ProcMod.html 52.4 KB
Newer Older
Eric Coissac committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495
<!DOCTYPE html>

<html xmlns="http://www.w3.org/1999/xhtml">

<head>

<meta charset="utf-8" />
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />

<meta name="viewport" content="width=device-width, initial-scale=1">

<meta name="author" content="Christelle Melodelima &amp; Eric Coissac" />

<meta name="date" content="2018-07-06" />

<title>ProcMod</title>



<style type="text/css">code{white-space: pre;}</style>
<style type="text/css">
a.sourceLine { display: inline-block; line-height: 1.25; }
a.sourceLine { pointer-events: none; color: inherit; text-decoration: inherit; }
a.sourceLine:empty { height: 1.2em; position: absolute; }
.sourceCode { overflow: visible; }
code.sourceCode { white-space: pre; position: relative; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
code.sourceCode { white-space: pre-wrap; }
a.sourceLine { text-indent: -1em; padding-left: 1em; }
}
pre.numberSource a.sourceLine
  { position: relative; }
pre.numberSource a.sourceLine:empty
  { position: absolute; }
pre.numberSource a.sourceLine::before
  { content: attr(data-line-number);
    position: absolute; left: -5em; text-align: right; vertical-align: baseline;
    border: none; pointer-events: all;
    -webkit-touch-callout: none; -webkit-user-select: none;
    -khtml-user-select: none; -moz-user-select: none;
    -ms-user-select: none; user-select: none;
    padding: 0 4px; width: 4em;
    color: #aaaaaa;
  }
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
div.sourceCode
  {  }
@media screen {
a.sourceLine::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
</style>



<style type="text/css">body {
background-color: #fff;
margin: 1em auto;
max-width: 700px;
overflow: visible;
padding-left: 2em;
padding-right: 2em;
font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
font-size: 14px;
line-height: 1.35;
}
#header {
text-align: center;
}
#TOC {
clear: both;
margin: 0 0 10px 10px;
padding: 4px;
width: 400px;
border: 1px solid #CCCCCC;
border-radius: 5px;
background-color: #f6f6f6;
font-size: 13px;
line-height: 1.3;
}
#TOC .toctitle {
font-weight: bold;
font-size: 15px;
margin-left: 5px;
}
#TOC ul {
padding-left: 40px;
margin-left: -1.5em;
margin-top: 5px;
margin-bottom: 5px;
}
#TOC ul ul {
margin-left: -2em;
}
#TOC li {
line-height: 16px;
}
table {
margin: 1em auto;
border-width: 1px;
border-color: #DDDDDD;
border-style: outset;
border-collapse: collapse;
}
table th {
border-width: 2px;
padding: 5px;
border-style: inset;
}
table td {
border-width: 1px;
border-style: inset;
line-height: 18px;
padding: 5px 5px;
}
table, table th, table td {
border-left-style: none;
border-right-style: none;
}
table thead, table tr.even {
background-color: #f7f7f7;
}
p {
margin: 0.5em 0;
}
blockquote {
background-color: #f6f6f6;
padding: 0.25em 0.75em;
}
hr {
border-style: solid;
border: none;
border-top: 1px solid #777;
margin: 28px 0;
}
dl {
margin-left: 0;
}
dl dd {
margin-bottom: 13px;
margin-left: 13px;
}
dl dt {
font-weight: bold;
}
ul {
margin-top: 0;
}
ul li {
list-style: circle outside;
}
ul ul {
margin-bottom: 0;
}
pre, code {
background-color: #f7f7f7;
border-radius: 3px;
color: #333;
white-space: pre-wrap; 
}
pre {
border-radius: 3px;
margin: 5px 0px 10px 0px;
padding: 10px;
}
pre:not([class]) {
background-color: #f7f7f7;
}
code {
font-family: Consolas, Monaco, 'Courier New', monospace;
font-size: 85%;
}
p > code, li > code {
padding: 2px 0px;
}
div.figure {
text-align: center;
}
img {
background-color: #FFFFFF;
padding: 2px;
border: 1px solid #DDDDDD;
border-radius: 3px;
border: 1px solid #CCCCCC;
margin: 0 5px;
}
h1 {
margin-top: 0;
font-size: 35px;
line-height: 40px;
}
h2 {
border-bottom: 4px solid #f7f7f7;
padding-top: 10px;
padding-bottom: 2px;
font-size: 145%;
}
h3 {
border-bottom: 2px solid #f7f7f7;
padding-top: 10px;
font-size: 120%;
}
h4 {
border-bottom: 1px solid #f7f7f7;
margin-left: 8px;
font-size: 105%;
}
h5, h6 {
border-bottom: 1px solid #ccc;
font-size: 105%;
}
a {
color: #0033dd;
text-decoration: none;
}
a:hover {
color: #6666ff; }
a:visited {
color: #800080; }
a:visited:hover {
color: #BB00BB; }
a[href^="http:"] {
text-decoration: underline; }
a[href^="https:"] {
text-decoration: underline; }

code > span.kw { color: #555; font-weight: bold; } 
code > span.dt { color: #902000; } 
code > span.dv { color: #40a070; } 
code > span.bn { color: #d14; } 
code > span.fl { color: #d14; } 
code > span.ch { color: #d14; } 
code > span.st { color: #d14; } 
code > span.co { color: #888888; font-style: italic; } 
code > span.ot { color: #007020; } 
code > span.al { color: #ff0000; font-weight: bold; } 
code > span.fu { color: #900; font-weight: bold; }  code > span.er { color: #a61717; background-color: #e3d2d2; } 
</style>

</head>

<body>




<h1 class="title toc-ignore">ProcMod</h1>
<h4 class="author"><em>Christelle Melodelima &amp; Eric Coissac</em></h4>
<h4 class="date"><em>2018-07-06</em></h4>



<div id="aims-of-the-module" class="section level2">
<h2>Aims of the module</h2>
<p>Expliquer un tableau multavariées decrivant des individus ou des sites (ci dessous dénommés individus) par un ensemble de tableaux eux-même multivariés décrivant les mêmes individus. Par exemple, expliquer les changement de communauté d’espèces entre différents sites géographiques à partir de tableaux de données climatiques, chimique, d’espèces d’autres groupes taxinomiques… Chaque tableau est considéré comme une variable explicative sans chercher à donner un rôle à chacune des variables qui le composent.</p>
</div>
<div id="model-principes" class="section level2">
<h2>Model principes</h2>
<p>L’idée est de s’appuyer sur les analyses procustéennes en les généralisant à plusieurs (<span class="math inline">\(k\)</span>) tableaux. Pour mémoire, l’analyse procustéenne consiste à superposer deux nuages de points dans un espace de dimensions quelconque en réalisant trois operations:</p>
<ol style="list-style-type: decimal">
<li>une translation (centrage des données)</li>
<li>une rotation</li>
<li>une mise à l’échelle.</li>
</ol>
<p>Dans notre cas, nous considérerons que les deux premières opérations ont pour seul but de projeter l’ensemble des tableaux réponse et explicatifs, dans un espace commun. La troisième operation d’homothétie servira de base à l’analyse de partition de la variance du tableau réponse. Cette approche a de forts liens avec les analyses de co-inerties développées par Chessel et al</p>
</div>
<div id="donnees-en-entree" class="section level2">
<h2>Données en entrée</h2>
<p>Les tableaux utilisés dans cette analyse doivent se projeter dans un espace orthogonal, ce qui implique aucune corrélation entre les colonnes des tableaux. Ils doivent tous décrire les mêmes individus et doivent donc tous avoir le même nombre de lignes <span class="math inline">\(n\)</span>.</p>
<div id="tableaux-de-variables-quelconques" class="section level3">
<h3>Tableaux de variables quelconques</h3>
<p>Comme posé en préambule, l’analyse vise à mesurer l’effet global de <span class="math inline">\(k\)</span> tableaux de variables sur un tableau réponse sans s’interresser à l’effet individuel de chacune des variables des différents tableaux explicatifs. Les tableaux utilisés peuvent donc sans perte d’information être projetés dans un espace orthogonal par une simple PCA.</p>
</div>
<div id="tableaux-de-distances" class="section level3">
<h3>Tableaux de distances</h3>
<p>Il est possible de caractériser la dissimilarité entre les individus par une autre mesure que la corrélation (<em>cf</em> PCA ci-dessus) en estimant un tableau de distances par une méthode appropriée au type de données étudiées. Par exemple une distance de Bray-Curtis ou de Jaccard, lorsqu’il s’agit de comparer les communautés d’espèces présentes dans plusieurs sites.</p>
<p>Si la distance utilisée est une métrique, le tableau de distance pourra être projeter dans un espace orthogonal à <span class="math inline">\(n-1\)</span> dimensions par une PCoA.</p>
<p>Si la distance utilisée n’est pas une métrique, il faudra recourrir à une méthode non paramétrique telque la NMDS ou alterer le tableau de distance pour le rendre diagonalisable.</p>
</div>
</div>
<div id="methode-de-calculs-du-modele-procusteen" class="section level2">
<h2>Méthode de calculs du modèle procustéen</h2>
<p>L’analyse procustéenne peut être assimilée à un modèle linéaire entre deux tableaux:</p>
<ul>
<li>Le tableau réponse : <span class="math inline">\(Y\)</span></li>
<li>Le tableau explicatif : <span class="math inline">\(X\)</span></li>
</ul>
<p>Si l’ensemble des variables de chaque tableau appartiennent à <span class="math inline">\(\mathbb{R}\)</span>:</p>
<ul>
<li>L’opération de translation est réalisée via le centrage des variables des tableaux <span class="math inline">\(X\)</span> et <span class="math inline">\(Y\)</span>. Dorénavant, la notation <span class="math inline">\(X\)</span> et <span class="math inline">\(Y\)</span> représentera les tableau après centrage.</li>
<li>La rotation pour projeter le tableau <span class="math inline">\(X\)</span> sur <span class="math inline">\(Y\)</span> est calculer à partir de la décomposition en valeurs singulières de la matrice <span class="math inline">\(Y'X\)</span> soit <span class="math inline">\(Y'X = U\Lambda V'\)</span>. On définit la rotation de <span class="math inline">\(X\)</span> sur <span class="math inline">\(Y\)</span> de la manière suivante:</li>
</ul>
<p><span class="math display">\[ Rot(X|Y) = XVU' \]</span></p>
<ul>
<li>Le facteur d’homothétie <span class="math inline">\(a\)</span> se calcule selon :</li>
</ul>
<p><span class="math display">\[ a = \frac{\sum diag(\Lambda)}{\sum diag(X'X)}\]</span></p>
<p><span class="math inline">\(\sum diag(\Lambda)\)</span> est la co-inertie entre les matrices <span class="math inline">\(X\)</span> et <span class="math inline">\(Y\)</span> et <span class="math inline">\(\sum diag(X'X)\)</span> est l’inertie du tableau <span class="math inline">\(X\)</span>. Co-inertie et inertie pouvant être assimilées à la covariance et à la variance de vecteurs. Le facteur <span class="math inline">\(a\)</span> est donc l’équivalent en dimention 1 de la pente de la droite de régression linéaire de <span class="math inline">\(Y\)</span> par <span class="math inline">\(X\)</span>:</p>
<p><span class="math display">\[
a=\frac{Cov_{XY}}{Var_X}
\]</span></p>
<p>Nous proposons ici de généraliser l’analyse procustéen à <span class="math inline">\(k\)</span> tableaux en résolvant la régression multiple du tableau de réponse <span class="math inline">\(Y\)</span> par <span class="math inline">\(k\)</span> matrices explicatives <span class="math inline">\(X_1,\,X_2,\,...\,X_k\)</span>.</p>
<p>Le calcul des coefficients d’échelles <span class="math inline">\(a_i\)</span> est réalisé par la même approche que pour ceux d’une régression linéaire multiple, mais ici à partir de la matrice d’inertie et de co-inertie des tableaux <span class="math inline">\(Y\)</span> et <span class="math inline">\(X_i\)</span>:</p>
<div id="calcul-de-linertie-dune-matrice-et-de-co-inertie-entre-deux-matrices" class="section level3">
<h3>Calcul de l’inertie d’une matrice et de co-inertie entre deux matrices</h3>
<p>Soit <span class="math inline">\(CoI_{XY}\)</span> la cointertie entre les tableaux <span class="math inline">\(X\)</span> et <span class="math inline">\(Y\)</span> et <span class="math inline">\(I_X\)</span> l’inertie du tableau <span class="math inline">\(X\)</span>. <span class="math inline">\(CoI_{XY}\)</span> se calcule à partir de la décomposition en valeur singulière de la matrice <span class="math inline">\(Y'X = U\Lambda V'\)</span>.</p>
<p><span class="math display">\[
CoI_{XY} = \frac{\sum{diag(\Lambda)}}{n-1}
\]</span></p>
<p>Comme pour la Covariance, <span class="math inline">\(CoI_{XY}=CoI{YX}\)</span> et <span class="math inline">\(CoI_{XX}=I_X\)</span></p>
</div>
<div id="calcul-du-coefficient-de-correlation-entre-deux-matrices" class="section level3">
<h3>Calcul du coefficient de corrélation entre deux matrices</h3>
<p>Par analogie on définit <span class="math inline">\(R_{XY}\)</span> comme le coefficient de corrélation entre deux matrices <span class="math inline">\(X\)</span> et <span class="math inline">\(Y\)</span> de la manière suivante :</p>
<p><span class="math display">\[
R_{XY} = \frac{CoI_{XY}}{\sqrt{I_{X}I_{Y}}}
\]</span></p>
</div>
<div id="calcul-des-facteurs-dechelle-en-procuste-multiple-a-k-tableaux" class="section level3">
<h3>Calcul des facteurs d’échelle en procuste multiple à <span class="math inline">\(k\)</span> tableaux</h3>
<p>On note à partir de maintenant :</p>
<ul>
<li><span class="math inline">\(X = \{X_1,\,X_2,\,...\,X_k\}\)</span> l’ensemble des <span class="math inline">\(k\)</span> tableaux explicatifs centrés</li>
<li><span class="math inline">\(Y\)</span> le tableau réponse centré</li>
<li><span class="math inline">\(M \in \{Y\} \cup X\)</span> tel que <span class="math inline">\(M\)</span> est la matrice de plus grande dimension.</li>
<li><span class="math inline">\(CoI_{YX}\)</span> la matrice colonne des co-inerties entre <span class="math inline">\(Y\)</span> et chacun des éléments de <span class="math inline">\(X\)</span></li>
<li><span class="math inline">\(CoI_{XX}\)</span> la matrice d’inertie, co-inerties entre tous les éléments de <span class="math inline">\(X\)</span></li>
<li><span class="math inline">\(a = \{a_1\,a_2,\,...\,a_k\}\)</span> l’ensemble des coefficients d’échelle associés à chacun des éléments de <span class="math inline">\(X\)</span> dans le modèle procustéen multiple.</li>
</ul>
<p><span class="math inline">\(a\)</span> se calcule par :</p>
<p><span class="math display">\[
  a = (CoI_{XX})^{-1} CoI_{YX}
\]</span></p>
<p>Les prédictions du modèle peuvent donc s’écrirent:</p>
<p><span class="math display">\[
\widehat{Rot(Y|M)} = a_1 Rot(X_1|M) + a_2 Rot(X_2|M)+\,...\,+ a_k Rot(X_k|M)
\]</span></p>
</div>
<div id="interaction-entre-deux-tableaux-explicatifs" class="section level3">
<h3>Interaction entre deux tableaux explicatifs</h3>
<p>L’interaction entre deux tableaux explicatifs <span class="math inline">\(X_i\)</span> et <span class="math inline">\(X_j\)</span> est estimée de manière analogue à l’interaction dans un modèle linéaire multiple. Le principe est de poser que <span class="math inline">\(a_i\)</span> le facteur d’échelle associé à <span class="math inline">\(X_i\)</span> est une fonction affine de <span class="math inline">\(X_j\)</span> et symétriquement <span class="math inline">\(a_j\)</span> est une fonction affine de <span class="math inline">\(X_i\)</span>. Pour réaliser ce calcul il est nécessaire de projeter les deux matrices explicatives sur <span class="math inline">\(M\)</span>.</p>
<p><span class="math display">\[
a_i = (b_i Rot(X_j|M) + c_i) \\
a_j = (b_j Rot(X_i|M) + c_j)
\]</span></p>
<p>Dans le cas de deux tableaux, le modèle procustéen expliquant <span class="math inline">\(Y\)</span> par <span class="math inline">\(X_1\)</span>, <span class="math inline">\(X_2\)</span> et l’interaction de <span class="math inline">\(X_1\)</span> et <span class="math inline">\(X_2\)</span> peut donc s’écrire :</p>
<p><span class="math display">\[
\begin{aligned}
\widehat{Rot(Y|M)} = &amp; a_1 \cdot Rot(X_1|M) +  a_2 \cdot Rot(X_2|M) \\
\\
  = &amp; (b_1 Rot(X_2|M) + c_1) \cdot Rot(X_1|M) + \\ 
&amp; (b_2 Rot(X_1|M) + c_2) \cdot Rot(X_2|M) \\
\\
  = &amp; c_1 Rot(X_1|M) + c_2 Rot(X_2|M) + (b_1+b_2) Rot(X_1|M) \cdot Rot(X_2|M)
\end{aligned}
\]</span></p>
<p>En renommant les facteurs d’échelle les prédictions s’écrivent:</p>
<p><span class="math display">\[
\widehat{Rot(Y|M)} =  a_1 Rot(X_1|M) + a_2 Rot(X_2|M) + a_{1,2} Rot(X_1|M) \cdot Rot(X_2|M)
\]</span></p>
<p>Ce qui revient à construire un nouveau modèle sans interaction incluant un tableau explicatif supplémentaire</p>
<p><span class="math display">\[
X_{1,2}=Rot(X_1|M) \cdot Rot(X_2|M)
\]</span></p>
<p>Ce principe peut être généralisé à l’interaction entre plus de deux tableaux.</p>
</div>
</div>
<div id="partition-de-linertie-de-y-selon-le-modele-procusteen" class="section level2">
<h2>Partition de l’inertie de <span class="math inline">\(Y\)</span> selon le modèle procustéen</h2>
<p>La variation total <span class="math inline">\(SCT\)</span> est définie comme suit:</p>
<p><span class="math display">\[
SCT = I_Y * (n-1)
\]</span> La variation résiduelle non expliquée par le modèle est :</p>
<p><span class="math display">\[
SCR = \sum{(Rot(Y|M)-\widehat{Rot(Y|M)})^2}
\]</span></p>
<p>Selon l’approche de Scherrer on propose de définir <span class="math inline">\(SCE_i\)</span> la contribution de <span class="math inline">\(X_i\)</span> à la variation de <span class="math inline">\(Y\)</span> peut s’écrire :</p>
<p><span class="math display">\[
SCE_i = a_i \; R_{X_iY} \; SCT
\]</span></p>
<p>On propose de tester la signignificativité de l’effet de chacun des tableaux explicatifs par une méthode de permutation des lignes de chacune des matrices explicatives.</p>
</div>
<div id="how-to-build-a-procrustean-model" class="section level2">
<h2>How to build a procrustean model</h2>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" data-line-number="1"><span class="kw">library</span>(ProcMod)</a></code></pre></div>
<div id="loading-of-the-demo-data" class="section level3">
<h3>Loading of the demo data</h3>
<p>They consist in two MOTUs tables describing bacterial and eukaryiote communities at 21 sites accros the eastern coast of Australia.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" data-line-number="1"><span class="kw">data</span>(<span class="st">&quot;eukaryotes&quot;</span>)</a>
<a class="sourceLine" id="cb2-2" data-line-number="2"><span class="kw">data</span>(<span class="st">&quot;bacteria&quot;</span>)</a></code></pre></div>
<p>At each site environmental data are also available to describe soil chemistry, climat and site location.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" data-line-number="1"><span class="kw">data</span>(<span class="st">&quot;soil&quot;</span>)</a>
<a class="sourceLine" id="cb3-2" data-line-number="2"><span class="kw">data</span>(<span class="st">&quot;climat&quot;</span>)</a>
<a class="sourceLine" id="cb3-3" data-line-number="3"><span class="kw">data</span>(<span class="st">&quot;geography&quot;</span>)</a></code></pre></div>
</div>
<div id="processing-of-the-motus-data" class="section level3">
<h3>Processing of the MOTUs data</h3>
<p>Using the <em>vegan</em> package MOTUs frequencies are transformed according to Hellinger by take the square root of the MOTUs relative frequencies at each site</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" data-line-number="1"><span class="kw">library</span>(vegan)</a>
<a class="sourceLine" id="cb4-2" data-line-number="2"><span class="co">#&gt; Le chargement a nécessité le package : permute</span></a>
<a class="sourceLine" id="cb4-3" data-line-number="3"><span class="co">#&gt; Le chargement a nécessité le package : lattice</span></a>
<a class="sourceLine" id="cb4-4" data-line-number="4"><span class="co">#&gt; This is vegan 2.5-2</span></a>
<a class="sourceLine" id="cb4-5" data-line-number="5"></a>
<a class="sourceLine" id="cb4-6" data-line-number="6">bac.hellinger =<span class="st"> </span><span class="kw">decostand</span>(bacteria,<span class="dt">method =</span><span class="st">&quot;hellinger&quot;</span>)</a>
<a class="sourceLine" id="cb4-7" data-line-number="7">euk.hellinger =<span class="st"> </span><span class="kw">decostand</span>(eukaryotes,<span class="dt">method =</span><span class="st">&quot;hellinger&quot;</span>)</a></code></pre></div>
<p>Bray Curtis distances among sites are computed according to both the communities</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" data-line-number="1">bac.bray =<span class="st"> </span><span class="kw">vegdist</span>(bac.hellinger,<span class="dt">method =</span> <span class="st">&quot;bray&quot;</span>)</a>
<a class="sourceLine" id="cb5-2" data-line-number="2">euk.bray =<span class="st"> </span><span class="kw">vegdist</span>(euk.hellinger,<span class="dt">method =</span> <span class="st">&quot;bray&quot;</span>)</a></code></pre></div>
</div>
<div id="processing-the-environmental-data" class="section level3">
<h3>Processing the environmental data</h3>
<p>Soil and climatic data are centered and rescaled for having the same influence</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" data-line-number="1">soil.rescaled   =<span class="st"> </span><span class="kw">scale</span>(soil,   <span class="dt">center =</span> <span class="ot">TRUE</span>, <span class="dt">scale =</span> <span class="ot">TRUE</span>)</a>
<a class="sourceLine" id="cb6-2" data-line-number="2">climat.rescaled =<span class="st"> </span><span class="kw">scale</span>(climat, <span class="dt">center =</span> <span class="ot">TRUE</span>, <span class="dt">scale =</span> <span class="ot">TRUE</span>)</a></code></pre></div>
</div>
<div id="assembling-the-data-for-the-model" class="section level3">
<h3>Assembling the data for the model</h3>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" data-line-number="1">data =<span class="st"> </span><span class="kw">procmod.frame</span>(<span class="dt">euk       =</span> euk.bray,</a>
<a class="sourceLine" id="cb7-2" data-line-number="2">                     <span class="dt">bac       =</span> bac.bray,</a>
<a class="sourceLine" id="cb7-3" data-line-number="3">                     <span class="dt">climat    =</span> climat,</a>
<a class="sourceLine" id="cb7-4" data-line-number="4">                     <span class="dt">soil      =</span> soil,</a>
<a class="sourceLine" id="cb7-5" data-line-number="5">                     <span class="dt">geography =</span> geography)</a></code></pre></div>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" data-line-number="1">euk.pm =<span class="st"> </span><span class="kw">pm</span>(<span class="dt">formula =</span> euk <span class="op">~</span><span class="st"> </span>soil <span class="op">+</span><span class="st"> </span>climat <span class="op">+</span><span class="st"> </span>geography, <span class="dt">data =</span> data)</a>
<a class="sourceLine" id="cb8-2" data-line-number="2">euk.pm</a>
<a class="sourceLine" id="cb8-3" data-line-number="3"><span class="co">#&gt; </span></a>
<a class="sourceLine" id="cb8-4" data-line-number="4"><span class="co">#&gt; Call:</span></a>
<a class="sourceLine" id="cb8-5" data-line-number="5"><span class="co">#&gt; pm(formula = euk ~ soil + climat + geography, data = data)</span></a>
<a class="sourceLine" id="cb8-6" data-line-number="6"><span class="co">#&gt; </span></a>
<a class="sourceLine" id="cb8-7" data-line-number="7"><span class="co">#&gt; Coefficients:</span></a>
<a class="sourceLine" id="cb8-8" data-line-number="8"><span class="co">#&gt;         soil       climat    geography </span></a>
<a class="sourceLine" id="cb8-9" data-line-number="9"><span class="co">#&gt; 0.1411894993 0.0002849650 0.0006001613</span></a></code></pre></div>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" data-line-number="1"><span class="kw">plot</span>(euk.pm)</a></code></pre></div>
<p><img src="data:image/png;base64,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" /><!-- --></p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" data-line-number="1"><span class="kw">anova</span>(euk.pm)</a>
<a class="sourceLine" id="cb10-2" data-line-number="2"><span class="co">#&gt; Analysis of Variance Table</span></a>
<a class="sourceLine" id="cb10-3" data-line-number="3"><span class="co">#&gt; </span></a>
<a class="sourceLine" id="cb10-4" data-line-number="4"><span class="co">#&gt; Response: euk</span></a>
<a class="sourceLine" id="cb10-5" data-line-number="5"><span class="co">#&gt;           Df  Sum Sq Mean Sq F value    Pr(&gt;F)    </span></a>
<a class="sourceLine" id="cb10-6" data-line-number="6"><span class="co">#&gt; soil       1 1.09067 1.09067 18.0414 0.0004843 ***</span></a>
<a class="sourceLine" id="cb10-7" data-line-number="7"><span class="co">#&gt; climat     1 0.03318 0.03318  0.5489 0.4683427    </span></a>
<a class="sourceLine" id="cb10-8" data-line-number="8"><span class="co">#&gt; geography  1 0.01281 0.01281  0.2118 0.6508585    </span></a>
<a class="sourceLine" id="cb10-9" data-line-number="9"><span class="co">#&gt; Residuals 18 1.08817 0.06045                      </span></a>
<a class="sourceLine" id="cb10-10" data-line-number="10"><span class="co">#&gt; ---</span></a>
<a class="sourceLine" id="cb10-11" data-line-number="11"><span class="co">#&gt; Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1</span></a></code></pre></div>
</div>
</div>



<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
  (function () {
    var script = document.createElement("script");
    script.type = "text/javascript";
    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
    document.getElementsByTagName("head")[0].appendChild(script);
  })();
</script>

</body>
</html>