateral </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.868cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="2.404cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">conditions were imposed. The model is written as follows:</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="2.827cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.391cm" svg:height="0.369cm" svg:x="10.054cm" svg:y="2.969cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(2)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="10.445cm" svg:y="2.827cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr11" draw:text-style-name="P11" draw:layer="layout" svg:width="0.561cm" svg:height="0.386cm" svg:x="1.596cm" svg:y="2.956cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T17">𝑦𝑦</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr12" draw:text-style-name="P12" draw:layer="layout" svg:width="0.391cm" svg:height="0.276cm" svg:x="1.789cm" svg:y="3.122cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T18">𝑖𝑖𝑖𝑖</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr11" draw:text-style-name="P11" draw:layer="layout" svg:width="2.589cm" svg:height="0.386cm" svg:x="2.073cm" svg:y="2.956cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T17"><text:s text:c="6"/></text:span><text:span text:style-name="T17">= 𝜇𝜇 + 𝜏𝜏</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr12" draw:text-style-name="P12" draw:layer="layout" svg:width="0.258cm" svg:height="0.276cm" svg:x="3.71cm" svg:y="3.122cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T18">𝑖𝑖</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr11" draw:text-style-name="P11" draw:layer="layout" svg:width="0.899cm" svg:height="0.386cm" svg:x="3.907cm" svg:y="2.956cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T17">+ 𝛿𝛿</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr12" draw:text-style-name="P12" draw:layer="layout" svg:width="0.258cm" svg:height="0.276cm" svg:x="4.414cm" svg:y="3.122cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T18">𝑖𝑖</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr11" draw:text-style-name="P11" draw:layer="layout" svg:width="0.857cm" svg:height="0.386cm" svg:x="4.64cm" svg:y="2.956cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T17">+ 𝜀𝜀</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr12" draw:text-style-name="P12" draw:layer="layout" svg:width="0.391cm" svg:height="0.276cm" svg:x="5.154cm" svg:y="3.122cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T18">𝑖𝑖𝑖𝑖</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T17">𝑖𝑖 </text:span><text:span text:style-name="T17">= 1,2, … , 𝑡𝑡 ; <text:s/>𝑖𝑖 = 1,2, … , 𝑏𝑏, <text:s text:c="34"/></text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">as the effect of the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">-th treatment and </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">τ</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">as the effect of the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">j</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">-th block that in matrix form is written as </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T12">Xβ</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">+</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T12">ε</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">. In model (2) </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">1 </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">1. <text:s/>To <text:s/>cover <text:s/>this <text:s/>deficiency, <text:s/>the <text:s/>usual <text:s/>non-estimable </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">functions in this design model were used, that is, </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">and </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="3.414cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="5.755cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">. Under the hypotheses H</text:span></text:p>
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    <draw:frame draw:style-name="gr10" draw:text-style-name="P10" draw:layer="layout" svg:width="0.194cm" svg:height="0.217cm" svg:x="4.593cm" svg:y="5.992cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T16">0</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="4.691cm" svg:y="5.755cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">:</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.476cm" svg:height="0.39cm" svg:x="4.784cm" svg:y="5.743cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">k=</text:span></text:p>
     </draw:text-box>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.395cm" svg:height="0.369cm" svg:x="5.159cm" svg:y="5.755cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">0 of the model in (1) we have the linear </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.925cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="6.179cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">model </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="2.151cm" svg:y="6.166cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="2.355cm" svg:y="6.179cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.502cm" svg:height="0.39cm" svg:x="2.544cm" svg:y="6.166cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Xβ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="2.939cm" svg:y="6.179cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="3.128cm" svg:y="6.166cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">ε</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.489cm" svg:height="0.369cm" svg:x="3.266cm" svg:y="6.179cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">and solving the problem of the range of </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="8.991cm" svg:y="6.166cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">X</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.264cm" svg:height="0.369cm" svg:x="9.214cm" svg:y="6.179cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">with the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.421cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="6.602cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">imposition of lateral conditions we proceeded to the estimation of the </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.43cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="7.11cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">parameters. For model (1), the logarithm of the likelihood is given by.</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="1.2cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">𝑙𝑙</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="1.305cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="1.188cm" svg:height="0.302cm" svg:x="1.431cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">𝜷𝜷</text:span><text:span text:style-name="T21">, 𝜎𝜎</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="1.936cm" svg:y="8.038cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">2</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.688cm" svg:height="0.302cm" svg:x="2.074cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">, 𝜅𝜅</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="2.356cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.574cm" svg:height="0.302cm" svg:x="2.564cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">= −</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.281cm" svg:height="0.213cm" svg:x="3.146cm" svg:y="7.971cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">𝑛𝑛</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:polygon draw:style-name="gr14" draw:text-style-name="P14" draw:layer="layout" svg:width="0.141cm" svg:height="0.021cm" svg:x="3.146cm" svg:y="8.222cm" svg:viewBox="0 0 142 22" draw:points="0,0 142,0 142,22 0,22">
     <text:p/>
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    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="3.156cm" svg:y="8.3cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">2</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="3.339cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">ln</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="3.588cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.701cm" svg:height="0.302cm" svg:x="3.714cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">2𝜋𝜋</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="4.063cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="4.255cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">−</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.281cm" svg:height="0.213cm" svg:x="4.546cm" svg:y="7.971cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">𝑛𝑛</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:polygon draw:style-name="gr14" draw:text-style-name="P14" draw:layer="layout" svg:width="0.141cm" svg:height="0.021cm" svg:x="4.546cm" svg:y="8.222cm" svg:viewBox="0 0 142 22" draw:points="0,0 142,0 142,22 0,22">
     <text:p/>
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    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="4.555cm" svg:y="8.3cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">2</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="4.736cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">ln</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="4.985cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.493cm" svg:height="0.302cm" svg:x="5.111cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">𝜎𝜎</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="5.303cm" svg:y="8.038cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">2</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="5.438cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="1.026cm" svg:height="0.302cm" svg:x="5.631cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">+ 𝑛𝑛ln</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="6.343cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">|</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="2.119cm" svg:height="0.302cm" svg:x="6.439cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">𝑰𝑰 − 𝜅𝜅𝑾𝑾</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="7.385cm" svg:y="8.068cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">|</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr15" draw:text-style-name="P15" draw:layer="layout" svg:width="0.299cm" svg:height="0.302cm" svg:x="7.547cm" svg:y="8.08cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T21">−</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="7.839cm" svg:y="7.962cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">‖</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="7.953cm" svg:y="7.959cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="1.835cm" svg:height="0.213cm" svg:x="8.04cm" svg:y="7.971cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">𝒀𝒀−𝜅𝜅𝑾𝑾𝒀𝒀</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.946cm" svg:height="0.213cm" svg:x="8.89cm" svg:y="7.971cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">−𝑿𝑿𝜷𝜷</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.212cm" svg:height="0.213cm" svg:x="9.337cm" svg:y="7.962cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">‖</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T23">2</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr16" draw:text-style-name="P16" draw:layer="layout" svg:width="0.485cm" svg:height="0.213cm" svg:x="8.508cm" svg:y="8.3cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T22">2𝜎𝜎</text:span></text:p>
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    </draw:frame>
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     <text:p/>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T23">2</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T24">, <text:s/></text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T25"><text:s/></text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T25">1 </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.391cm" svg:height="0.369cm" svg:x="10.052cm" svg:y="7.936cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(3)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.684cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="8.761cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">with </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.043cm" svg:height="0.39cm" svg:x="2.38cm" svg:y="8.749cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">|</text:span><text:span text:style-name="T12">I</text:span><text:span text:style-name="T11">-κ</text:span><text:span text:style-name="T12">W</text:span><text:span text:style-name="T11">|</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="4.49cm" svg:height="0.369cm" svg:x="3.265cm" svg:y="8.761cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">like the Jacobian transformation.</text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">One <text:s/>use <text:s/>of <text:s/>the <text:s/>lateral <text:s/>conditions <text:s/>is <text:s/>the <text:s/>reparameterization <text:s/>of </text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>model, <text:s/>where <text:s/>the <text:s/>Besag- <text:s/>Kempton <text:s/>incomplete-range <text:s/>model <text:s/>is </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.616cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.031cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">transformed <text:s/>into <text:s/>a <text:s/>full-range <text:s/>model. This <text:s/>simplifies <text:s/>the <text:s/>estimation </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.497cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.454cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">procedure and allows obtaining unique estimators (Chistensen, 2011). </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="6.115cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.878cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">The method on model (1) is described below:</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.531cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Let </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="2.376cm" svg:y="11.289cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="2.631cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.502cm" svg:height="0.39cm" svg:x="2.871cm" svg:y="11.289cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Xβ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.447cm" svg:height="0.369cm" svg:x="3.316cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+ κ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.612cm" svg:height="0.39cm" svg:x="3.724cm" svg:y="11.289cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">WY</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="4.277cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="4.517cm" svg:y="11.289cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">ε</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="4.654cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.404cm" svg:height="0.369cm" svg:x="4.884cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">be </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.497cm" svg:height="0.369cm" svg:x="5.43cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.925cm" svg:height="0.369cm" svg:x="6.069cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">model </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.574cm" svg:height="0.369cm" svg:x="7.137cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">and </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.455cm" svg:height="0.39cm" svg:x="7.851cm" svg:y="11.289cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Lβ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="8.294cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="8.533cm" svg:y="11.289cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">0</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="8.701cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.497cm" svg:height="0.369cm" svg:x="8.931cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.959cm" svg:height="0.369cm" svg:x="9.57cm" svg:y="11.301cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">matrix </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.563cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="11.724cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">expression associated with the lateral conditions, where </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="8.343cm" svg:y="11.712cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">L</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.034cm" svg:height="0.369cm" svg:x="8.534cm" svg:y="11.724cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is a matrix <text:s/>of </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.488cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="12.148cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">dimension </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="2.614cm" svg:y="12.135cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">l</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="2.701cm" svg:y="12.148cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">×</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="2.883cm" svg:y="12.135cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">p</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.336cm" svg:height="0.369cm" svg:x="3.044cm" svg:y="12.148cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">, which is linked to the two-way model </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="8.105cm" svg:y="12.135cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">l</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="8.198cm" svg:y="12.148cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.548cm" svg:height="0.39cm" svg:x="8.387cm" svg:y="12.135cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T11">p-q</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="8.834cm" svg:y="12.148cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">. </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.455cm" svg:height="0.39cm" svg:x="9.003cm" svg:y="12.135cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Lβ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.086cm" svg:height="0.369cm" svg:x="9.446cm" svg:y="12.148cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">is a set </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="4.079cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="12.571cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of non-estimable functions. If </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.455cm" svg:height="0.39cm" svg:x="5.28cm" svg:y="12.559cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Lβ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="5.724cm" svg:y="12.571cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">0</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.836cm" svg:height="0.369cm" svg:x="6.131cm" svg:y="12.571cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">, then </text:span></text:p>
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    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β&apos;L&apos;</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="7.579cm" svg:y="12.571cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="7.818cm" svg:y="12.559cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">0</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.145cm" svg:height="0.369cm" svg:x="7.985cm" svg:y="12.571cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">, so that </text:span></text:p>
     </draw:text-box>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β&apos; </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.137cm" svg:height="0.369cm" svg:x="9.483cm" svg:y="12.571cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">belongs </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.101cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="12.994cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">to the orthogonal complement onto column space of </text:span></text:p>
     </draw:text-box>
    </draw:frame>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">L&apos;</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="8.4cm" svg:y="12.994cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.463cm" svg:height="0.39cm" svg:x="8.512cm" svg:y="12.982cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β&apos; </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.472cm" svg:height="0.369cm" svg:x="8.877cm" svg:y="12.994cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">ϵC(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="9.347cm" svg:y="12.982cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">L&apos;</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.849cm" svg:height="0.369cm" svg:x="9.695cm" svg:y="12.994cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">)). To </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.989cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="13.418cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">identify the reparametrized model it is necessary to select a matrix </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="10.24cm" svg:y="13.405cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Z</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="10.445cm" svg:y="13.418cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="7.063cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="13.841cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(Supplemental Material) such that it has the same C(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="8.345cm" svg:y="13.829cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">L&apos;</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.865cm" svg:height="0.369cm" svg:x="8.643cm" svg:y="13.841cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">); and, in this </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.318cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="14.264cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">way, <text:s/>the <text:s/>vector </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="3.45cm" svg:y="14.252cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.156cm" svg:height="0.369cm" svg:x="3.622cm" svg:y="14.264cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">belongs <text:s/>to <text:s/>C(</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="5.643cm" svg:y="14.252cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Z</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.433cm" svg:height="0.369cm" svg:x="5.848cm" svg:y="14.264cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">), <text:s/>that <text:s/>is, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.23cm" svg:height="0.39cm" svg:x="7.236cm" svg:y="14.252cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β = Zγ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.614cm" svg:height="0.369cm" svg:x="8.043cm" svg:y="14.264cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">, <text:s/>for <text:s/>some <text:s/>vector </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="1.2cm" svg:y="14.675cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">γ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.309cm" svg:height="0.369cm" svg:x="1.339cm" svg:y="14.688cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">. By substituting </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.23cm" svg:height="0.39cm" svg:x="3.721cm" svg:y="14.675cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">β = Zγ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.794cm" svg:height="0.369cm" svg:x="4.528cm" svg:y="14.688cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">in model (1) the reparameterized model is </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.255cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="15.111cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">obtained:</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="4.304cm" svg:y="15.522cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="4.559cm" svg:y="15.534cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.73cm" svg:height="0.39cm" svg:x="4.799cm" svg:y="15.522cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">XZγ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.447cm" svg:height="0.369cm" svg:x="5.417cm" svg:y="15.534cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+ κ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.612cm" svg:height="0.39cm" svg:x="5.825cm" svg:y="15.522cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">WY</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="6.378cm" svg:y="15.534cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="6.617cm" svg:y="15.522cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">ε</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="6.755cm" svg:y="15.534cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.391cm" svg:height="0.369cm" svg:x="10.052cm" svg:y="15.534cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(4)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.782cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="15.958cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">and <text:s/>doing <text:s text:c="3"/>the <text:s/>reparameterized <text:s/>model <text:s/>of <text:s/>Besag-Kempton <text:s/>is </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="2.368cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="16.381cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">finally written as:</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="4.304cm" svg:y="16.792cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="4.559cm" svg:y="16.804cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">=</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.476cm" svg:height="0.39cm" svg:x="4.799cm" svg:y="16.792cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Pγ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.447cm" svg:height="0.369cm" svg:x="5.193cm" svg:y="16.804cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+ κ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.612cm" svg:height="0.39cm" svg:x="5.601cm" svg:y="16.792cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">WY</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="6.154cm" svg:y="16.804cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">+</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.39cm" svg:x="6.394cm" svg:y="16.792cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">ε</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.334cm" svg:height="0.369cm" svg:x="6.531cm" svg:y="16.804cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="0.391cm" svg:height="0.369cm" svg:x="10.052cm" svg:y="16.804cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">(5)</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.956cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="17.328cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">From <text:s/>model <text:s/>(5) <text:s/>we <text:s/>can <text:s/>obtain <text:s/>the <text:s/>logarithm <text:s/>function <text:s/>of <text:s/>the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="6.259cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="17.751cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">likelihood as well as the estimators for γ and σ</text:span></text:p>
     </draw:text-box>
    </draw:frame>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">not present a closed solution (6), the least square estimation was used.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">is <text:s/>the <text:s/>perpendicular <text:s/>projection <text:s/>matrix </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">represents the trace. In the case of the least-square </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">estimation, <text:s/>for <text:s/>which <text:s/>no <text:s/>distributional <text:s/>assumption <text:s/>is <text:s/>required, <text:s/>we </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">(7)</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Note that the predicted value </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">estimates E(</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">y</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">) and not </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">, however, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">it is usually written as </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">. To find the estimator for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">from (7) we </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">and set it equal to zero and obtained </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">that was used to detect the edge effect of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">agronomic trials and computationally studied its distributional pattern </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">based on simulation Monte Carlo. The estimator turned out to be:</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">(8)</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Once the design matrix </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T12">X</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">, the matrix </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T12">Z</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">for the reparameterization </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of <text:s/>the <text:s/>model, <text:s/>and <text:s/>the <text:s/>neighborhood <text:s/>pattern </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">W</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">were <text:s/>defined, <text:s/>the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">functions were created in the RStudio software to perform the Monte </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Carlo simulations of all the scenarios. This involved randomizing the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">treatments so that the response vector </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T12">Y</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">associated with performance </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">did </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">not </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">show </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">edge </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">effect. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Higher </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">response </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">measures </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">were </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">generated in the treatments that resulted in the complete edge, and </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">a double row of higher response was generated in the two outer and </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">complete <text:s/>edges. <text:s/>Unilateral, <text:s/>bilateral, <text:s/>and <text:s/>trilateral <text:s/>partial <text:s/>borders </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">with edge effect were generated. <text:s/>For the blocking reason, the reader </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">can abstract to some situation that can be linked with simplicity and </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">that causes some randomization restriction to create the blocks, such </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">as the origin of the seed.</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Finally, <text:s/>whatever <text:s/>the <text:s/>estimation <text:s/>methodology <text:s/>is <text:s/>used <text:s/>in <text:s/>the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">estimation <text:s/>of <text:s/>parameters, <text:s/>for <text:s/>example, <text:s/>the <text:s/>lateral <text:s/>conditions, <text:s/>the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">current <text:s/>interest <text:s/>is <text:s/>related <text:s/>to <text:s/>the <text:s/>competition <text:s/>coefficient <text:s/>associated </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">with <text:s/>the <text:s/>edge <text:s/>effect <text:s/>in <text:s/>this <text:s/>case, <text:s/>so <text:s/>there <text:s/>is <text:s/>no <text:s/>It <text:s/>is <text:s/>of <text:s/>interest <text:s/>to </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">search for information on the edge effect with different proposals for </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">estimating the competition coefficient, since it is unprecedented as an </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">alternative to study the edge effect.</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Scope of the methodology</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">The usefulness of the statistical-computational approach is subject </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">to a previous exploration of the data set to detect the possible presence </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of the edge effect, since the simple obtaining of the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">statistic is not </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">directly associated to the absence or presence of the edge effect but </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">rather to the presence or absence of the competition effect such as the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">nature of the model used for the construction of the statistic. </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Motivating dataset</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">Figure 1 illustrates the arrangement of the treatments and blocks </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">in <text:s/>the <text:s/>study <text:s/>area. <text:s/>The <text:s/>label <text:s/>associated <text:s/>with <text:s/>the <text:s/>treatment, <text:s/>block, </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">and repetition appears. The number above each label represents the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">response as it was recorded in the field and the number to the right </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">represents the position in the response vector due to randomization. </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">In the case of the simulated responses, they were generated by Monte </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Carlo <text:s/>method <text:s/>to <text:s/>obtain <text:s/>all <text:s/>the <text:s/>scenarios <text:s/>described <text:s/>above. <text:s/>For <text:s/>all </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>scenarios <text:s/>where <text:s/>the <text:s/>response <text:s/>was <text:s/>generated <text:s/>it <text:s/>was <text:s/>guaranteed </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">that <text:s/>the <text:s/>treatment <text:s/>means <text:s/>were <text:s/>not <text:s/>different. <text:s/>Therefore, <text:s/>once <text:s/>the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">analysis of variance (aov) of the two-way model without competition </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">or edge effect was run (standard linear model in 2), no differences </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">in <text:s/>the <text:s/>treatment <text:s/>means <text:s/>were <text:s/>seen. <text:s/>Therefore, <text:s/>the <text:s/>distribution <text:s/>of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>F-statistic <text:s/>of <text:s/>the <text:s/>3000 <text:s/>simulations <text:s/>followed <text:s/>the <text:s/>characteristic </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.692cm" svg:height="0.369cm" svg:x="11.12cm" svg:y="18.49cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">F-distribution <text:s/>under <text:s/>the <text:s/>null <text:s/>hypothesis <text:s/>and <text:s/>thus <text:s/>could <text:s/>detect <text:s/>any </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.497cm" svg:height="0.369cm" svg:x="11.12cm" svg:y="18.914cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">departure <text:s/>from <text:s/>this <text:s/>distribution <text:s/>not <text:s/>because <text:s/>of <text:s/>the <text:s/>differences <text:s/>in </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">means <text:s/>but <text:s/>because <text:s/>of <text:s/>the <text:s/>spatial <text:s/>dependence <text:s/>induced <text:s/>by <text:s/>the <text:s/>edge </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">effect.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T8">This scientific publication in digital format is a continuation of the Printed Review: Legal Deposit pp 196802ZU42, ISSN 0378-7818.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T9"><text:s text:c="2"/></text:span><text:span text:style-name="T9">Rev. Fac. Agron. (LUZ). 2022, 39(1): e223916. January - March. ISSN 2477-9407.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">The following <text:s/>figures <text:s/>show <text:s/>different patterns of <text:s/>the different </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">(right).</text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="12.571cm" svg:height="0.39cm" svg:x="1.2cm" svg:y="7.78cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure <text:s/>2. <text:s/>Distribution <text:s/>of <text:s/>responses <text:s/>in <text:s/>the <text:s/>three <text:s/>main <text:s/>border </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="1.746cm" svg:height="0.39cm" svg:x="2.7cm" svg:y="8.183cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Figure <text:s/>3 <text:s/>shows <text:s/>all <text:s/>possible <text:s/>cases <text:s/>to <text:s/>illustrate <text:s/>the <text:s/>unilateral </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">edge effect, for which a higher yield was associated with the more </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">effect than those of the previous figure.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure 4. Distribution of responses on the bilateral border with </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Finally, the trilateral border patterns that are the most similar </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">statistic is expected to be much more like that </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">obtained in the presence of a simple edge (Fig. 5).</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure 5. Distribution of responses at the trilateral borders.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Mathematical <text:s/>classification <text:s/>and <text:s/>construction <text:s/>of <text:s/>simulated </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">a two-dimensional spatial array. The indicator function </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">With </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">mathematically <text:s/>formalized <text:s/>and <text:s/>will <text:s/>be <text:s/>illustrated <text:s/>when <text:s/>a <text:s/>user </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">The <text:s/>selection <text:s/>of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T20">i</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">depends <text:s/>on <text:s/>the <text:s/>distribution <text:s/>of <text:s/>the <text:s/>units <text:s/>in </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>field <text:s/>and <text:s/>as <text:s/>in <text:s/>our <text:s/>case <text:s/>it <text:s/>was <text:s/>a <text:s/>staggered <text:s/>planting <text:s/>with <text:s/>a </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">common <text:s/>y-coordinate <text:s/>were <text:s/>identified. <text:s/>For <text:s/>the <text:s/>single <text:s/>edge <text:s/>effect </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">if </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T16">1</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T20"><text:s/></text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">indicates <text:s/>the <text:s/>combination <text:s/>of <text:s/>blocks </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and <text:s/>treatments <text:s/>on <text:s/>this, <text:s/>the <text:s/>outermost <text:s/>edge. <text:s/>For <text:s/>the <text:s/>case <text:s/>of <text:s/>two </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">outer edges, for the purposes of the algorithm (see supplementary </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">in Ψ, i.e., we obtain Ψ-</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T16">1 </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">=Ψ</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T16">*</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">(Ψ\</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">again identify the points with the minimum common x-coordinate </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and maximum common x-coordinate as well as the minimum and </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">maximum <text:s/>common <text:s/>y-coordinate <text:s/>but <text:s/>inΨ</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">the <text:s/>selected </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">points <text:s/>on <text:s/>this <text:s/>inner <text:s/>edge. <text:s/>To <text:s/>count <text:s/>the <text:s/>two <text:s/>outer <text:s/>edges <text:s/>we <text:s/>do </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">, in this way, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">if Ψ</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T28">∈</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">we proceed to propose a computational method that the user can </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">an experimental test only generates a measure of the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">that <text:s/>we <text:s/>have <text:s/>associated <text:s/>with <text:s/>the <text:s/>edge <text:s/>effect, <text:s/>so <text:s/>it <text:s/>would <text:s/>not <text:s/>be </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">simple to clearly discriminate the presence of the edge effect. To </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">avoid this problem, we use RStudio’s</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">simulate</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">() function (R Core </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Team, 2021) to generate a simulated density for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">(found by the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">researcher) <text:s/>using RStudio’s lm() function for the formula: response </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">~ </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T16">1</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and do the desired simulations to construct the density of the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">outermost <text:s/>edge. The <text:s/>element <text:s/>vector <text:s/>incontaining <text:s/>zeros <text:s/>and <text:s/>ones </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of length equal to the evaluated response is simulated over a user-</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">defined number of simulations, in our case 500 simulations were </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">used and then we plotted the density, and we can notice the pattern </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">that certainly tells us if it is contained to zero or not to decide if </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">we have the effect associated with the outer edge. If the formula </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">response <text:s/>~ </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T16">1</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">+</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">S</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T16">2</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s text:c="2"/></text:span><text:span text:style-name="T5">is <text:s/>used <text:s/>and <text:s/>the <text:s/>linear <text:s/>model <text:s/>is <text:s/>fitted, <text:s/>we <text:s/>now </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">have the possibility to obtain the density for the outermost edges </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and again the edge effect considered will be clear (supplementary </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">material).</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Results and discussion</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">When the usual aov is used in linear modeling the technique </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">uses spatial dependence to modify the usual inferential procedures </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">(Gotway and Cressie 1990). In fact, the distributional assumption </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">based <text:s/>on <text:s/>the <text:s/>F-curve <text:s/>may <text:s/>not <text:s/>be <text:s/>valid. <text:s/>By <text:s/>maintaining <text:s/>the <text:s/>null </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">hypothesis <text:s/>of <text:s/>equality <text:s/>of <text:s/>means <text:s/>of <text:s/>the <text:s/>treatments, <text:s/>it <text:s/>is <text:s/>possible </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">by simulation to see the effect in the F-distribution. Figure 6-left </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">shows the distribution that is expected for two degrees of freedom </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">associated with the treatments and 92 degrees of freedom for the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">error in the two-way model. Figures 6-center and 6-right show the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T8">This scientific publication in digital format is a continuation of the Printed Review: Legal Deposit pp 196802ZU42, ISSN 0378-7818.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T2"><text:s/></text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T9">Darghan </text:span><text:span text:style-name="T13">et al</text:span><text:span text:style-name="T14">.</text:span><text:span text:style-name="T15"> Rev. Fac. Agron. (LUZ). 2022, 39(1): e223916</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">5-6 </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T9">|</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">departure from this distribution when there is a clear edge effect </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">generating <text:s/>spatial <text:s/>dependence. <text:s/>Some <text:s/>might <text:s/>confuse <text:s/>the <text:s/>result <text:s/>of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">these two final figures if they do not realize that the samples did not </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.947cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="2.404cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T30">provide statistical evidence against the null hypothesis of equality </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.795cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="2.827cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T30">of means in the simulations generated. The figure also shows the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.939cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="3.25cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T30">results of the Kolmogorov-Smirnov test for the adjustment for the </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.63cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="3.674cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T30">distribution and its D statistic. Only in the case of no edge (Fig. </text:span></text:p>
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      <text:p/>
     </draw:image>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T30">6-left) the distribution is precisely the F. </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="11.758cm" svg:height="0.39cm" svg:x="1.2cm" svg:y="7.641cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure 6. Distribution of the F statistic generated in the 3000 </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="4.709cm" svg:height="0.39cm" svg:x="2.6cm" svg:y="8.043cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Monte Carlo simulations.</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.443cm" svg:height="0.369cm" svg:x="1.7cm" svg:y="8.881cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">In Figure 7 the distribution of the p values of the Moran index </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.298cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="9.305cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of <text:s/>the <text:s/>cases <text:s/>associated <text:s/>with <text:s/>figure <text:s/>2 <text:s/>(no <text:s/>border, <text:s/>single <text:s/>border, </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.731cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="9.728cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">and double border) is illustrated. As can be seen in 7 (left), most </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.981cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.151cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of the simulations did not provide evidence against the hypothesis </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.011cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.575cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">of spatial independence of the residuals of the analysis of variance </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.396cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="10.998cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">model, <text:s/>with <text:s/>which <text:s/>the <text:s/>results <text:s/>of <text:s/>the <text:s/>technique <text:s/>are <text:s/>applicable <text:s/>if </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.281cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="11.421cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">the <text:s/>assumptions <text:s/>are <text:s/>met. <text:s text:c="3"/>In <text:s/>Figures <text:s/>7-center <text:s/>and <text:s/>7-right <text:s/>most </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.438cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="11.845cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">simulations <text:s/>show <text:s/>spatial <text:s/>dependence, <text:s/>especially <text:s/>in <text:s/>the <text:s/>case <text:s/>with </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.404cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="12.268cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">two <text:s/>edges. <text:s/>The <text:s/>vertical <text:s/>lines <text:s/>illustratively <text:s/>demarcate <text:s/>the <text:s/>cut <text:s/>for </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.201cm" svg:height="0.369cm" svg:x="1.2cm" svg:y="12.691cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">α=5% and the simulation count is also printed where the hypothesis </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of spatial independence is rejected. Undoubtedly, the presence of an </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">edge is associated with a modality of spatial dependence, so results </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of an aov to the standard linear model may not be valid, and hence </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the importance of taking some remedial measure in the presence </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of an edge effect. This is done in the study of the speed of the root </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">front of corn and soybeans (Ordóñez </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T11">et al</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">., 2018).Although an edge </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">effect could not always be present in our research as was the case of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">pasture and gramineous, some authors have concluded that both the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">vegetation and soil properties are influenced by the proximity to the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">edge (Ruwanza, 2018) .</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure <text:s/>7. <text:s/>Distribution <text:s/>of <text:s/>the <text:s/>p <text:s/>value <text:s/>of <text:s/>the <text:s/>Moran <text:s/>index </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">generated in the 3000 simulations.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">From <text:s/>(5), <text:s/>the <text:s/>coefficient <text:s/>associated <text:s/>with <text:s/>the <text:s/>edge <text:s/>effect <text:s/>in </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">model <text:s/>(1) <text:s/>was <text:s/>obtained <text:s/>by <text:s/>the <text:s/>least-squared <text:s/>estimation <text:s/>for <text:s/>all </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">scenarios, showing a clear normal distribution by simulation, that </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">was corroborated with the Shapiro-Wilks Normality test (p-values </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">within each image in figure 8). With the mean for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">in the distribution </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of the simulations, a 95% confidence interval was constructed for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">, specifically for the cases without edge effect, single and double </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">edge effect, and it is here where one of the most important results. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Clearly the first interval (Fig. 8-left) contains zero, with which we </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">assert the absence of edge effect, while Figures 8-center and 8-right </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">not only do not contain zero, but also obtain negative lower and </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">upper <text:s/>limits, <text:s/>that <text:s/>is, <text:s/>the <text:s/>negative <text:s/>coefficient <text:s/>associated <text:s/>with <text:s/>the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">edge effect shows the effect of interest. </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="12.279cm" svg:height="0.39cm" svg:x="11.395cm" svg:y="5.621cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure <text:s/>8. <text:s/>Distribution <text:s/>of <text:s/>the <text:s/>coefficient <text:s/>associated <text:s/>with <text:s/>the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">competition model or edges.</text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">It is reasonable to think that even with many simulations for the </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.981cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="7.285cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">first three cases it is possible to detect partial edges effect with the </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">same statistic. The cases of unilateral edge effect (Fig. 9) were run, </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.298cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="8.131cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">finding again the detection of unilateral partial edge but with a mean </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">for a normal distribution closer to zero on the left, especially at the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">edges of shorter length (lower and upper). So, a greater distance </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">from zero on the left shows a more defined edge effect.</text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="12.164cm" svg:height="0.39cm" svg:x="11.395cm" svg:y="13.541cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure 9. Distribution of the coefficient associated with the one-</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="3.689cm" svg:height="0.39cm" svg:x="12.795cm" svg:y="13.943cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T10">sided edges model.</text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.027cm" svg:height="0.369cm" svg:x="11.895cm" svg:y="14.781cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">In <text:s/>the <text:s/>cases <text:s/>of <text:s/>more <text:s/>defined <text:s/>but <text:s/>partial <text:s/>edges <text:s/>effect <text:s/>such <text:s/>as </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">bilateral ones, the distribution of the statistic is maintained but its </text:span></text:p>
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    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.773cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="15.628cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">means are shifted further to the left. This defines the partial edge </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.027cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="16.051cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">more clearly, especially when the edges are those with the greatest </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.824cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="16.475cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">perimeter (Fig. 10). This result, which is becoming systematic, is </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="9.417cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="16.898cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">validated <text:s/>with <text:s/>the <text:s/>trilateral <text:s/>cases <text:s/>of <text:s/>Figure <text:s/>11. <text:s/>When <text:s/>the <text:s/>edges </text:span></text:p>
     </draw:text-box>
    </draw:frame>
    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="8.786cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="17.321cm">
     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T5">involve the widest perimeters, the coefficient associated with the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T8">This scientific publication in digital format is a continuation of the Printed Review: Legal Deposit pp 196802ZU42, ISSN 0378-7818.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T9"><text:s text:c="2"/></text:span><text:span text:style-name="T9">Rev. Fac. Agron. (LUZ). 2022, 39(1): e223916. January - March. ISSN 2477-9407.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure <text:s/>11. <text:s/>Distribution <text:s/>of <text:s/>the <text:s/>coefficient <text:s/>associated <text:s/>with <text:s/>the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">) <text:s/>and <text:s/>using <text:s/>simulate() <text:s/>the <text:s/>simulations <text:s/>were <text:s/>generated. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">of quadratic forms associated with the proposed estimator.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">Figure 12. Simulated density plot for application example the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T10">line indicate the experimental kappa.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Conclusions</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Current </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">research </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">uses </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Besag-Kempton </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">model </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">least-quadratic <text:s/>estimation <text:s/>of <text:s/>parameters. <text:s/>From <text:s/>this <text:s/>model <text:s/>was </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">possible to obtain the estimator for the competition coefficient that </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">was associated with the edge effect. The results made it possible </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">to visualize the effect on the distribution of the F statistic of the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">analysis of variance in the presence of spatial dependence evaluated </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">using <text:s/>the <text:s/>Moran <text:s/>index, <text:s/>evident <text:s/>in <text:s/>the <text:s/>case <text:s/>of <text:s/>the <text:s/>synthetically </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">generated edges effect.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">Once a series of Monte Carlo simulations had been made for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">a <text:s/>normally <text:s/>distributed <text:s/>response, <text:s/>the <text:s/>distributional <text:s/>pattern <text:s/>of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">statistic associated with the edge effect was studied. In all cases, the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">normal distribution was evident </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5"><text:s/></text:span><text:span text:style-name="T5">in the scenarios of single, double, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">no border, partial borders, and the contrasting pattern of opposite </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">borders effect. We observed that in the absence of the edge effect, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">this <text:s/>interval <text:s/>contained <text:s/>zero, <text:s/>while <text:s/>in <text:s/>the <text:s/>case <text:s/>of <text:s/>the <text:s/>presence <text:s/>of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">partial unilateral, bilateral, and trilateral borders.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">The use of the sets of points associated with the edges of interest </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">and <text:s/>the <text:s/>linear <text:s/>modeling <text:s/>allowed <text:s/>the <text:s/>construction <text:s/>of <text:s/>a <text:s/>simulated </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">density for </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">, which eliminated the ambiguity that could arise when </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">making a point estimate for , so that a user of the method can easily </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T5">judge the presence or absence of edge effect.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Supplemental material</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">Z and L matrices are available. Repository on Github of R code: </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T30">The code for all the simulations in: </text:span><text:span text:style-name="T5">CarlosRivera1212/BorderEffect </text:span></text:p>
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    <draw:frame draw:style-name="gr7" draw:text-style-name="P7" draw:layer="layout" svg:width="5.09cm" svg:height="0.369cm" svg:x="11.395cm" svg:y="2.858cm">
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      <text:p text:style-name="P2"><text:span text:style-name="T5">(github.com)(edge effect coefficients)</text:span></text:p>
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    </draw:frame>
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      <text:p text:style-name="P2"><text:span text:style-name="T4">Cited literature</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">Arny, A. <text:s/>C. <text:s/>(1922). <text:s/>Border <text:s/>Effect <text:s/>and <text:s/>Ways <text:s/>of <text:s/>avoiding <text:s/>it. <text:s text:c="2"/></text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">Journal <text:s/>of <text:s/>the </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">American Society of Agronomy</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">, </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">14(7), 266-278. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">Besag, J. E. &amp; Kempton, R. A. (1986). Statistical Analysis of field experiments </text:span></text:p>
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     <draw:text-box>
      <text:p text:style-name="P2"><text:span text:style-name="T27">using neighbouring plots. </text:span></text:p>
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    </draw:frame>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">Biometrics, 42(2), 231-251. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">Kuemmel, Bernd (2003). Theoretical investigation of the effects of field margin </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">and <text:s/>hedges <text:s/>on <text:s/>crop <text:s/>yields. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">Connolly, T., Currie, I. D., Bradshaw, J. E., McNicol, J. W. (1993). Inter-plot </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">competition <text:s/>in <text:s/>yield <text:s/>trials <text:s/>of <text:s/>potatoes <text:s/>(</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">Solanum <text:s/>tuberosum</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27"><text:s text:c="2"/></text:span><text:span text:style-name="T27">L.) <text:s/>with </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">single-drill plots. Ann. Appl. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">Biol.,123(2),367-377</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">Christensen, R. (2011). Plane Answers to Complex Questions. </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">The Theory of </text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T31">Linear Models. Fourth edition</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">. Springer, New York, Inc.</text:span></text:p>
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      <text:p text:style-name="P2"><text:span text:style-name="T27">Gałęzewski, <text:s/>L., <text:s/>Piekarczyk, <text:s/>M., <text:s/>Jaskulska, <text:s/>I., Wasilewski, <text:s/>P. <text:s/>(2013). <text:s/>Border </text:span></text:p>
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