{"id":299,"date":"2014-10-09T17:05:47","date_gmt":"2014-10-09T15:05:47","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/la-regression-logistique\/"},"modified":"2023-10-14T20:14:38","modified_gmt":"2023-10-14T18:14:38","slug":"la-regression-logistique","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-regressions-avec-r\/la-regression-logistique\/","title":{"rendered":"La r\u00e9gression logistique"},"content":{"rendered":"<h2>Un fichier de donn\u00e9es<\/h2>\n<p>Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d&rsquo;un cours de FUN (France Unit\u00e9 Num\u00e9rique). Les fichiers sont disponibles <a href=\"https:\/\/filedn.com\/lpKG7uY9hIHVel5exA5Ik80\/Wordpress\/Logiciels%20math%C3%A9matiques\/R\/\">ici<\/a>.<\/p>\n<p>Par la suite, ces donn\u00e9es seront stock\u00e9es dans la variable <em>satis<\/em> .<\/p>\n<p>Dans ces donn\u00e9es comme souvent, les observations sont en lignes et les variables en colonnes.<\/p>\n<h2>Pr\u00e9sentation<\/h2>\n<p>On cherche \u00e0 expliquer une variable binaire Y \u00e0 l&rsquo;aide d&rsquo;autres variables.<\/p>\n<p>Pour que d\u00e9boucher sur une valeur num\u00e9rique, on utilise le mod\u00e8le suivant :<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\"> \\ln \\left( \\frac{P(Y=1)}{P(Y=0} \\right)=\\ln \\left( \\frac{P(Y=1)}{1-P(Y=1} \\right) =a+b \\times X_1+c \\times X_2 + \\cdots =K\u00a0<\/span>\n<p>On aura alors pour les pr\u00e9dictions :<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\"> p(Y=1)=\\frac{e^K}{1+e^K}\u00a0<\/span>\n<p>La proc\u00e9dure est voisine de la celle de la r\u00e9gression multiple.<\/p>\n<h2>Un exemple<\/h2>\n<p>On cherche \u00e0 expliquer la variable binaire recommander.b en fonction de plusieurs variables :<br \/>\n&#8211; sexe.cat<br \/>\n&#8211; age<br \/>\n&#8211; score.relation<br \/>\n&#8211; profession.cat<\/p>\n<h2>Les variables cat\u00e9gorielles<\/h2>\n<p>Il faudra faire tr\u00e8s attention \u00e0 bien convertir les variables cat\u00e9gorielles pour qu&rsquo;elles ne soient pas interpr\u00e9t\u00e9es comme des variables quantitatives.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">satis$sexe.cat&lt;-factor(satis$sexe,labels=c(\"H\",\"F\")) \nsatis$profession.cat&lt;-factor(satis$profession) \nsatis$service.cat&lt;-factor(satis$service)<\/pre>\n<p>Dans le logiciel, la premi\u00e8re cat\u00e9gorie servira de r\u00e9f\u00e9rence. Par exemple, pour le sexe cod\u00e9 (\u00ab\u00a0H\u00a0\u00bb,\u00a0\u00bbF\u00a0\u00bb), \u00ab\u00a0H\u00a0\u00bb sera la r\u00e9f\u00e9rence. On cherchera donc \u00e0 savoir si le fait d&rsquo;\u00eatre une femme modifie le score de relation.<\/p>\n<p>Pour changer cette r\u00e9f\u00e9rence, on peut le faire de la sorte :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">satis$sexe.cat &lt;- relevel(satis$sexe.cat,ref=\"F\")<\/pre>\n<h2>La variable binaire<\/h2>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">satis$recommander.b&lt;-ifelse(satis$recommander==2,1,0)<\/pre>\n<h2>La r\u00e9gression logistique<\/h2>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">mod.r.m&lt;-glm(recommander.b~sexe.cat+age+score.relation+profession.cat,data=satis,family=binomial(\"logit\"))<\/pre>\n<p>Calculons les valeurs de p par cat\u00e9gorie :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">drop1(mod.r.m,.~.,test=\"Chisq\")<\/pre>\n<p><code><br \/>\nSingle term deletions<\/code><\/p>\n<p><code><br \/>\n<\/code><\/p>\n<p><code>Model:<br \/>\nrecommander.b ~ sexe.cat + age + score.relation + profession.cat<br \/>\nDf Deviance    AIC    LRT Pr(&gt;Chi)<br \/>\n332.48 354.48<br \/>\nsexe.cat        1   336.74 356.74  4.259  0.03905 *<br \/>\nage             1   333.00 353.00  0.516  0.47243<br \/>\nscore.relation  1   409.14 429.14 76.665  &lt; 2e-16 ***<br \/>\nprofession.cat  7   341.19 349.19  8.711  0.27408<\/code><\/p>\n<p><code><br \/>\n<\/code><\/p>\n<p><code>\u2014\u00a0-<br \/>\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1<br \/>\n<\/code><\/p>\n<p>La valeur de p pour l&rsquo;\u00e2ge est faible (inf\u00e9rieure \u00e0 0.05).<\/p>\n<p>Regardons l&rsquo;ensemble des r\u00e9sultats :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">summary(mod.r.m)<\/pre>\n<p><code><br \/>\nCall:<br \/>\nglm(formula = recommander.b ~ sexe.cat + age + score.relation +<br \/>\nprofession.cat, family = binomial(\"logit\"), data = satis)<\/code><\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Deviance Residuals:<br \/>\nMin 1Q Median 3Q Max<br \/>\n-2.2358 -0.8142 0.5003 0.6937 2.0298<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Coefficients:<br \/>\nEstimate Std. Error z value Pr(&gt;|z|)<br \/>\n(Intercept) -23.745655 882.744298 -0.027 0.9785<br \/>\nsexe.catF 0.595364 0.293048 2.032 0.0422 *<br \/>\nage 0.006309 0.008796 0.717 0.4732<br \/>\nscore.relation 0.256624 0.034247 7.493 6.71e-14 ***<br \/>\nprofession.cat2 15.641720 882.743601 0.018 0.9859<br \/>\nprofession.cat3 15.338964 882.743436 0.017 0.9861<br \/>\nprofession.cat4 14.630198 882.743434 0.017 0.9868<br \/>\nprofession.cat5 14.881076 882.743450 0.017 0.9866<br \/>\nprofession.cat6 15.129875 882.743504 0.017 0.9863<br \/>\nprofession.cat7 15.301040 882.743609 0.017 0.9862<br \/>\nprofession.cat8 14.363204 882.743485 0.016 0.9870<\/p>\n<p>\u2014\u00a0&#8211;<br \/>\nSignif. codes: 0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>(Dispersion parameter for binomial family taken to be 1)<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Null deviance: 419.70 on 334 degrees of freedom<br \/>\nResidual deviance: 332.48 on 324 degrees of freedom<br \/>\n(199 observations deleted due to missingness)<br \/>\nAIC: 354.48<\/p>\n<p><code><br \/>\n<\/code><\/p>\n<p><code>Number of Fisher Scoring iterations: 13<br \/>\n<\/code><\/p>\n<h2>Interpr\u00e9tation<\/h2>\n<p>Servons-nous de deux pr\u00e9dictions pour mieux comprendre ce qui se passe :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">predict(mod.r.m,data=satis,data.frame(sexe.cat=\"H\",age=30,score.relation=40,profession.cat=\"5\"))<\/pre>\n<p><code><br \/>\n1<br \/>\n1.589661<br \/>\n<\/code><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">predict(mod.r.m,data=satis,data.frame(sexe.cat=\"F\",age=30,score.relation=40,profession.cat=\"5\"))<\/pre>\n<p><code><br \/>\n1<br \/>\n2.185025<br \/>\n<\/code><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">2.185025-1.589661<\/pre>\n<p><code><br \/>\n[1] 0.595364<br \/>\n<\/code><\/p>\n<p>Les autres param\u00e8tres \u00e9tant inchang\u00e9s, on a une augmentation de la valeur pr\u00e9dite de 0.595364.<\/p>\n<p>Mais interpr\u00e9tons les pr\u00e9dictions.<\/p>\n<p>Pour un homme :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">exp(1.589661)\/(1+exp(1.589661))<\/pre>\n<p><code><br \/>\n[1] 0.8305684<br \/>\n<\/code><\/p>\n<p>Pour une femme :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">exp(2.185025)\/(1+exp(2.185025))<\/pre>\n<p><code><br \/>\n[1] 0.8988967<br \/>\n<\/code><\/p>\n<p>La probabilit\u00e9 de recommander est de 0.8305684 pour homme et de 0.8988967 pour une femme (avec les autres param\u00e8tres choisis fix\u00e9s).<\/p>\n<h2>Cas particulier : une seule variable explicative binaire<\/h2>\n<p>Cherchons \u00e0 expliquer la variable recommander.b \u00e0 l&rsquo;aide de la variable binaire sexe.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">mod.r.s&lt;-glm(recommander.b~sexe,data=satis,family=binomial(\"logit\")) \nsummary(mod.r.s)<\/pre>\n<p><code><br \/>\nCall:<br \/>\nglm(formula = recommander.b ~ sexe, family = binomial(\"logit\"),<br \/>\ndata = satis)<\/code><\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Deviance Residuals:<br \/>\nMin 1Q Median 3Q Max<br \/>\n-1.4964 -1.4602 0.8890 0.9188 0.9188<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Coefficients:<br \/>\nEstimate Std. Error z value Pr(&gt;|z|)<br \/>\n(Intercept) 0.64401 0.14454 4.456 8.37e-06 ***<br \/>\nsexe 0.08039 0.21085 0.381 0.703<\/p>\n<p>\u2014\u00a0&#8211;<br \/>\nSignif. codes: 0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>(Dispersion parameter for binomial family taken to be 1)<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Null deviance: 516.95 on 404 degrees of freedom<br \/>\nResidual deviance: 516.81 on 403 degrees of freedom<br \/>\n(129 observations deleted due to missingness)<br \/>\nAIC: 520.81<\/p>\n<p><code><br \/>\n<\/code><\/p>\n<p><code>Number of Fisher Scoring iterations: 4<br \/>\n<\/code><\/p>\n<p>Comparons avec l&rsquo;odds-ratio.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">twoby2(1-satis$sexe,1-satis$recommander.b)<\/pre>\n<p><code><br \/>\n2 by 2 table analysis: <\/code><\/p>\n<p><code><code><\/code><\/code><\/p>\n<hr \/>\n<p><code><code><\/code><\/code><\/p>\n<p>Outcome : 0<br \/>\nComparing : 0 vs. 1<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>0 1 P(0) 95% conf. interval<br \/>\n0 130 63 0.6736 0.6043 0.7360<br \/>\n1 139 73 0.6557 0.5892 0.7165<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>95% conf. interval<br \/>\nRelative Risk: 1.0273 0.8945 1.1798<br \/>\nSample Odds Ratio: 1.0837 0.7169 1.6383<br \/>\nConditional MLE Odds Ratio: 1.0835 0.7021 1.6745<br \/>\nProbability difference: 0.0179 -0.0740 0.1088<\/p>\n<p><code><code><\/code><\/code><\/p>\n<p>Exact P-value: 0.7523<br \/>\nAsymptotic P-value: 0.703<\/p>\n<p><code><code><\/code><\/code><\/p>\n<hr \/>\n<p><code><br \/>\n<\/code>exp(0.08039)<\/p>\n<p><code><\/code><\/p>\n<p><code><br \/>\n[1] 1.08371<br \/>\n<\/code><\/p>\n<p>Calculons le p-value avec le test du Chi2 :<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">chisq.test(satis$recommander.b,satis$sexe,correct=FALSE)<\/pre>\n<p><code><br \/>\nPearson's Chi-squared test<\/code><\/p>\n<p><code><br \/>\n<\/code><\/p>\n<p><code>data:  satis$recommander.b and satis$sexe<br \/>\nX-squared = 0.1454, df = 1, p-value = 0.703<br \/>\n<\/code><\/p>\n<p>On retrouve la m\u00eame p-value.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Un fichier de donn\u00e9es Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d&rsquo;un cours de FUN (France Unit\u00e9 Num\u00e9rique). Les fichiers sont disponibles ici. Par la suite,&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2076,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-299","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>La r\u00e9gression logistique - Maths &amp; Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-regressions-avec-r\/la-regression-logistique\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"La r\u00e9gression logistique - Maths &amp; Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Un fichier de donn\u00e9es Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d&rsquo;un cours de FUN (France Unit\u00e9 Num\u00e9rique). 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