Résumé minimal du script AFC_precip_v2.R pour les AFC sur les précipitations en France en 2010 (données brutes)

Résumé des principales étapes du code R
1. Import des données
2. Lecture des données
3. Graphe, table de contingence et khi-deux
- 3.1 Graphe
- 3.2 Khi-deux
4. Module AFC
5. Les sorties de la fonction CA
6. Aide à l’interprétation
7. Le couteau suisse

Analyse factorielles de correspondances binaires (AFC) avec R et FactoMineR sur des données brutes de précipitations (Sources : www.meteociel.fr) Reconstitution de l’année 2010 (exemple de novembre) : http://www.meteociel.fr/climatologie/climato.php?mois=11&annee=2010

Pour aller plus loin :

Résumé des principales étapes du code R

Import des données ;
Module AFC ;
Valeurs propres et vecteurs propres ;
Coordonnées ;
Contributions ;
Qualités (COS2) ;
Aide à l’interprétation ;
Edition des rapports.

1. Import des données

Avec mes fichiers exemples, préférez les paramètres nord-américains (“.” séparateur de décimales, “,” séparateur de miliers).

Salle C210, identifiant => “geographie2” !

### setwd("D:/Users/geographie2/vgodard/ADD/precipitation/R")
### respecter ce cheminement si "geographie2"
### getwd()

# Remove all objects
rm(list = ls() )

2. Lecture des données

precipit <- read.csv("precipitation.csv",
                      sep = ";",
                      dec =".",### Si param. régio. non US, remplacer le "." par une ","
                      stringsAsFactors = FALSE) # si stringsAsFactors = FALSE on perd les modalités si qualitative

3. Graphe, table de contingence et khi-deux

3.1 Graphe

Installer et exécuter préalablement la librairie “gplots”

### Avec la librairie gplots
## install.packages("gplots") ## si pas déjà installé !
 library("gplots")

Quand la table de contingence ne contient pas trop de variables ou d’individus, il est possible de représenter les relations entre eux. Ici, ce n’est pas le cas.

# 1. Convertion des données en table
#dt <- as.table(as.matrix(precipit))

# 2. Graphe
#balloonplot(t(dt), main ="precipit", xlab ="", ylab="",
#            label = FALSE, show.margins = FALSE)

3.2 Khi-deux

Pour une petite table de contingence, il est possible de tester la significativité du lien de dépendance à l’aide d’un test du khi-deux.

# Calcul de la statistique du Chi-square (Khi-deux)
chisq <- chisq.test(precipit[,2:13])
chisq

## 
##  Pearson's Chi-squared test
## 
## data:  precipit[, 2:13]
## X-squared = 13818, df = 803, p-value < 2.2e-16

# Calcul de la valeur du Khi-deux
chisq$statistic

## X-squared 
##  13818.48

# Calcul du degrés de liberté (Degree of freedom)
df <- (nrow(precipit) - 1) * (ncol(precipit) - 1)
df

## [1] 876

# Calcul de la P-value
pval <- pchisq(chisq$statistic, df = df, lower.tail = FALSE)
pval

## X-squared 
##         0

# ou
chisq$p.value

## [1] 0

Au risque 5% (communément admis), on rejette l’hypothèse nulle d’indépendance entre les lignes et les colonnes.

Sur les grosses tables, il est pratiquement toujours significatif (p-value < 0.05)

4. Module AFC

Installer et exécuter préalablement les librairies “FactoMineR”, “factoextra”, puis les charger

### Avec la librairie FactoMineR et factoextra
## install.packages(c("FactoMineR", "factoextra")) ## si pas déjà installés !

library("FactoMineR")
library("factoextra")

L’AFC avec tous les éléments actifs (73 lignes et 12 variables)

CA est le nom de l’AFC dans Factominer
CA fonctionne a minima avec : – X : le data frame (la table de contingence) ; – ncp : nb de dimensions gardé dans le résultat final – graph : le graphe par défaut (pour ne pas afficher le graphe graph = FALSE)

res.precipit.ca <- CA(precipit[,2:13],
                       col.sup = NULL,
                       row.sup = NULL,
                       axes = 1:2,
                       ncp = 12,
                       graph = TRUE)

Le graphique avec la fonction Biplot (cf. infra) apporte un net gain de lisibilité.

5. Les sorties de la fonction CA

Si ce n’est déjà fait, installer le package “factoextra”, puis le charger

## install.packages("factoextra")

library("factoextra")

Si on veut connaître tous les résultats de la fonction CA dans Factominer et/ou factoextra :

### Listage des résultats

print(res.precipit.ca)

## **Results of the Correspondence Analysis (CA)**
## The row variable has  74  categories; the column variable has 12 categories
## The chi square of independence between the two variables is equal to 13818.48 (p-value =  0 ).
## *The results are available in the following objects:
## 
##    name              description                   
## 1  "$eig"            "eigenvalues"                 
## 2  "$col"            "results for the columns"     
## 3  "$col$coord"      "coord. for the columns"      
## 4  "$col$cos2"       "cos2 for the columns"        
## 5  "$col$contrib"    "contributions of the columns"
## 6  "$row"            "results for the rows"        
## 7  "$row$coord"      "coord. for the rows"         
## 8  "$row$cos2"       "cos2 for the rows"           
## 9  "$row$contrib"    "contributions of the rows"   
## 10 "$call"           "summary called parameters"   
## 11 "$call$marge.col" "weights of the columns"      
## 12 "$call$marge.row" "weights of the rows"

5.1. Les eigenvalues ou valeurs propres

La somme des eigenvalues égale le nombre d’axes (ici 12).

Contrairement à l’ACP eigenvalue n’est jamais supérieure à 1.

eig.val <- get_eigenvalue(res.precipit.ca)
eig.val

##         eigenvalue variance.percent cumulative.variance.percent
## Dim.1  0.078385677        33.448734                    33.44873
## Dim.2  0.044568340        19.018201                    52.46694
## Dim.3  0.026971508        11.509281                    63.97622
## Dim.4  0.019014946         8.114057                    72.09027
## Dim.5  0.015945733         6.804363                    78.89464
## Dim.6  0.014238942         6.076041                    84.97068
## Dim.7  0.011521787         4.916577                    89.88725
## Dim.8  0.009147320         3.903344                    93.79060
## Dim.9  0.005853046         2.497612                    96.28821
## Dim.10 0.005762790         2.459098                    98.74731
## Dim.11 0.002935629         1.252691                   100.00000

Il est aussi possible d’apprécier les ruptures dans la succession des eigenvalues.

 # Visualisation des eigenvalues
fviz_eig(res.precipit.ca, addlabels = TRUE, ylim = c(0, 40)) # calibrer le ylim avec la lecture du tableau précédent

Il n’y a pas de règles pour choisir le nombre d’axes. Eventuellement, retenir les axes qui ont une eigenvalues d’une valeur supérieure à :

1/(nrow(precipit[, 2:13])-1) ou
1/(ncol(precipit[, 2:13])-1) Sources : http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/113-ca-correspondence-analysis-in-r-essentials/#r-code-to-compute-ca (According to M. T. Bendixen 1995)

Les paramètres les plus utiles :

get_ca_row(res.precipit.ca)

## Correspondence Analysis - Results for rows
##  ===================================================
##   Name       Description                
## 1 "$coord"   "Coordinates for the rows" 
## 2 "$cos2"    "Cos2 for the rows"        
## 3 "$contrib" "contributions of the rows"
## 4 "$inertia" "Inertia of the rows"

5.2. Coordonnées des variables et des individus sur les axes

Interprétation des coordonnées des variables sur les axes factoriels (les colonnes : col).

res.precipit.ca$col$coord ### [toutes les lignes ; colonnes 1 à 12, cf résultats *eigenvalue*]

##               Dim 1        Dim 2        Dim 3       Dim 4         Dim 5
## P_janv -0.403800560 -0.041928299  0.009358527  0.11648500  0.0692840303
## P_fevr -0.071271015 -0.213459205  0.023102932 -0.11710062  0.0277582325
## P_mars -0.163810218 -0.001082994  0.230502787 -0.18681302  0.0690136959
## P_avri -0.183343425  0.122745976  0.106176639  0.16848158  0.0003444635
## P_mai   0.034689204  0.385134518  0.158044012  0.06301770  0.1104083329
## P_juin  0.005007464  0.323680069 -0.372161938 -0.09508621 -0.0054007993
## P_juil  0.689269122  0.192208430  0.085267742  0.26446960 -0.0932188287
## P_aou   0.576659824 -0.288014160  0.066486741  0.01990929  0.1540788800
## P_sept  0.250921349  0.044682807  0.097314291 -0.26885550 -0.2416328772
## P_octo -0.296738918  0.038696168  0.125846124  0.01546063 -0.0431004248
## P_nove -0.089758233 -0.203982909 -0.099171534  0.13934105 -0.1666921217
## P_dece  0.076778840 -0.161040381 -0.184617994 -0.04211552  0.1956272693
##              Dim 6       Dim 7        Dim 8        Dim 9      Dim 10
## P_janv  0.13594673  0.15672570  0.014433476  0.040410609  0.06260620
## P_fevr  0.08548207 -0.08711814 -0.137017764  0.122433592 -0.09247056
## P_mars  0.04902179  0.04296783  0.202814283 -0.084166513 -0.13580632
## P_avri  0.12856902  0.17544944 -0.005907378  0.065225768  0.06664950
## P_mai  -0.19714924  0.03563827 -0.113163234  0.001832712 -0.04378141
## P_juin  0.11413299 -0.01230885 -0.018789194 -0.054857616 -0.02314662
## P_juil  0.14294313 -0.11943949  0.154976571  0.108555942 -0.03974039
## P_aou   0.09612039  0.04934552 -0.105798347 -0.147175530  0.04803331
## P_sept -0.05552090  0.11134824 -0.001309708  0.044990607  0.10090203
## P_octo  0.01484442 -0.22720469 -0.002918824 -0.060334421  0.10113278
## P_nove -0.11086329  0.02901191 -0.002694029 -0.045422906 -0.05990113
## P_dece -0.17527323 -0.03244614  0.122350399  0.072108900  0.06557244
##              Dim 11
## P_janv -0.099149348
## P_fevr  0.006953993
## P_mars  0.011735366
## P_avri  0.227349761
## P_mai  -0.019525795
## P_juin  0.005832896
## P_juil -0.035071269
## P_aou   0.001258808
## P_sept -0.018016478
## P_octo  0.005093524
## P_nove  0.003456651
## P_dece  0.016948388

Valeur des coordonnées des variables quantitatives supplémentaires (les cols.).

res.precipit.ca$quali.sup$coord  ## coord. for the supplementary categories

## NULL

Interprétation du degré d’association entre les colonnes et un axe particulier des variables quantitatives supplémentaires

res.precipit.ca$quali.sup$v.test ## v-test of the supplementary categories, signif. si > 1.96 (on arrondi à 2 !)

## NULL

Interprétation des coordonnées des individus sur les axes factoriels

res.precipit.ca$row$coord ### [ligne 1 à 74 ; colonnes 1 à 12, mais 11 dimensions !]

##           Dim 1        Dim 2        Dim 3        Dim 4        Dim 5
## 1   0.100641865 -0.126061489  0.046967819 -0.131036570 -0.138682833
## 2  -0.348397228 -0.143078975 -0.155069119  0.211866042  0.108879517
## 3  -0.303502424 -0.129296938  0.010109548 -0.108013637  0.045719357
## 4  -0.441853426 -0.047439925  0.213657240  0.060716056  0.251085106
## 5   0.054478616 -0.028972351  0.079485069 -0.180015490  0.034601790
## 6  -0.019640833  0.300960720  0.181028584  0.283944959 -0.028874474
## 7  -0.051216174  0.006686847  0.094811117 -0.200722201 -0.181457412
## 8   0.237117274 -0.146432897 -0.135107194 -0.133756024  0.149599060
## 9  -0.459357020  0.040955675  0.189673932 -0.108451740  0.256352149
## 10  0.283953818 -0.186270616  0.184980896 -0.075007223  0.001018159
## 11 -0.162015066  0.074021450 -0.019219248 -0.059192652 -0.062703128
## 12 -0.206675959 -0.111020077 -0.249845039  0.198442900 -0.072760234
## 13 -0.274644339 -0.216193755 -0.195927651  0.111331469 -0.352282352
## 14  0.230815057  0.035277309 -0.033455963 -0.139266591  0.118134274
## 15  0.277901165  0.271653598 -0.015367883  0.102941279  0.175199903
## 16  0.087818266 -0.291426451  0.082121862  0.079086716 -0.104956320
## 17  0.119425980 -0.290325619 -0.055710183 -0.103772387 -0.020910133
## 18 -0.476909484 -0.165177756  0.104388765  0.124407161 -0.068748916
## 19 -0.235082437 -0.140295651 -0.065318826 -0.035789393  0.163278018
## 20 -0.487257592  0.238395528  0.290625976  0.074214096  0.062102124
## 21 -0.303145407  0.122782133  0.233458463 -0.235425874 -0.214923104
## 22  0.445627804 -0.304936608  0.166126457  0.065361710  0.080183857
## 23 -0.069542316 -0.364170966 -0.084840705 -0.065430705 -0.042035553
## 24  0.286348011  0.461231696 -0.133174567  0.034410519 -0.153470524
## 25  0.017191619 -0.022268191  0.126042635  0.084215654 -0.015560809
## 26  0.137185362  0.134347193  0.177257024 -0.192361361 -0.009772365
## 27 -0.463563786 -0.118070624  0.068721270  0.219405895  0.059198828
## 28 -0.029474490  0.330634403 -0.180206587 -0.049103228 -0.093304770
## 29  0.005253725  0.223381369  0.148526897 -0.092784451 -0.018815958
## 30 -0.321124558  0.089936006 -0.492450779 -0.087351511  0.067287820
## 31  0.042562534 -0.290298424  0.039346458  0.023246516 -0.095124123
## 32  0.297087336 -0.052747807 -0.013995244 -0.028933695 -0.027259218
## 33  0.085575668 -0.219045233 -0.036136398  0.146685834 -0.057703578
## 34  0.111019722 -0.281478017  0.024258229  0.065421790 -0.104991655
## 35 -0.126760786 -0.205926102  0.156960388 -0.156949320  0.028747419
## 36  0.442593832 -0.012260561 -0.012598384  0.025076197  0.035042337
## 37  0.094352057 -0.303881017 -0.093416883 -0.125133634 -0.193072023
## 38 -0.233870833  0.274579315 -0.509902275 -0.108702547  0.045340208
## 39 -0.135098308 -0.011636473 -0.127641177 -0.248790038  0.068083465
## 40  0.131360563  0.451977971  0.080446577  0.108095514 -0.093465312
## 41  0.424176114 -0.176036095  0.178565757  0.114784688 -0.092809048
## 42 -0.079670133  0.073093851 -0.244551973 -0.077641320 -0.007313507
## 43  0.047081250  0.245383841  0.119884647 -0.084848822 -0.055233828
## 44  0.213663048  0.195970809  0.074212036  0.040313069 -0.021639413
## 45 -0.277996388 -0.079853663  0.035815290  0.012989746  0.034935623
## 46  0.376727394 -0.131485929 -0.011452997 -0.082251466  0.125623389
## 47 -0.065488139  0.196622557  0.190318087 -0.193090470 -0.180707520
## 48 -0.054869111  0.329144878 -0.173989557  0.072374576 -0.051325937
## 49  0.399748047 -0.042890884 -0.140871673 -0.059494104  0.127440863
## 50  0.485010165 -0.142183662 -0.023397787  0.007569813  0.179031550
## 51 -0.151861029 -0.172174728 -0.084828376 -0.004136974 -0.016387626
## 52  0.067137143  0.163212735 -0.008048224 -0.160357890  0.164391354
## 53 -0.246053759 -0.230390513 -0.005748284  0.020427526  0.204279491
## 54 -0.355168805  0.007587291  0.153854238  0.015199730  0.126979081
## 55 -0.163288029  0.032300118  0.104824041 -0.326528342 -0.199594447
## 56  0.476068361 -0.016563230 -0.040962835  0.073266263 -0.005306268
## 57 -0.158535220  0.055482978 -0.047325819  0.262850038 -0.118667754
## 58 -0.510125958  0.268482645  0.605486674 -0.071323033  0.128804630
## 59  0.078844315 -0.028354181 -0.127540307 -0.054121145  0.046283560
## 60 -0.104555669 -0.297163001  0.101080964  0.066246713 -0.136066459
## 61 -0.159723965  0.164822119  0.158965649 -0.117268805 -0.105836955
## 62  0.538178882 -0.118383318  0.026952520  0.091499802 -0.029389592
## 63 -0.210822599  0.081971355 -0.156188671 -0.171758396  0.125199926
## 64  0.306340913  0.451152990 -0.004016468 -0.021886874 -0.200859830
## 65 -0.033975605  0.291022607  0.079461625  0.231380998  0.080048182
## 66  0.508768888 -0.256876916  0.060553805 -0.001184838  0.068733213
## 67  0.559818529  0.177154802 -0.007275366  0.253360890  0.277201747
## 68 -0.063552023  0.143686171  0.017987365  0.322820304 -0.130624629
## 69 -0.474482084 -0.095096064 -0.142899861  0.024460344  0.105264233
## 70 -0.170898759  0.425841861  0.052706341  0.072798620  0.033771346
## 71  0.209277200 -0.007191197 -0.041617719 -0.215356062 -0.068626188
## 72  0.266326232  0.093797981 -0.123086002 -0.047343268 -0.005982765
## 73  0.383622185 -0.170235342 -0.004882415 -0.093530219  0.244475508
## 74  0.419968336  0.290713776  0.051179000  0.056119383 -0.036696928
##           Dim 6        Dim 7         Dim 8         Dim 9        Dim 10
## 1   0.101542647  0.065645483 -0.1379556316 -0.0708256780  9.666568e-02
## 2  -0.087591022  0.130379663  0.0709122456 -0.0202935548 -9.302594e-03
## 3   0.009916303 -0.047587227  0.0930159426 -0.0672962045 -1.397838e-01
## 4   0.145547075  0.030399049 -0.0434629511  0.1240994189  1.639433e-01
## 5  -0.034166917  0.091356741 -0.0771306111 -0.0125905228  4.450003e-02
## 6  -0.043994038 -0.065872475 -0.0281185334  0.0444052010 -7.884806e-03
## 7  -0.101992384  0.097346298  0.0186361018  0.0010240528  2.126865e-02
## 8  -0.079970021  0.092491096  0.1009341840  0.0110425369  1.412596e-01
## 9   0.206664770  0.130118219  0.1286977546  0.0130845911 -1.146875e-01
## 10  0.214594541 -0.020071383 -0.1481313451  0.0309031878 -8.970932e-02
## 11 -0.040065818  0.092623369  0.0349207869 -0.0569253826 -1.217338e-01
## 12 -0.125728620  0.005008566  0.0030706666 -0.0742999500  2.526517e-03
## 13 -0.257514834 -0.077474440  0.1016027975 -0.1461605116  8.305622e-02
## 14 -0.101754117 -0.017305672  0.2026498458  0.1112586977 -1.928935e-02
## 15 -0.156062816  0.053185206 -0.0661597643 -0.0514023457 -1.428416e-01
## 16  0.061463360 -0.012319332  0.0163266418  0.0297023250  7.306832e-03
## 17  0.081747454 -0.101574100 -0.1558425024 -0.0650679682  4.875396e-02
## 18 -0.015655527  0.203846403  0.2494936039 -0.1405349057 -3.471928e-02
## 19 -0.194092462 -0.144226456 -0.0047759584  0.0250743378  1.010901e-01
## 20  0.172026872 -0.118609068 -0.0339493825 -0.1107951908  1.620837e-01
## 21  0.099477536  0.094024358  0.0115611836  0.0466857651  1.588367e-01
## 22  0.134126372  0.065212996 -0.0149116697 -0.0807287845 -9.343433e-02
## 23  0.042926020 -0.170957458 -0.0245684909 -0.0128815214 -3.150056e-02
## 24  0.078384537 -0.127429559  0.1097247576 -0.0034137148  5.466933e-02
## 25 -0.259972156 -0.115644868 -0.2213729388  0.0657229058 -9.485601e-02
## 26 -0.099759879 -0.073600119  0.0049731852 -0.0254796768 -2.945664e-02
## 27  0.109485009 -0.072984835  0.0485963884  0.0238949100  1.413920e-01
## 28  0.216045729 -0.071675898  0.1086267617 -0.0039705165 -8.589829e-02
## 29 -0.076133919  0.196816742 -0.1543092937 -0.0530419549 -8.013351e-02
## 30  0.181300840  0.017160406 -0.1390179094  0.0993076286 -4.978752e-02
## 31  0.038919196 -0.052998821 -0.0452536504  0.1029089098 -4.998799e-02
## 32  0.030638585  0.067914445  0.0394535941  0.1252121997  1.194688e-02
## 33 -0.012834668 -0.108376935 -0.0225285061  0.1645592624 -9.889750e-02
## 34  0.062238490 -0.045750517 -0.0001556227  0.0267387603 -6.204418e-02
## 35 -0.046618257 -0.023279529  0.1117059668  0.0019500248 -4.220777e-02
## 36  0.127414378 -0.024821042  0.0703846405 -0.0563387910 -2.332934e-02
## 37 -0.049911933  0.064750749 -0.0505058152 -0.0904829305  2.488804e-02
## 38  0.079505861 -0.072895305 -0.0871430279 -0.0930514230  3.603395e-02
## 39 -0.015009890 -0.063556609  0.1367450062 -0.1087629771 -1.200465e-01
## 40 -0.022120394 -0.312985434 -0.0222425557 -0.0161028088 -5.235500e-02
## 41  0.092060334  0.008421823 -0.1327170482 -0.1447233762  1.079165e-01
## 42  0.074698395  0.010128533 -0.0864943205 -0.0750859446 -9.385162e-02
## 43 -0.067474263  0.130193970 -0.0988316758  0.0558374532 -7.212592e-02
## 44 -0.042073202 -0.023893891  0.0305778128  0.0577155276  2.847857e-02
## 45  0.122918453  0.097444895 -0.0495158720 -0.1409237072  7.820165e-03
## 46 -0.107034394  0.079016501 -0.0587581453 -0.0638643878  4.559164e-02
## 47 -0.131643027  0.016792223 -0.0253621011  0.0905876554 -3.214702e-02
## 48  0.221406233  0.095997212  0.0342588233  0.0191386605  6.681862e-02
## 49 -0.080376678  0.053758313  0.0482009014 -0.0140332873  8.189326e-02
## 50 -0.038064327  0.017230682  0.0002469065 -0.0503739879  1.081622e-01
## 51 -0.117470916 -0.103758315  0.1038228163 -0.0073903749 -2.261064e-03
## 52 -0.179303982  0.031644080 -0.0372986617 -0.0100637225 -1.037040e-01
## 53 -0.163009996 -0.275947045 -0.1333589871  0.0367757663  4.217060e-02
## 54 -0.116025592 -0.113964019 -0.0119193080  0.0235792643 -1.484657e-01
## 55 -0.098428765  0.011594345 -0.0557282886  0.1131926166  7.223021e-02
## 56  0.196302870  0.006862720  0.1067338433 -0.0499061915 -1.808109e-02
## 57 -0.075413526  0.140881750  0.0131795023  0.0559483492 -1.867215e-02
## 58  0.086444145 -0.308616801  0.1390269904 -0.1869803498  3.469632e-03
## 59 -0.041289448  0.005049207  0.2223852352  0.0606878871 -5.432230e-02
## 60  0.096270800 -0.032870965 -0.0692518710  0.0346171884 -6.299886e-02
## 61 -0.147330214  0.156995437 -0.0256578185  0.0173238984  2.565013e-02
## 62  0.181182816 -0.074271405  0.0793772276  0.0601539731  2.901035e-02
## 63  0.061280921 -0.007205265 -0.0482095168  0.0038835594  3.482703e-02
## 64  0.054862086 -0.106800445 -0.0432005983  0.0037949083  1.003473e-01
## 65 -0.018713652  0.215625665 -0.1159654125 -0.0096488081  6.671435e-02
## 66  0.250154557  0.040143229 -0.1077489440 -0.1039389627 -6.205664e-02
## 67 -0.141704599 -0.038807639  0.0499748412  0.0448038543  3.695158e-02
## 68 -0.021434901  0.152128624  0.0119864486  0.0657836666 -2.862476e-02
## 69  0.170371892  0.097983994 -0.0631609070  0.2028762894  2.608728e-02
## 70 -0.031278003 -0.021156317 -0.1060782378 -0.0630677878 -2.206293e-03
## 71 -0.065111317  0.001920356  0.2761923088  0.1820575442  6.552925e-02
## 72  0.116552880 -0.036083000  0.1183041652  0.0284309259 -1.945284e-02
## 73 -0.173777064  0.143104206  0.0285243276 -0.0585323794  1.127842e-01
## 74  0.032299656 -0.072076372  0.1054463668 -0.0001084125 -6.817010e-06
##           Dim 11
## 1  -0.0497103047
## 2   0.0488865958
## 3  -0.0356056112
## 4   0.1103016880
## 5  -0.0219399284
## 6   0.0868120826
## 7  -0.0139326062
## 8   0.0005556039
## 9  -0.0243934092
## 10  0.0274303749
## 11 -0.0582446744
## 12  0.0094688768
## 13  0.0059179057
## 14 -0.0469299226
## 15 -0.0762307707
## 16 -0.0313961911
## 17  0.0168106920
## 18 -0.0194444402
## 19 -0.0849694473
## 20 -0.1011302020
## 21  0.0534046988
## 22  0.0764786819
## 23  0.0352810465
## 24  0.0418577454
## 25 -0.0343430985
## 26  0.0881873426
## 27  0.0307027618
## 28 -0.0917320058
## 29  0.0889174780
## 30 -0.0782560011
## 31  0.0130166118
## 32  0.0050600077
## 33  0.0282211946
## 34  0.0116274594
## 35  0.0083890534
## 36 -0.0284777140
## 37 -0.0502237107
## 38  0.0639714762
## 39  0.0328695158
## 40  0.0265948544
## 41  0.0041681759
## 42  0.0193116256
## 43 -0.0163677831
## 44  0.0243154123
## 45 -0.0606993952
## 46  0.0189392492
## 47 -0.0970610498
## 48  0.1355321968
## 49  0.0062553928
## 50 -0.0242152959
## 51  0.0018667263
## 52 -0.0041188310
## 53 -0.0281510093
## 54  0.1135432565
## 55  0.0813594929
## 56 -0.0164015684
## 57 -0.0040181946
## 58 -0.0648972240
## 59  0.1454788872
## 60 -0.0088324383
## 61 -0.0587443388
## 62 -0.0370156995
## 63  0.0437687425
## 64 -0.0520353050
## 65 -0.0170548063
## 66  0.0204985283
## 67 -0.0210575697
## 68 -0.0189589671
## 69 -0.1433180143
## 70  0.0668149693
## 71  0.0063694311
## 72 -0.0086636037
## 73 -0.0017532762
## 74 -0.0602449294

5.3. Contribution des variables et des individus sur les axes

Interprétation des contributions des variables sur les axes factoriels.

res.precipit.ca$col$contrib ### [toutes les lignes ; colonnes toutes, cf résultats *eigenvalue*] pour rechercher les plus contributives dans un tableur.

##               Dim 1        Dim 2       Dim 3      Dim 4        Dim 5      Dim 6
## P_janv 17.483375175 3.315249e-01  0.02729216  5.9975389 2.530172e+00 10.9090763
## P_fevr  0.637688629 1.006058e+01  0.19473700  7.0964771 4.755089e-01  5.0500053
## P_mars  2.324071100 1.786609e-04 13.37369088 12.4601521 2.027824e+00  1.1457892
## P_avri  1.611030529 1.269983e+00  1.57022731  5.6081494 2.795449e-05  4.3611876
## P_mai   0.140250317 3.040537e+01  8.46063119  1.9080157 6.984111e+00 24.9381596
## P_juin  0.003032439 2.228428e+01 48.68013922  4.5074724 1.734062e-02  8.6723701
## P_juil 29.728028913 4.065777e+00  1.32217664 18.0418717 2.672932e+00  7.0384013
## P_aou  28.352734481 1.243923e+01  1.09536066  0.1393185 9.950251e+00  4.3365620
## P_sept  6.095222874 3.399425e-01  2.66439799 28.8465479 2.778553e+01  1.6428062
## P_octo 11.491335280 3.436906e-01  6.00665456  0.1285931 1.191727e+00  0.1583095
## P_nove  1.451521192 1.318477e+01  5.14968111 14.4203082 2.460918e+01 12.1901575
## P_dece  0.681709072 5.274676e+00 11.45501127  0.8455550 2.175540e+01 19.5571753
##             Dim 7        Dim 8        Dim 9     Dim 10       Dim 11
## P_janv 17.9179697  0.191415090  2.344968334  5.7164973 28.145355659
## P_fevr  6.4821165 20.196652591 25.202214138 14.6013707  0.162101410
## P_mars  1.0878551 30.528633760  8.216764531 21.7275763  0.318490360
## P_avri 10.0367701  0.014331956  2.730651178  2.8958145 66.145098231
## P_mai   1.0070830 12.789946974  0.005242742  3.0387746  1.186501276
## P_juin  0.1246546  0.365860557  4.873994340  0.8813237  0.109865288
## P_juil  6.0729716 12.878444867  9.875302409  1.3441772  2.055071859
## P_aou   1.4124331  8.178170953 24.733268841  2.6757432  0.003607532
## P_sept  8.1657849  0.001423005  2.624295984 13.4065820  0.839053639
## P_octo 45.8324374  0.009527523  6.362188261 18.1555422  0.090405267
## P_nove  1.0316786  0.011205270  4.978280440  8.7932368  0.057480630
## P_dece  0.8282453 14.834387453  8.052828802  6.7633616  0.886968850

Interprétation des contributions des individus sur les axes factoriels.

res.precipit.ca$row$contrib ### [ligne toutes ; colonnes toutes] pour rechercher les plus contributifs dans un tableur.

##           Dim 1       Dim 2        Dim 3        Dim 4        Dim 5      Dim 6
## 1  0.1375528594 0.379566074 8.706519e-02 9.612557e-01 1.283955e+00 0.77084706
## 2  2.2442561090 0.665709764 1.292127e+00 3.421270e+00 1.077476e+00 0.78091040
## 3  1.2640934601 0.403498190 4.076147e-03 6.600148e-01 1.410092e-01 0.00742871
## 4  3.4999474955 0.070958319 2.378328e+00 2.724293e-01 5.555706e+00 2.09060038
## 5  0.0663111332 0.032984662 4.102390e-01 2.984666e+00 1.314994e-01 0.14358362
## 6  0.0057370610 2.369188194 1.416431e+00 4.942875e+00 6.095230e-02 0.15845878
## 7  0.0562460307 0.001686284 5.601800e-01 3.561312e+00 3.470718e+00 1.22792571
## 8  0.7821634281 0.524636710 7.380054e-01 1.025981e+00 1.530457e+00 0.48976136
## 9  4.1840159422 0.058496657 2.073191e+00 9.614070e-01 6.405585e+00 4.66213129
## 10 0.9620576267 0.728122774 1.186563e+00 2.767282e-01 6.080362e-05 3.02483710
## 11 0.3825934209 0.140459824 1.564700e-02 2.105251e-01 2.817068e-01 0.12880529
## 12 1.3739262182 0.697263267 5.835209e+00 5.221511e+00 8.370741e-01 2.79905072
## 13 1.3199047554 1.438460122 1.952200e+00 8.940849e-01 1.067518e+01 6.38799808
## 14 0.7962340550 0.032712491 4.861732e-02 1.194945e+00 1.025313e+00 0.85187416
## 15 1.4880707205 2.500829083 1.322521e-02 8.417121e-01 2.907387e+00 2.58345382
## 16 0.2160391959 4.184379074 5.490500e-01 7.222899e-01 1.516953e+00 0.58257845
## 17 0.2139644445 2.223949676 1.353146e-01 6.659616e-01 3.224407e-02 0.55188862
## 18 4.4050631312 0.929380586 6.133653e-01 1.235699e+00 4.499914e-01 0.02613212
## 19 1.2047270820 0.754652430 2.703065e-01 1.151062e-01 2.856906e+00 4.52089717
## 20 2.8487690360 1.199351467 2.945373e+00 2.724297e-01 2.274810e-01 1.95475163
## 21 1.2464085002 0.359616005 2.148370e+00 3.098906e+00 3.079760e+00 0.73886900
## 22 3.5299222203 2.907032962 1.425705e+00 3.130466e-01 5.618064e-01 1.76038606
## 23 0.0859749118 4.146620771 3.718891e-01 3.137460e-01 1.544185e-01 0.18033236
## 24 1.2829416510 5.854193898 8.064782e-01 7.637349e-02 1.811593e+00 0.52922255
## 25 0.0050425528 0.014879799 7.877408e-01 4.988204e-01 2.030830e-02 6.34789271
## 26 0.2590822228 0.437008130 1.257073e+00 2.099904e+00 6.462695e-03 0.75421104
## 27 4.5576204063 0.520011704 2.910938e-01 4.208791e+00 3.653740e-01 1.39954689
## 28 0.0145683541 3.224216638 1.582671e+00 1.666785e-01 7.176585e-01 4.30891811
## 29 0.0005371504 1.707911886 1.247679e+00 6.906426e-01 3.386930e-02 0.62097865
## 30 2.0498787355 0.282786438 1.401000e+01 6.252642e-01 4.424318e-01 3.59699431
## 31 0.0424858561 3.476074180 1.055194e-01 5.224525e-02 1.043189e+00 0.19555824
## 32 1.4690079858 0.081446973 9.474326e-03 5.743879e-02 6.079598e-02 0.08601066
## 33 0.1378415018 1.588390430 7.143328e-02 1.669542e+00 3.080897e-01 0.01706898
## 34 0.2762880431 3.123640435 3.833641e-02 3.955016e-01 1.214685e+00 0.47801211
## 35 0.2141811269 0.994132797 9.543836e-01 1.353542e+00 5.415035e-02 0.15947125
## 36 2.4712341747 0.003335294 5.819214e-03 3.270154e-02 7.615204e-02 1.12745456
## 37 0.1491517097 2.721089856 4.249205e-01 1.081472e+00 3.070128e+00 0.22976996
## 38 1.3951666178 3.382360043 1.927433e+01 1.242496e+00 2.577705e-01 0.88762848
## 39 0.2364908156 0.003085797 6.135183e-01 3.306146e+00 2.952501e-01 0.01607047
## 40 0.2771584409 5.770891319 3.020958e-01 7.736688e-01 6.897493e-01 0.04326561
## 41 2.6922014249 0.815509136 1.386574e+00 8.126895e-01 6.335604e-01 0.69810253
## 42 0.1202284864 0.177986979 3.292230e+00 4.706995e-01 4.980351e-03 0.58183230
## 43 0.0377185365 1.802025963 7.107510e-01 5.050009e-01 2.551887e-01 0.42647557
## 44 0.8083223872 1.195965877 2.834040e-01 1.186203e-01 4.075763e-02 0.17254242
## 45 1.0020346311 0.145413376 4.833624e-02 9.018771e-03 7.779177e-02 1.07844395
## 46 2.1819246686 0.467470448 5.860776e-03 4.287600e-01 1.192665e+00 0.96959651
## 47 0.0543358562 0.861466003 1.333684e+00 1.947263e+00 2.033789e+00 1.20869276
## 48 0.0402470631 2.547198528 1.176132e+00 2.886636e-01 1.731188e-01 3.60758868
## 49 2.7564785131 0.055811302 9.948572e-01 2.516931e-01 1.377183e+00 0.61348083
## 50 4.2791206415 0.646788796 2.894236e-02 4.296995e-03 2.866185e+00 0.14509357
## 51 0.3547999081 0.802121004 3.217397e-01 1.085420e-03 2.031024e-02 1.16872013
## 52 0.0742698918 0.771978872 3.101835e-03 1.746664e+00 2.188957e+00 2.91625795
## 53 1.1537121360 1.779003838 1.829976e-03 3.278013e-02 3.909122e+00 2.78756440
## 54 2.0594278224 0.001652954 1.123123e+00 1.554856e-02 1.293998e+00 1.20988341
## 55 0.4980591069 0.034276042 5.965206e-01 8.210235e+00 3.658149e+00 0.99626585
## 56 3.3946352542 0.007226945 7.304088e-02 3.314394e-01 2.073123e-03 3.17736247
## 57 0.5738901282 0.123625203 1.486295e-01 6.503317e+00 1.580647e+00 0.71488258
## 58 3.3893114978 1.651198649 1.387705e+01 2.731227e-01 1.062214e+00 0.53578036
## 59 0.0895053462 0.020358823 6.806669e-01 1.738536e-01 1.516191e-01 0.13512800
## 60 0.2730307932 3.878967898 7.416290e-01 4.518422e-01 2.273060e+00 1.27427926
## 61 0.4030344206 0.754819673 1.160219e+00 8.955887e-01 8.698991e-01 1.88775054
## 62 4.0612102304 0.345615675 2.960277e-02 4.839317e-01 5.953626e-02 2.53393323
## 63 0.7879350679 0.209503163 1.256859e+00 2.155925e+00 1.366018e+00 0.36649298
## 64 1.6922937699 6.455407775 8.454460e-04 3.561023e-02 3.576384e+00 0.29879227
## 65 0.0243350262 3.140227598 3.868511e-01 4.652586e+00 6.640375e-01 0.04064185
## 66 3.6199501174 1.623012639 1.490307e-01 8.093216e-05 3.247783e-01 4.81767298
## 67 5.3354889944 0.939714225 2.618911e-03 4.505059e+00 6.430783e+00 1.88194345
## 68 0.0803908705 0.722750108 1.871607e-02 8.550889e+00 1.669515e+00 0.05034426
## 69 3.5858787094 0.253332723 9.452595e-01 3.928463e-02 8.675807e-01 2.54513508
## 70 0.3710428035 4.051848010 1.025660e-01 2.775454e-01 7.122545e-02 0.06842002
## 71 0.5574460324 0.001157635 6.406886e-02 2.433407e+00 2.946666e-01 0.29705094
## 72 1.0571685141 0.230628811 6.562437e-01 1.377128e-01 2.622481e-03 1.11460589
## 73 2.0788073507 0.719973513 9.786056e-04 5.093922e-01 4.150207e+00 2.34828451
## 74 3.3591078163 2.830950810 1.449793e-01 2.472625e-01 1.260789e-01 0.10938194
##           Dim 7        Dim 8        Dim 9       Dim 10       Dim 11
## 1  3.981428e-01 2.214797e+00 9.123227e-01 1.726079e+00 0.8960674439
## 2  2.138256e+00 7.967249e-01 1.019751e-01 2.176382e-02 1.1798809795
## 3  2.114232e-01 1.017449e+00 8.323208e-01 3.647307e+00 0.4645444973
## 4  1.127047e-01 2.901926e-01 3.697424e+00 6.553850e+00 5.8237800614
## 5  1.268622e+00 1.139018e+00 4.743256e-02 6.018093e-01 0.2871708190
## 6  4.390303e-01 1.007623e-01 3.927282e-01 1.257638e-02 2.9927166301
## 7  1.382399e+00 6.381615e-02 3.011460e-04 1.319354e-01 0.1111419270
## 8  8.096324e-01 1.214480e+00 2.271766e-02 3.775815e+00 0.0001146667
## 9  2.283945e+00 2.814346e+00 4.546400e-02 3.547550e+00 0.3150454346
## 10 3.270221e-02 2.243585e+00 1.526044e-01 1.306125e+00 0.2397202504
## 11 8.507163e-01 1.523132e-01 6.325478e-01 2.938010e+00 1.3203063429
## 12 5.489429e-03 2.598913e-03 2.378019e+00 2.792748e-03 0.0770044802
## 13 7.145540e-01 1.547945e+00 5.006292e+00 1.641911e+00 0.0163633772
## 14 3.045133e-02 5.259542e+00 2.477623e+00 7.564003e-02 0.8789167155
## 15 3.708014e-01 7.227259e-01 6.818101e-01 5.347569e+00 2.9897786155
## 16 2.892371e-02 6.398813e-02 3.309775e-01 2.034347e-02 0.7373137595
## 17 1.052996e+00 3.122185e+00 8.506153e-01 4.850290e-01 0.1132011239
## 18 5.475241e+00 1.033099e+01 5.122752e+00 3.175598e-01 0.1955269755
## 19 3.084999e+00 4.261007e-03 1.835532e-01 3.030186e+00 4.2025168646
## 20 1.148399e+00 1.185077e-01 1.972589e+00 4.287684e+00 3.2767049242
## 21 8.157481e-01 1.553481e-02 3.958969e-01 4.654405e+00 1.0328872801
## 22 5.142873e-01 3.387006e-02 1.551430e+00 2.110753e+00 2.7761117143
## 23 3.534813e+00 9.195456e-02 3.950595e-02 2.399462e-01 0.5908699767
## 24 1.728526e+00 1.614250e+00 2.441899e-03 6.360774e-01 0.7319910999
## 25 1.552339e+00 7.164879e+00 9.869728e-01 2.088096e+00 0.5373180651
## 26 5.073364e-01 2.917657e-03 1.196919e-01 1.624772e-01 2.8587103514
## 27 7.686016e-01 4.292102e-01 1.621753e-01 5.767304e+00 0.5338381516
## 28 5.861126e-01 1.695643e+00 3.540517e-03 1.683026e+00 3.7678641515
## 29 5.128641e+00 3.970894e+00 7.332551e-01 1.699783e+00 4.1083852260
## 30 3.982476e-02 3.292043e+00 2.625434e+00 6.702334e-01 3.2505137628
## 31 4.481658e-01 4.115660e-01 3.326213e+00 7.971218e-01 0.1061013494
## 32 5.222724e-01 2.220097e-01 3.494652e+00 3.231236e-02 0.0113787306
## 33 1.504077e+00 8.186289e-02 6.826197e+00 2.504113e+00 0.4002817201
## 34 3.192058e-01 4.652114e-06 2.146343e-01 1.173729e+00 0.0809220835
## 35 4.914469e-02 1.425302e+00 6.788071e-04 3.229982e-01 0.0250479881
## 36 5.287618e-02 5.355522e-01 5.362570e-01 9.339251e-02 0.2731800672
## 37 4.778944e-01 3.662276e-01 1.837019e+00 1.411597e-01 1.1284404811
## 38 9.221253e-01 1.659901e+00 2.957840e+00 4.505072e-01 2.7872907265
## 39 3.560843e-01 2.076253e+00 2.052728e+00 2.539906e+00 0.3737977177
## 40 1.070442e+01 6.809423e-02 5.577712e-02 5.988503e-01 0.3033394652
## 41 7.220117e-03 2.258455e+00 4.197080e+00 2.370255e+00 0.0069413313
## 42 1.321984e-02 1.214323e+00 1.430172e+00 2.269362e+00 0.1886207805
## 43 1.962264e+00 1.424276e+00 7.105012e-01 1.204053e+00 0.1217234271
## 44 6.877276e-02 1.418670e-01 7.898886e-01 1.953287e-01 0.2795275477
## 45 8.376055e-01 2.724182e-01 3.448477e+00 1.078550e-02 1.2755830053
## 46 6.530371e-01 4.548460e-01 8.397647e-01 4.346701e-01 0.1472469947
## 47 2.430494e-02 6.983522e-02 1.392368e+00 1.780929e-01 3.1870344359
## 48 8.381321e-01 1.344516e-01 6.557770e-02 8.118528e-01 6.5569046751
## 49 3.391486e-01 3.434275e-01 4.549414e-02 1.573556e+00 0.0180229822
## 50 3.674300e-02 9.502997e-06 6.181875e-01 2.894727e+00 0.2848183620
## 51 1.126817e+00 1.421083e+00 1.125326e-02 1.069844e-03 0.0014314879
## 52 1.122507e-01 1.964339e-01 2.234905e-02 2.410362e+00 0.0074639821
## 53 9.872016e+00 2.904189e+00 3.451562e-01 4.609576e-01 0.4032375489
## 54 1.442545e+00 1.987568e-02 1.215604e-01 4.894781e+00 5.6199857164
## 55 1.708368e-02 4.971260e-01 3.205259e+00 1.325604e+00 3.3015982802
## 56 4.799145e-03 1.462183e+00 4.995950e-01 6.660511e-02 0.1075872501
## 57 3.083214e+00 3.398741e-02 9.572085e-01 1.082853e-01 0.0098440708
## 58 8.439421e+00 2.157236e+00 6.098223e+00 2.132688e-03 1.4646857311
## 59 2.497304e-03 6.101870e+00 7.101776e-01 5.779209e-01 8.1366141145
## 60 1.835939e-01 1.026413e+00 4.008250e-01 1.348297e+00 0.0520251410
## 61 2.649067e+00 8.912187e-02 6.349623e-02 1.413791e-01 1.4556923082
## 62 5.262139e-01 7.570715e-01 6.794939e-01 1.605137e-01 0.5129909019
## 63 6.261421e-03 3.530730e-01 3.580723e-03 2.924778e-01 0.9068173410
## 64 1.399358e+00 2.883953e-01 3.477948e-03 2.469909e+00 1.3037596410
## 65 6.668301e+00 2.429390e+00 2.628449e-02 1.276262e+00 0.1637293652
## 66 1.533215e-01 1.391331e+00 2.023359e+00 7.325577e-01 0.1569070408
## 67 1.744340e-01 3.643556e-01 4.576834e-01 3.161911e-01 0.2015727208
## 68 3.133912e+00 2.450597e-02 1.153556e+00 2.218378e-01 0.1910349772
## 69 1.040359e+00 5.444971e-01 8.779571e+00 1.474408e-01 8.7356071849
## 70 3.868506e-02 1.225016e+00 6.767311e-01 8.411556e-04 1.5143606388
## 71 3.193298e-04 8.320032e+00 5.649774e+00 7.434183e-01 0.0137878281
## 72 1.320196e-01 1.787554e+00 1.613441e-01 7.671607e-02 0.0298709519
## 73 1.968015e+00 9.848736e-02 6.481177e-01 2.444033e+00 0.0011594261
## 74 6.731217e-01 1.814667e+00 2.997813e-06 1.203878e-08 1.8457268113

5.4. Qualité de la représentation (COS2) des variables et des individus sur les axes

Interprétation des COS2 des variables sur les axes factoriels.

res.precipit.ca$col$cos2 ### [toutes les lignes ; colonnes toutes, cf résultats *eigenvalue*] pour rechercher les mieux représentées dans un tableur.

##               Dim 1        Dim 2        Dim 3       Dim 4        Dim 5
## P_janv 0.6740439769 7.267230e-03 0.0003620507 0.056091158 1.984361e-02
## P_fevr 0.0413237649 3.706839e-01 0.0043421837 0.111555862 6.268413e-03
## P_mars 0.1407293374 6.151124e-06 0.2786474201 0.183027757 2.497890e-02
## P_avri 0.1714403789 7.684170e-02 0.0574963646 0.144772911 6.051580e-07
## P_mai  0.0048932938 6.031669e-01 0.1015707640 0.016148708 4.956970e-02
## P_juin 0.0000930488 3.887828e-01 0.5139715231 0.033551365 1.082409e-04
## P_juil 0.7077714656 5.503770e-02 0.0108314083 0.104199805 1.294561e-02
## P_aou  0.6774256973 1.689857e-01 0.0090051794 0.000807484 4.836247e-02
## P_sept 0.2700929674 8.564834e-03 0.0406248057 0.310081543 2.504668e-01
## P_octo 0.5083062740 8.643953e-03 0.0914231422 0.001379847 1.072357e-02
## P_nove 0.0641926237 3.315310e-01 0.0783629173 0.154701553 2.213944e-01
## P_dece 0.0362799205 1.596073e-01 0.2097641600 0.010916100 2.355277e-01
##              Dim 6        Dim 7        Dim 8        Dim 9      Dim 10
## P_janv 0.076399752 0.1015394631 8.611846e-04 6.750644e-03 0.016202763
## P_fevr 0.059446194 0.0617434873 1.527312e-01 1.219481e-01 0.069563424
## P_mars 0.012603205 0.0096825425 2.157246e-01 3.715193e-02 0.096725867
## P_avri 0.084305348 0.1569952213 1.779803e-04 2.169806e-02 0.022655633
## P_mai  0.158053041 0.0051647083 5.207429e-02 1.365844e-05 0.007794568
## P_juin 0.048338987 0.0005622251 1.310061e-03 1.116732e-02 0.001988155
## P_juil 0.030439812 0.0212525622 3.578059e-02 1.755588e-02 0.002352771
## P_aou  0.018821459 0.0049604114 2.280237e-02 4.412589e-02 0.004700102
## P_sept 0.013223641 0.0531869069 7.358467e-06 8.683239e-03 0.043675498
## P_octo 0.001272047 0.2979964148 4.918041e-05 2.101390e-02 0.059041898
## P_nove 0.097929171 0.0067063973 5.782840e-05 1.643942e-02 0.028589504
## P_dece 0.189066417 0.0064790207 9.212850e-02 3.200081e-02 0.026462202
##              Dim 11
## P_janv 4.063817e-02
## P_fevr 3.934073e-04
## P_mars 7.222640e-04
## P_avri 2.636158e-01
## P_mai  1.550351e-03
## P_juin 1.262536e-04
## P_juil 1.832392e-03
## P_aou  3.228058e-06
## P_sept 1.392444e-03
## P_octo 1.497660e-04
## P_nove 9.520236e-05
## P_dece 1.767828e-03

Interprétation des qualités de représentation des individus sur les axes factoriels.

res.precipit.ca$row$cos2 ### [ligne toutes ; colonnes toutes] pour rechercher les mieux représentées dans un tableur.

##           Dim 1        Dim 2        Dim 3        Dim 4        Dim 5
## 1  0.0879896174 0.1380508050 1.916350e-02 1.491623e-01 1.670781e-01
## 2  0.4755763511 0.0802088909 9.421532e-02 1.758707e-01 4.644760e-02
## 3  0.5791796255 0.1051151785 6.426174e-04 7.335777e-02 1.314284e-02
## 4  0.5027847746 0.0057958036 1.175604e-01 9.493640e-03 1.623557e-01
## 5  0.0480162349 0.0135801147 1.022132e-01 5.242709e-01 1.937016e-02
## 6  0.0017390108 0.4083213934 1.477328e-01 3.634551e-01 3.758466e-03
## 7  0.0248054622 0.0004228398 8.500639e-02 3.809990e-01 3.113741e-01
## 8  0.3099384044 0.1182024050 1.006250e-01 9.862243e-02 1.233692e-01
## 9  0.5069108090 0.0040295729 8.642634e-02 2.825556e-02 1.578719e-01
## 10 0.3455709704 0.1487066980 1.466546e-01 2.411282e-02 4.442970e-06
## 11 0.3626098187 0.0756909456 5.102718e-03 4.840212e-02 5.431342e-02
## 12 0.2326581806 0.0671338344 3.400007e-01 2.144912e-01 2.883544e-02
## 13 0.1848807853 0.1145609905 9.408967e-02 3.037990e-02 3.041811e-01
## 14 0.3422481980 0.0079947297 7.190514e-03 1.245968e-01 8.965298e-02
## 15 0.3052878610 0.2917156477 9.335915e-04 4.188976e-02 1.213379e-01
## 16 0.0628153142 0.6917573072 5.493048e-02 5.094516e-02 8.972491e-02
## 17 0.0885646315 0.5233996344 1.927223e-02 6.686923e-02 2.715040e-03
## 18 0.5531112271 0.0663504210 2.650013e-02 3.763841e-02 1.149403e-02
## 19 0.3008083842 0.1071366317 2.322343e-02 6.972014e-03 1.451126e-01
## 20 0.4929118455 0.1179908243 1.753561e-01 1.143470e-02 8.006910e-03
## 21 0.2943312904 0.0482841726 1.745636e-01 1.775182e-01 1.479451e-01
## 22 0.5317824659 0.2490052955 7.390385e-02 1.144027e-02 1.721723e-02
## 23 0.0261726123 0.7177271934 3.895447e-02 2.316925e-02 9.562739e-03
## 24 0.2178538501 0.5652169629 4.712154e-02 3.146005e-03 6.257874e-02
## 25 0.0017542825 0.0029433092 9.429767e-02 4.209705e-02 1.437244e-03
## 26 0.1446842954 0.1387596020 2.415532e-01 2.844733e-01 7.341845e-04
## 27 0.6584109579 0.0427131664 1.446973e-02 1.474941e-01 1.073753e-02
## 28 0.0037253052 0.4687759608 1.392549e-01 1.033926e-02 3.733163e-02
## 29 0.0001658395 0.2998107525 1.325451e-01 5.172538e-02 2.127189e-03
## 30 0.2360663868 0.0185163043 5.551531e-01 1.746739e-02 1.036478e-02
## 31 0.0155031308 0.7211968525 1.324878e-02 4.624664e-03 7.743651e-02
## 32 0.7623588345 0.0240325570 1.691812e-03 7.231010e-03 6.418269e-03
## 33 0.0556765667 0.3647870917 9.927996e-03 1.635868e-01 2.531497e-02
## 34 0.1043520994 0.6707951070 4.982177e-03 3.623646e-02 9.332768e-02
## 35 0.1279129304 0.3375727647 1.961213e-01 1.960936e-01 6.578734e-03
## 36 0.8729900556 0.0006699143 7.073400e-04 2.802347e-03 5.472487e-03
## 37 0.0485214578 0.5033131041 4.756438e-02 8.534522e-02 2.031748e-01
## 38 0.1250928209 0.1724312175 5.946401e-01 2.702463e-02 4.701617e-03
## 39 0.1204755019 0.0008938026 1.075426e-01 4.085685e-01 3.059724e-02
## 40 0.0491495824 0.5818678576 1.843338e-02 3.328167e-02 2.488231e-02
## 41 0.5564296563 0.0958343716 9.860847e-02 4.074607e-02 2.663781e-02
## 42 0.0601300467 0.0506130072 5.665559e-01 5.710660e-02 5.067011e-04
## 43 0.0174661138 0.4744519592 1.132472e-01 5.672728e-02 2.403868e-02
## 44 0.4580455758 0.3853298238 5.525843e-02 1.630578e-02 4.698301e-03
## 45 0.5641354702 0.0465473310 9.363583e-03 1.231704e-03 8.909269e-03
## 46 0.6772510364 0.0824999787 6.259412e-04 3.228365e-02 7.530716e-02
## 47 0.0230544408 0.2078241294 1.947105e-01 2.004246e-01 1.755423e-01
## 48 0.0129711265 0.4667625951 1.304272e-01 2.256804e-02 1.134999e-02
## 49 0.7267534279 0.0083665109 9.025302e-02 1.609764e-02 7.386383e-02
## 50 0.7720796455 0.0663528849 1.796842e-03 1.880749e-04 1.052009e-01
## 51 0.2412444728 0.3101012462 7.527435e-02 1.790318e-04 2.809291e-03
## 52 0.0348424782 0.2059166244 5.007067e-04 1.987760e-01 2.089014e-01
## 53 0.2160458683 0.1894153361 1.179132e-04 1.489078e-03 1.489140e-01
## 54 0.5525152540 0.0002521437 1.036797e-01 1.011920e-03 7.062184e-02
## 55 0.1197096119 0.0046841259 4.933352e-02 4.786985e-01 1.788617e-01
## 56 0.7895524367 0.0009557238 5.845509e-03 1.870038e-02 9.808910e-05
## 57 0.1759707115 0.0215530334 1.568141e-02 4.837322e-01 9.859487e-02
## 58 0.2950992144 0.0817420721 4.157405e-01 5.768632e-03 1.881378e-02
## 59 0.0579124843 0.0074897209 1.515397e-01 2.728760e-02 1.995653e-02
## 60 0.0715683991 0.5781168228 6.689057e-02 2.873127e-02 1.212072e-01
## 61 0.1653143649 0.1760359691 1.637484e-01 8.911184e-02 7.258470e-02
## 62 0.7955124146 0.0384923717 1.995227e-03 2.299503e-02 2.372361e-03
## 63 0.3418634340 0.0516823861 1.876365e-01 2.269103e-01 1.205664e-01
## 64 0.2555004935 0.5541526551 4.392081e-05 1.304215e-03 1.098419e-01
## 65 0.0053137950 0.3898736196 2.906600e-02 2.464483e-01 2.949669e-02
## 66 0.6103455692 0.1555911396 8.646047e-03 3.310189e-06 1.113956e-02
## 67 0.6099990442 0.0610858297 1.030254e-04 1.249435e-01 1.495638e-01
## 68 0.0230086701 0.1176149969 1.843181e-03 5.936828e-01 9.720372e-02
## 69 0.6063837853 0.0243575176 5.500112e-02 1.611510e-03 2.984486e-02
## 70 0.1212431960 0.7527941908 1.153202e-02 2.200016e-02 4.734524e-03
## 71 0.2040166009 0.0002408929 8.068229e-03 2.160408e-01 2.193822e-02
## 72 0.5571882136 0.0691132014 1.190122e-01 1.760721e-02 2.811758e-04
## 73 0.4711929449 0.0927877844 7.632394e-05 2.800885e-02 1.913648e-01
## 74 0.6103098935 0.2924479218 9.063604e-03 1.089791e-02 4.659902e-03
##           Dim 6        Dim 7        Dim 8        Dim 9       Dim 10
## 1  0.0895717461 0.0374355117 1.653305e-01 4.357682e-02 8.117432e-02
## 2  0.0300600747 0.0666025067 1.970214e-02 1.613567e-03 3.390619e-04
## 3  0.0006182847 0.0142386805 5.440061e-02 2.847542e-02 1.228577e-01
## 4  0.0545547572 0.0023798285 4.864790e-03 3.966114e-02 6.921707e-02
## 5  0.0188863296 0.1350259286 9.624751e-02 2.564623e-03 3.203735e-02
## 6  0.0087250947 0.0195609735 3.564247e-03 8.888944e-03 2.802622e-04
## 7  0.0983713317 0.0896131918 3.284303e-03 9.916942e-06 4.277726e-03
## 8  0.0352535960 0.0471572915 5.615980e-02 6.721818e-04 1.099980e-01
## 9  0.1026038682 0.0406730794 3.978989e-02 4.112928e-04 3.159824e-02
## 10 0.1973691042 0.0017266186 9.404501e-02 4.093063e-03 3.449189e-02
## 11 0.0221756720 0.1185140670 1.684600e-02 4.476521e-02 2.047158e-01
## 12 0.0861007032 0.0001366360 5.135748e-05 3.006876e-02 3.476824e-05
## 13 0.1625380232 0.0147118526 2.530241e-02 5.236132e-02 1.690810e-02
## 14 0.0665145839 0.0019239326 2.638186e-01 7.952082e-02 2.390277e-03
## 15 0.0962781375 0.0111817685 1.730281e-02 1.044467e-02 8.065633e-02
## 16 0.0307700650 0.0012361471 2.171149e-03 7.185826e-03 4.348646e-04
## 17 0.0414964707 0.0640661543 1.508115e-01 2.629040e-02 1.475987e-02
## 18 0.0005960407 0.1010524065 1.513768e-01 4.802960e-02 2.931447e-03
## 19 0.2050533672 0.1132242446 1.241568e-04 3.422225e-03 5.562456e-02
## 20 0.0614390670 0.0292070579 2.392852e-03 2.548554e-02 5.454198e-02
## 21 0.0316945427 0.0283149109 4.280939e-04 6.980771e-03 8.080463e-02
## 22 0.0481745660 0.0113882701 5.954455e-04 1.745204e-02 2.337773e-02
## 23 0.0099721777 0.1581702744 3.266673e-03 8.980140e-04 5.370137e-03
## 24 0.0163244173 0.0431436870 3.198793e-02 3.096217e-05 7.940803e-03
## 25 0.4011618941 0.0793813956 2.908808e-01 2.563891e-02 5.340669e-02
## 26 0.0765099072 0.0416450010 1.901407e-04 4.991070e-03 6.670712e-03
## 27 0.0367271615 0.0163208701 7.235791e-03 1.749399e-03 6.125307e-02
## 28 0.2001523170 0.0220300530 5.059911e-02 6.760258e-05 3.164013e-02
## 29 0.0348264874 0.2327434049 1.430663e-01 1.690411e-02 3.858172e-02
## 30 0.0752465766 0.0006741278 4.424138e-02 2.257628e-02 5.674508e-03
## 31 0.0129626017 0.0240379195 1.752555e-02 9.062967e-02 2.138434e-02
## 32 0.0081082769 0.0398396464 1.344511e-02 1.354205e-01 1.232821e-03
## 33 0.0012523945 0.0892987906 3.858661e-03 2.058811e-01 7.436052e-02
## 34 0.0327958594 0.0177211923 2.050438e-07 6.053178e-03 3.259140e-02
## 35 0.0173004209 0.0043141277 9.933387e-02 3.027087e-05 1.418174e-02
## 36 0.0723494872 0.0027456085 2.207773e-02 1.414535e-02 2.425513e-03
## 37 0.0135781271 0.0228518147 1.390317e-02 4.462358e-02 3.376078e-03
## 38 0.0144570123 0.0121528846 1.736783e-02 1.980279e-02 2.969642e-03
## 39 0.0014871472 0.0266636968 1.234303e-01 7.808383e-02 9.512577e-02
## 40 0.0013937201 0.2790217669 1.409156e-03 7.385724e-04 7.807394e-03
## 41 0.0262097538 0.0002193462 5.447174e-02 6.477318e-02 3.601587e-02
## 42 0.0528594941 0.0009718374 7.087216e-02 5.340941e-02 8.344186e-02
## 43 0.0358737371 0.1335617396 7.696489e-02 2.456697e-02 4.099048e-02
## 44 0.0177607374 0.0057282719 9.381293e-03 3.342221e-02 8.137411e-03
## 45 0.1102907951 0.0693143703 1.789757e-02 1.449684e-01 4.464131e-04
## 46 0.0546691075 0.0297941406 1.647523e-02 1.946313e-02 9.918952e-03
## 47 0.0931590416 0.0015158132 3.457799e-03 4.411307e-02 5.555342e-03
## 48 0.2112037038 0.0397044409 5.056695e-03 1.578138e-03 1.923609e-02
## 49 0.0293815356 0.0131433370 1.056634e-02 8.956395e-04 3.050076e-02
## 50 0.0047555061 0.0009744630 2.000900e-07 8.328621e-03 3.839824e-02
## 51 0.1443528662 0.1126187030 1.127588e-01 5.713440e-04 5.347988e-05
## 52 0.2485210582 0.0077404868 1.075399e-02 7.828898e-04 8.313324e-02
## 53 0.0948231607 0.2717299145 6.346445e-02 4.826246e-03 6.346081e-03
## 54 0.0589633610 0.0568866235 6.222669e-04 2.435203e-03 9.654439e-02
## 55 0.0434975100 0.0006035493 1.394350e-02 5.752499e-02 2.342384e-02
## 56 0.1342442324 0.0001640721 3.968685e-02 8.676632e-03 1.138916e-03
## 57 0.0398187262 0.1389627339 1.216149e-03 2.191611e-02 2.441054e-03
## 58 0.0084739203 0.1080071075 2.191853e-02 3.964653e-02 1.365149e-05
## 59 0.0158821605 0.0002375077 4.607266e-01 3.431116e-02 2.749082e-02
## 60 0.0606757705 0.0070737718 3.139707e-02 7.845303e-03 2.598313e-02
## 61 0.1406546422 0.1597145522 4.265892e-03 1.944741e-03 4.263337e-03
## 62 0.0901628582 0.0151508479 1.730555e-02 9.938533e-03 2.311531e-03
## 63 0.0288847684 0.0003993174 1.787656e-02 1.160054e-04 9.329347e-03
## 64 0.0081945737 0.0310547378 5.081141e-03 3.920887e-05 2.741531e-02
## 65 0.0016120833 0.2140283479 6.190523e-02 4.285660e-04 2.048844e-02
## 66 0.1475541880 0.0037997875 2.737542e-02 2.547367e-02 9.080529e-03
## 67 0.0390843154 0.0029313594 4.861133e-03 3.907198e-03 2.657668e-03
## 68 0.0026174340 0.1318422594 8.184908e-04 2.465295e-02 4.667846e-03
## 69 0.0781814704 0.0258593865 1.074496e-02 1.108589e-01 1.833013e-03
## 70 0.0040612299 0.0018580599 4.671240e-02 1.651181e-02 2.020718e-05
## 71 0.0197485234 0.0000171785 3.553406e-01 1.543971e-01 2.000286e-02
## 72 0.1067136684 0.0102277311 1.099447e-01 6.349741e-03 2.972625e-03
## 73 0.0966888204 0.0655686358 2.605087e-03 1.096942e-02 4.072749e-02
## 74 0.0036100491 0.0179764178 3.847517e-02 4.067020e-08 1.608071e-10
##          Dim 11
## 1  2.146678e-02
## 2  9.363764e-03
## 3  7.971239e-03
## 4  3.133213e-02
## 5  7.787649e-03
## 6  3.397370e-02
## 7  1.835683e-03
## 8  1.701687e-06
## 9  1.429473e-03
## 10 3.224819e-03
## 11 4.686420e-02
## 12 4.883547e-04
## 13 8.583938e-05
## 14 1.414857e-02
## 15 2.297150e-02
## 16 8.028784e-03
## 17 1.754825e-03
## 18 9.194570e-04
## 19 3.929843e-02
## 20 2.123312e-02
## 21 9.134681e-03
## 22 1.566283e-02
## 23 6.736459e-03
## 24 4.655095e-03
## 25 7.000756e-03
## 26 5.978860e-02
## 27 2.888238e-03
## 28 3.608370e-02
## 29 4.750372e-02
## 30 1.401917e-02
## 31 1.449975e-03
## 32 2.211534e-04
## 33 6.055118e-03
## 34 1.144644e-03
## 35 5.602354e-04
## 36 3.614172e-03
## 37 1.374829e-02
## 38 9.359508e-03
## 39 7.131576e-03
## 40 2.014583e-03
## 41 5.372914e-05
## 42 3.532955e-03
## 43 2.110960e-03
## 44 5.932164e-03
## 45 2.689514e-02
## 46 1.711673e-03
## 47 5.064298e-02
## 48 7.914196e-02
## 49 1.779605e-04
## 50 1.924598e-03
## 51 3.645239e-05
## 52 1.311388e-04
## 53 2.827964e-03
## 54 5.646734e-02
## 55 2.971918e-02
## 56 9.371586e-04
## 57 1.130449e-04
## 58 4.776012e-03
## 59 1.971657e-01
## 60 5.107253e-04
## 61 2.236158e-02
## 62 3.763272e-03
## 63 1.473488e-02
## 64 7.371875e-03
## 65 1.338949e-03
## 66 9.907865e-04
## 67 8.630801e-04
## 68 2.047680e-03
## 69 5.532348e-02
## 70 1.853221e-02
## 71 1.889831e-04
## 72 5.896186e-04
## 73 9.842197e-06
## 74 1.255909e-02

6. Aide à l’interprétation

6.1. Graphiques de la contribution

des variables

          fviz_ca_col(res.precipit.ca,
                  col.col = "contrib",
                  axes = 1:2,
                  gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))

des individus

          fviz_ca_row(res.precipit.ca,
                      col.row = "contrib",
                      axes = 1:2,
                      gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))

6.2. Graphiques de la qualité

des variables

          fviz_ca_col(res.precipit.ca,
                  col.col = "cos2",
                  axes = 1:2,
                  gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))

des filtrages sont possibles

– en fonction du Cos2

          ## Lignes avec un cos2 > 0.8
          fviz_ca_row(res.precipit.ca,
                      select.row = list(cos2 = 0.8),
                      col.row = "cos2",
                      axes = 1:2,
                      gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"))

– en fonction des contributions

          ## Top 5 des contributions lignes et colonnes
          fviz_ca_biplot(res.precipit.ca,
                      select.row = list(contrib = 5), 
                      select.col = list(contrib = 5), # si on veut toutes les variables mettre un "#" devant
                      #arrow = c (TRUE, TRUE), # pour mieux voir la proximité avec les axes
                      axes = 1:2,
                      repel = TRUE, # pour éviter les chevauchements dans biplot
                      )

Il est possible de faire des Biplots asymétriques, où les coordonnées sont pondérées par le poids de la valeur propre (en fait la racine carrée de la valeur propre eigenvalue). - Voir : Biplot asymétrique in : http://www.sthda.com/french/articles/38-methodes-des-composantes-principales-dans-r-guide-pratique/74-afc-analyse-factorielle-des-correspondances-avec-r-l-essentiel/#r-code-to-comput-ca

6.3. Aide à la description et à l’interprétation

Identification des variables les plus remarquables (moins efficace que dans PCA car pas significatives en l’absence de test) par composante. Simple tri des coordonnées.

### fonction dimdesc() [in FactoMineR]

res.desc <- dimdesc(res.precipit.ca, axes = c(1,2))

Aide sur l’axe 1

– Pour les lignes (pour nous, les individus)

### Description de la dimension 1 pour 4 lignes
head(res.desc[[1]]$row, 4)

##         coord
## 58 -0.5101260
## 20 -0.4872576
## 18 -0.4769095
## 69 -0.4744821

– Pour les colonnes (pour nous, les variables)

### Description de la dimension 1 pour 4 colonnes

head(res.desc[[1]]$col, 4)

##             coord
## P_janv -0.4038006
## P_octo -0.2967389
## P_avri -0.1833434
## P_mars -0.1638102

Aide sur l’axe 2