{"id":565,"date":"2016-04-18T07:33:33","date_gmt":"2016-04-18T07:33:33","guid":{"rendered":"http:\/\/blog.tiran.info\/?p=565"},"modified":"2017-12-05T14:21:16","modified_gmt":"2017-12-05T13:21:16","slug":"analyse-de-correlation-avec-r","status":"publish","type":"post","link":"https:\/\/blog.tiran.stream\/?p=565","title":{"rendered":"Analyse de corr\u00e9lation avec R"},"content":{"rendered":"

Dans la continuit\u00e9 du pr\u00e9c\u00e9dent billet<\/a>, je r\u00e9alise cette fois-ci l’analyse de corr\u00e9lation \u00e0 l’aide de R.<\/p>\n

Les donn\u00e9es sont initialement charg\u00e9es dans un dataframe debits_loire depuis le fichier Excel d\u00e9j\u00e0 utilis\u00e9:\u00a0Debits_Loire.xlsx<\/a><\/p>\n

> require(xlsx)\r\nLe chargement a n\u00e9cessit\u00e9 le package : xlsx\r\nLe chargement a n\u00e9cessit\u00e9 le package : rJava\r\nLe chargement a n\u00e9cessit\u00e9 le package : xlsxjars\r\n> setwd("C:\/RTI\/Stats\/Correlation")\r\n> debits_loire <- read.xlsx("Debits_Loire.xlsx", sheetIndex = 1)\r\n> names(debits_loire) <- c("Date","Nevers","Saint-Satur","Orleans","Blois","Tours")\r\n> summary(debits_loire)\r\n                 Date          Nevers       Saint-Satur        Orleans           Blois            Tours       \r\n 01 FEV. 2016 00:00:   1   Min.   :143.0   Min.   : 281.0   Min.   : 294.0   Min.   : 311.0   Min.   : 350.0  \r\n 01 FEV. 2016 01:00:   1   1st Qu.:214.0   1st Qu.: 379.5   1st Qu.: 401.8   1st Qu.: 414.0   1st Qu.: 444.8  \r\n 01 FEV. 2016 02:00:   1   Median :289.0   Median : 453.0   Median : 479.0   Median : 527.0   Median : 572.0  \r\n 01 FEV. 2016 03:00:   1   Mean   :335.7   Mean   : 523.3   Mean   : 532.2   Mean   : 577.3   Mean   : 619.8  \r\n 01 FEV. 2016 04:00:   1   3rd Qu.:391.0   3rd Qu.: 577.2   3rd Qu.: 571.2   3rd Qu.: 640.5   3rd Qu.: 654.0  \r\n 01 FEV. 2016 05:00:   1   Max.   :928.0   Max.   :1360.0   Max.   :1270.0   Max.   :1310.0   Max.   :1430.0  \r\n (Other)           :1266                                                                                      \r\n>\r\n<\/pre>\n
La commande cor permet d’obtenir les matrices de corr\u00e9lation (Pearson & Spearman) pour les diverses combinaisons:<\/p>\n
> cor(debits_loire[,-1])\r\n               Nevers Saint-Satur   Orleans     Blois     Tours\r\nNevers      1.0000000   0.9581882 0.8398289 0.7659756 0.7212110\r\nSaint-Satur 0.9581882   1.0000000 0.9431337 0.8879669 0.8468633\r\nOrleans     0.8398289   0.9431337 1.0000000 0.9852670 0.9628878\r\nBlois       0.7659756   0.8879669 0.9852670 1.0000000 0.9890436\r\nTours       0.7212110   0.8468633 0.9628878 0.9890436 1.0000000\r\n> \r\n> cor(debits_loire[,-1], method="spearman")\r\n               Nevers Saint-Satur   Orleans     Blois     Tours\r\nNevers      1.0000000   0.9167092 0.8043585 0.7286661 0.6889871\r\nSaint-Satur 0.9167092   1.0000000 0.9506001 0.9021153 0.8676888\r\nOrleans     0.8043585   0.9506001 1.0000000 0.9845628 0.9441848\r\nBlois       0.7286661   0.9021153 0.9845628 1.0000000 0.9752079\r\nTours       0.6889871   0.8676888 0.9441848 0.9752079 1.0000000\r\n> \r\n<\/pre>\n
On peut repr\u00e9senter sur un m\u00eame graphique l’\u00e9volution temporelle des d\u00e9bits pour ces 3 villes:<\/p>\n
> plot(debits_loire$Tours,type="l",col="red", ylim=c(0,1500),yaxs="i",xlab="# Mesure",ylab="D\u00e9bit m3\/s")\r\n> lines(debits_loire$Nevers,col="green")\r\n> lines(debits_loire$Orleans,col="blue")\r\n> title("Evolution compar\u00e9e du d\u00e9bit")\r\n> legend(950,1400, c("Tours","Orleans","Nevers"), lty=c(1,1,1), lwd=c(2.5,2.5,2.5),col=c("red","blue","green"))\r\n> \r\n<\/pre>\n
\"evol_debit_lag\"<\/a><\/p>\n
La commande pairs permet d’obtenir une matrice de scatterplots. Ici, on s’int\u00e9resse aux \u00e9chantillons issus de Nevers, Orl\u00e9ans & Tours:<\/p>\n
> pairs(debits_loire[,c("Nevers","Orleans","Tours")])\r\n> \r\n<\/pre>\n
\"pairs_lag\"<\/a><\/p>\n
On remarque la forme singuli\u00e8re – en \u00ab\u00a0lasso\u00a0\u00bb – des graphes. Celle-ci s’explique par la latence des \u00e9pisodes de crues\/d\u00e9crues entre les points de mesure.<\/p>\n
La recherche de cette latence peut \u00eatre r\u00e9alis\u00e9e \u00e0 l’aide de la fonction ccf pour cross correlation function<\/a>.<\/p>\n
> nevers_tours <- ccf(debits_loire$Tours,debits_loire$Nevers, lag.max=120)\r\n> \r\n<\/pre>\n
\"ccf_tours\"<\/a><\/p>\n
Le sommet de la courbe correspond au d\u00e9calage pour lequel le coefficient de corr\u00e9lation est maximal. On peut retrouver directement sa valeur num\u00e9rique (54 heures pour Tours) via les attributs du r\u00e9sultat de ccf:<\/p>\n
> nevers_tours$lag[which.max(nevers_tours$acf)]\r\n[1] 54\r\n> \r\n<\/pre>\n
M\u00eame chose pour Orl\u00e9ans:<\/p>\n
> nevers_orleans <- ccf(debits_loire$Orleans,debits_loire$Nevers, lag.max=120)\r\n> \r\n<\/pre>\n
\"ccf_orleans\"<\/a><\/p>\n
On trouve cette fois un d\u00e9calage de 35 heures:<\/p>\n
> nevers_orleans$lag[which.max(nevers_orleans$acf)]\r\n[1] 35\r\n> \r\n<\/pre>\n
Une fois d\u00e9termin\u00e9 la latence de propagation des ph\u00e9nom\u00e8nes de crues\/d\u00e9crues – respectivement 35 et 54 heures pour Orleans et Tours – on peut de nouveau repr\u00e9senter l’\u00e9volution des d\u00e9bits apr\u00e8s avoir d\u00e9cal\u00e9 les \u00e9chantillons.<\/p>\n
> plot(debits_loire$Tours[seq(54,length(debits_loire$Tours))],type="l",col="red", ylim=c(0,1500),yaxs="i",xlab="# Mesure",ylab="D\u00e9bit m3\/s")\r\n> lines(debits_loire$Nevers,col="green")\r\n> lines(debits_loire$Orleans[seq(35,length(debits_loire$Orleans))],col="blue")\r\n> title("Evolution compar\u00e9e du d\u00e9bit (apr\u00e8s d\u00e9calage temporel)")\r\n> legend(950,1400, c("Tours","Orleans","Nevers"), lty=c(1,1,1), lwd=c(2.5,2.5,2.5),col=c("red","blue","green"))\r\n> \r\n<\/pre>\n
\"evol_debit_nolag\"<\/a><\/p>\n
On constate une parfaite correspondance des profils.<\/p>\n
On peut aussi produire une nouvelle matrice de scatterplots en tenant compte de ces d\u00e9calages:<\/p>\n
> d\u00e9bits_d\u00e9cal\u00e9s <- data.frame(debits_loire$Tours[seq(54,length(debits_loire$Tours))])\r\n> names(d\u00e9bits_d\u00e9cal\u00e9s) <- "Tours"\r\n> d\u00e9bits_d\u00e9cal\u00e9s$Orleans <- debits_loire$Orleans[seq(35,length(debits_loire$Orleans)-(54-35))]\r\n> d\u00e9bits_d\u00e9cal\u00e9s$Nevers <- debits_loire$Nevers[seq(1,length(debits_loire$Nevers)-53)]\r\n> pairs(d\u00e9bits_d\u00e9cal\u00e9s)\r\n> \r\n<\/pre>\n
\"pairs_nolag\"<\/a><\/p>\n
La relation entre les d\u00e9bits est d\u00e9sormais quasi-lin\u00e9aire.<\/p>\n","protected":false},"excerpt":{"rendered":"
Dans la continuit\u00e9 du pr\u00e9c\u00e9dent billet, je r\u00e9alise cette fois-ci l’analyse de corr\u00e9lation \u00e0 l’aide de R. Les donn\u00e9es sont<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"categories":[12,14],"tags":[],"class_list":["post-565","post","type-post","status-publish","format-standard","hentry","category-r","category-statistique"],"_links":{"self":[{"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=\/wp\/v2\/posts\/565","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=565"}],"version-history":[{"count":2,"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=\/wp\/v2\/posts\/565\/revisions"}],"predecessor-version":[{"id":1162,"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=\/wp\/v2\/posts\/565\/revisions\/1162"}],"wp:attachment":[{"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.tiran.stream\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}