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<title>Effets d’interaction dans un modèle</title>
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<h1 class="title toc-ignore">Effets d’interaction dans un modèle</h1>
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<ul>
<li><a href="#exemple-dinteraction" id="toc-exemple-dinteraction">Exemple d’interaction</a></li>
<li><a href="#un-second-exemple-dinteraction" id="toc-un-second-exemple-dinteraction">Un second exemple d’interaction</a></li>
<li><a href="#explorer-les-différentes-interactions-possibles" id="toc-explorer-les-différentes-interactions-possibles">Explorer les différentes interactions possibles</a></li>
<li><a href="#pour-aller-plus-loin" id="toc-pour-aller-plus-loin">Pour aller plus loin</a></li>
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<p>Une version actualisée de ce chapitre est disponible sur <strong>guide-R</strong> : <a href="https://larmarange.github.io/guide-R/analyses/interactions.html">Interactions</a></p>
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<p>Ce chapitre est évoqué dans le webin-R #07 (régression logistique partie 2) sur <a href="https://youtu.be/BUo9i7XTLYQ">YouTube</a>.</p>
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<p>Dans un modèle statistique classique, on fait l’hypothèse implicite que chaque variable explicative est indépendante des autres. Cependant, cela ne se vérifie pas toujours. Par exemple, l’effet de l’âge peut varier en fonction du sexe. Il est dès lors nécessaire de prendre en compte dans son modèle les <dfn data-index="effet d'interaction">effets d’interaction</dfn><dfn data-index="interaction"></dfn><a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a>.</p>
<div id="exemple-dinteraction" class="section level2 hasAnchor">
<h2 class="hasAnchor">Exemple d’interaction<a href="#exemple-dinteraction" class="anchor-section" aria-label="Anchor link to header"></a></h2>
<p>Reprenons le modèle que nous avons utilisé dans le chapitre sur la <a href="regression-logistique.html">régression logistique</a>.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a><span class="fu">library</span>(questionr)</span>
<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a><span class="fu">data</span>(hdv2003)</span>
<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a>d <span class="ot"><-</span> hdv2003</span>
<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a>d<span class="sc">$</span>sexe <span class="ot"><-</span> <span class="fu">relevel</span>(d<span class="sc">$</span>sexe, <span class="st">"Femme"</span>)</span>
<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a>d<span class="sc">$</span>grpage <span class="ot"><-</span> <span class="fu">cut</span>(d<span class="sc">$</span>age, <span class="fu">c</span>(<span class="dv">16</span>, <span class="dv">25</span>, <span class="dv">45</span>, <span class="dv">65</span>, <span class="dv">99</span>), <span class="at">right =</span> <span class="cn">FALSE</span>, <span class="at">include.lowest =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a>d<span class="sc">$</span>etud <span class="ot"><-</span> d<span class="sc">$</span>nivetud</span>
<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a><span class="fu">levels</span>(d<span class="sc">$</span>etud) <span class="ot"><-</span> <span class="fu">c</span>(</span>
<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a> <span class="st">"Primaire"</span>, <span class="st">"Primaire"</span>, <span class="st">"Primaire"</span>,</span>
<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a> <span class="st">"Secondaire"</span>, <span class="st">"Secondaire"</span>, <span class="st">"Technique/Professionnel"</span>,</span>
<span id="cb1-10"><a href="#cb1-10" tabindex="-1"></a> <span class="st">"Technique/Professionnel"</span>, <span class="st">"Supérieur"</span></span>
<span id="cb1-11"><a href="#cb1-11" tabindex="-1"></a>)</span>
<span id="cb1-12"><a href="#cb1-12" tabindex="-1"></a>d<span class="sc">$</span>etud <span class="ot"><-</span> <span class="fu">addNAstr</span>(d<span class="sc">$</span>etud, <span class="st">"Manquant"</span>)</span>
<span id="cb1-13"><a href="#cb1-13" tabindex="-1"></a><span class="fu">library</span>(labelled)</span>
<span id="cb1-14"><a href="#cb1-14" tabindex="-1"></a><span class="fu">var_label</span>(d<span class="sc">$</span>sport) <span class="ot"><-</span> <span class="st">"Pratique du sport ?"</span></span>
<span id="cb1-15"><a href="#cb1-15" tabindex="-1"></a><span class="fu">var_label</span>(d<span class="sc">$</span>sexe) <span class="ot"><-</span> <span class="st">"Sexe"</span></span>
<span id="cb1-16"><a href="#cb1-16" tabindex="-1"></a><span class="fu">var_label</span>(d<span class="sc">$</span>grpage) <span class="ot"><-</span> <span class="st">"Groupe d'âges"</span></span>
<span id="cb1-17"><a href="#cb1-17" tabindex="-1"></a><span class="fu">var_label</span>(d<span class="sc">$</span>etud) <span class="ot"><-</span> <span class="st">"Niveau d'étude"</span></span>
<span id="cb1-18"><a href="#cb1-18" tabindex="-1"></a><span class="fu">var_label</span>(d<span class="sc">$</span>relig) <span class="ot"><-</span> <span class="st">"Pratique religieuse"</span></span>
<span id="cb1-19"><a href="#cb1-19" tabindex="-1"></a><span class="fu">var_label</span>(d<span class="sc">$</span>heures.tv) <span class="ot"><-</span> <span class="st">"Nombre d'heures passées devant la télévision par jour"</span></span></code></pre></div>
<p>Nous avions alors exploré les facteurs associés au fait de pratiquer du sport.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a>mod <span class="ot"><-</span> <span class="fu">glm</span>(sport <span class="sc">~</span> sexe <span class="sc">+</span> grpage <span class="sc">+</span> etud <span class="sc">+</span> heures.tv <span class="sc">+</span> relig, <span class="at">data =</span> d, <span class="at">family =</span> <span class="fu">binomial</span>())</span>
<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a><span class="fu">library</span>(gtsummary)</span>
<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a><span class="fu">tbl_regression</span>(mod, <span class="at">exponentiate =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
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#jwfpsyznlw .gt_sourcenotes {
color: #333333;
background-color: #FFFFFF;
border-bottom-style: none;
border-bottom-width: 2px;
border-bottom-color: #D3D3D3;
border-left-style: none;
border-left-width: 2px;
border-left-color: #D3D3D3;
border-right-style: none;
border-right-width: 2px;
border-right-color: #D3D3D3;
}
#jwfpsyznlw .gt_sourcenote {
font-size: 90%;
padding-top: 4px;
padding-bottom: 4px;
padding-left: 5px;
padding-right: 5px;
}
#jwfpsyznlw .gt_left {
text-align: left;
}
#jwfpsyznlw .gt_center {
text-align: center;
}
#jwfpsyznlw .gt_right {
text-align: right;
font-variant-numeric: tabular-nums;
}
#jwfpsyznlw .gt_font_normal {
font-weight: normal;
}
#jwfpsyznlw .gt_font_bold {
font-weight: bold;
}
#jwfpsyznlw .gt_font_italic {
font-style: italic;
}
#jwfpsyznlw .gt_super {
font-size: 65%;
}
#jwfpsyznlw .gt_footnote_marks {
font-style: italic;
font-weight: normal;
font-size: 75%;
vertical-align: 0.4em;
}
#jwfpsyznlw .gt_asterisk {
font-size: 100%;
vertical-align: 0;
}
#jwfpsyznlw .gt_indent_1 {
text-indent: 5px;
}
#jwfpsyznlw .gt_indent_2 {
text-indent: 10px;
}
#jwfpsyznlw .gt_indent_3 {
text-indent: 15px;
}
#jwfpsyznlw .gt_indent_4 {
text-indent: 20px;
}
#jwfpsyznlw .gt_indent_5 {
text-indent: 25px;
}
</style>
<table class="gt_table">
<thead class="gt_col_headings">
<tr>
<th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1" scope="col" id="<strong>Caractéristique</strong>"><strong>Caractéristique</strong></th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>OR</strong><sup class="gt_footnote_marks">1</sup>"><strong>OR</strong><sup class="gt_footnote_marks">1</sup></th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>95% IC</strong><sup class="gt_footnote_marks">1</sup>"><strong>95% IC</strong><sup class="gt_footnote_marks">1</sup></th>
<th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="<strong>p-valeur</strong>"><strong>p-valeur</strong></th>
</tr>
</thead>
<tbody class="gt_table_body">
<tr><td headers="label" class="gt_row gt_left">Sexe</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
<tr><td headers="label" class="gt_row gt_left"> Femme</td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
<tr><td headers="label" class="gt_row gt_left"> Homme</td>
<td headers="estimate" class="gt_row gt_center">1,55</td>
<td headers="ci" class="gt_row gt_center">1,26 – 1,91</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>
<tr><td headers="label" class="gt_row gt_left">Groupe d'âges</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
<tr><td headers="label" class="gt_row gt_left"> [16,25)</td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
<tr><td headers="label" class="gt_row gt_left"> [25,45)</td>
<td headers="estimate" class="gt_row gt_center">0,66</td>
<td headers="ci" class="gt_row gt_center">0,42 – 1,03</td>
<td headers="p.value" class="gt_row gt_center">0,065</td></tr>
<tr><td headers="label" class="gt_row gt_left"> [45,65)</td>
<td headers="estimate" class="gt_row gt_center">0,34</td>
<td headers="ci" class="gt_row gt_center">0,21 – 0,54</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>
<tr><td headers="label" class="gt_row gt_left"> [65,99]</td>
<td headers="estimate" class="gt_row gt_center">0,25</td>
<td headers="ci" class="gt_row gt_center">0,15 – 0,43</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>
<tr><td headers="label" class="gt_row gt_left">Niveau d'étude</td>
<td headers="estimate" class="gt_row gt_center"></td>
<td headers="ci" class="gt_row gt_center"></td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
<tr><td headers="label" class="gt_row gt_left"> Primaire</td>
<td headers="estimate" class="gt_row gt_center">—</td>
<td headers="ci" class="gt_row gt_center">—</td>
<td headers="p.value" class="gt_row gt_center"></td></tr>
<tr><td headers="label" class="gt_row gt_left"> Secondaire</td>
<td headers="estimate" class="gt_row gt_center">2,59</td>
<td headers="ci" class="gt_row gt_center">1,77 – 3,83</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>
<tr><td headers="label" class="gt_row gt_left"> Technique/Professionnel</td>
<td headers="estimate" class="gt_row gt_center">2,86</td>
<td headers="ci" class="gt_row gt_center">1,98 – 4,17</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>
<tr><td headers="label" class="gt_row gt_left"> Supérieur</td>
<td headers="estimate" class="gt_row gt_center">6,63</td>
<td headers="ci" class="gt_row gt_center">4,55 – 9,80</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>
<tr><td headers="label" class="gt_row gt_left"> Manquant</td>
<td headers="estimate" class="gt_row gt_center">8,59</td>
<td headers="ci" class="gt_row gt_center">4,53 – 16,6</td>
<td headers="p.value" class="gt_row gt_center"><0,001</td></tr>