Résumé minimal du script AFC_Temperat_Max_v2.R pour les AFC sur les températures maximales (toutes positives) 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 températures maximales (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/temperMaxation/R")
### respecter ce cheminement si "geographie2"
### getwd()

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

2. Lecture des données

temperMax <- read.csv("temperature_max.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(temperMax))

# 2. Graphe
#balloonplot(t(dt), main ="temperMax", 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(temperMax[,2:13])

## Warning in chisq.test(temperMax[, 2:13]): Chi-squared approximation may be
## incorrect

chisq

## 
##  Pearson's Chi-squared test
## 
## data:  temperMax[, 2:13]
## X-squared = 278.62, df = 803, p-value = 1

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

## X-squared 
##  278.6179

# Calcul du degrés de liberté (Degree of freedom)
df <- (nrow(temperMax[, 2:13]) - 1) * (ncol(temperMax[, 2:13]) - 1)
df

## [1] 803

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

## X-squared 
##         1

# ou
chisq$p.value

## [1] 1

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) ;

- Si le nom des stations est en première colonne :

le tableau “utile” va de la deuxième colonne à la 17ème [,2:17] ;
les variables quantitatives supplémentaires sont ici les coordonnées en latitude et longitude des stations (en colonnes 13 et 14 => col.sup = 13:14) ;
les variables qualitatives (supplémentaires) sont les dernières (quali.sup=c(15:16)) et sont à raccourcir pour rendre lisible les graphiques et tableaux.

res.temperMax.ca <- CA(temperMax[,2:17],
                       col.sup = 13:14,
                       row.sup = NULL,
                       quali.sup=c(15:16),
                       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.temperMax.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 278.6179 (p-value =  1 ).
## *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$contrib"     "contributions of the rows"                
## 10 "$col.sup$coord"   "coord. for supplementary columns"         
## 11 "$col.sup$cos2"    "cos2 for supplementary columns"           
## 12 "$quali.sup$coord" "coord. for supplementary categorical var."
## 13 "$quali.sup$cos2"  "cos2 for supplementary categorical var."  
## 14 "$call"            "summary called parameters"                
## 15 "$call$marge.col"  "weights of the columns"                   
## 16 "$call$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.temperMax.ca)
eig.val

##          eigenvalue variance.percent cumulative.variance.percent
## Dim.1  1.783547e-02      91.70786911                    91.70787
## Dim.2  9.211452e-04       4.73641827                    96.44429
## Dim.3  2.423211e-04       1.24598614                    97.69027
## Dim.4  1.301831e-04       0.66938583                    98.35966
## Dim.5  1.035333e-04       0.53235571                    98.89202
## Dim.6  7.697635e-05       0.39580316                    99.28782
## Dim.7  5.142354e-05       0.26441367                    99.55223
## Dim.8  3.854812e-05       0.19820983                    99.75044
## Dim.9  2.136465e-05       0.10985446                    99.86030
## Dim.10 1.706588e-05       0.08775070                    99.94805
## Dim.11 1.010392e-05       0.05195312                   100.00000

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

 # Visualisation des eigenvalues
fviz_eig(res.temperMax.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(temperMax)-1 = 1/72 soit environ 1.4%) ou
1/(ncol(temperMax[, 2:13])-1 = 1/12 soit environ 8.3%) 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)

 # Visualisation des eigenvalues
sp <- fviz_eig(res.temperMax.ca,addlabels = TRUE, ylim = c(0, 40)) # calibrer le ylim avec la lecture du tableau précédent
         
sp + geom_hline (yintercept = 8.3, linetype = 2, color = "red") # tracer le yintercept avec la valeur de la *eigenvalues* moyenne

Les paramètres les plus utiles :

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

##                   Dim 1        Dim 2        Dim 3        Dim 4         Dim 5
## Tmax_janv  4.676522e-01  0.059139375 -0.020730147 -0.028961251  0.0221056454
## Tmax_fevr  1.734267e-01  0.044808905 -0.011591979  0.025787076  0.0059646214
## Tmax_mars -8.440914e-05  0.038579648  0.023919566  0.010815256  0.0120764873
## Tmax_avri -6.240442e-02 -0.007189021  0.026421023  0.008954528  0.0039739861
## Tmax_mai  -3.408238e-02  0.011484187 -0.002196634  0.006235600  0.0030450627
## Tmax_juin -8.508948e-02  0.010269865 -0.007960547  0.002246295 -0.0073779203
## Tmax_juil -8.928686e-02 -0.016485094 -0.019045246 -0.001431463  0.0015409013
## Tmax_aou  -5.271022e-02 -0.034207237 -0.008489538 -0.001714790  0.0107809524
## Tmax_sept -2.697403e-02 -0.003618042  0.011469657 -0.016040154 -0.0002682142
## Tmax_octo  1.143947e-03  0.020837565  0.014237049 -0.015093683 -0.0148868677
## Tmax_nove  1.018774e-01  0.018288574 -0.016059550  0.010325735 -0.0236322259
## Tmax_dece  4.620334e-01 -0.106322745  0.016916133  0.009634358 -0.0098971399
##                  Dim 6         Dim 7         Dim 8         Dim 9        Dim 10
## Tmax_janv -0.012012697  0.0007619958  0.0103038547  3.986100e-03  0.0004727101
## Tmax_fevr  0.008014642 -0.0136208580 -0.0156477062  2.101983e-03  0.0019475555
## Tmax_mars  0.010489763  0.0151185383  0.0006166102  4.243781e-05  0.0012554547
## Tmax_avri -0.006406254 -0.0059737091  0.0082813377  5.895982e-03 -0.0008212265
## Tmax_mai  -0.011474636  0.0024921314 -0.0008011784 -9.952083e-03 -0.0062996481
## Tmax_juin -0.013809089 -0.0024552454 -0.0010628513  1.975791e-03  0.0042446984
## Tmax_juil  0.002401785  0.0076542614 -0.0026462253  5.694728e-03 -0.0033124953
## Tmax_aou   0.006318660 -0.0030366921  0.0032492658 -4.638169e-03  0.0056184874
## Tmax_sept  0.007004874 -0.0095207665 -0.0036504621  5.021817e-05 -0.0049909537
## Tmax_octo  0.001375418  0.0058469537 -0.0050737468 -1.912136e-03  0.0049103500
## Tmax_nove  0.013752011 -0.0020407839  0.0139422249 -1.644049e-03 -0.0022081202
## Tmax_dece -0.006902081  0.0067381313 -0.0059945844  2.353148e-04 -0.0005589627
##                  Dim 11
## Tmax_janv  0.0007795822
## Tmax_fevr  0.0030648641
## Tmax_mars -0.0051246215
## Tmax_avri  0.0038825180
## Tmax_mai   0.0015980732
## Tmax_juin -0.0046011938
## Tmax_juil  0.0015650796
## Tmax_aou   0.0005303625
## Tmax_sept -0.0032592796
## Tmax_octo  0.0048706914
## Tmax_nove -0.0007632761
## Tmax_dece -0.0024360867

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

res.temperMax.ca$col.sup$coord  ## coord. for the supplementary columns

##           Dim 1       Dim 2       Dim 3       Dim 4       Dim 5        Dim 6
## lat  -0.1386426  0.05986123  0.04131603 -0.04911599 -0.05930403 -0.001905762
## long -0.2452963 -0.33568280 -0.76341496  0.32838082  0.04398546  0.121025028
##            Dim 7       Dim 8      Dim 9      Dim 10        Dim 11
## lat  -0.01034257 -0.01945372 0.01001001  0.01111334  0.0004328574
## long  0.39203709  0.04476180 0.10074090 -0.07467782 -0.0033595854

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

res.temperMax.ca$col.sup$cos2  ##   "cos2 for supplementary columns"

##           Dim 1      Dim 2      Dim 3      Dim 4       Dim 5        Dim 6
## lat  0.55942746 0.10428973 0.04968068 0.07020953 0.102357262 0.0001057031
## long 0.04516227 0.08457691 0.43743646 0.08093739 0.001452151 0.0109937037
##            Dim 7       Dim 8       Dim 9      Dim 10       Dim 11
## lat  0.003113198 0.011014263 0.002916216 0.003594508 5.453055e-06
## long 0.115358067 0.001503865 0.007617375 0.004185784 8.471592e-06

Interprétation des coordonnées des individus sur les axes factoriels

res.temperMax.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  -0.12678445  0.036893509  0.0019013097 -0.0112881921 -0.0105914701
## 2   0.22608358  0.012116271 -0.0078538075 -0.0027101718 -0.0083416997
## 3  -0.10698456  0.023224955  0.0009257370 -0.0135099463 -0.0036022941
## 4   0.22531956 -0.003191371 -0.0271183373  0.0025473721 -0.0043242049
## 5  -0.10071221 -0.035343697  0.0017767226  0.0257617283 -0.0108046368
## 6   0.07316297 -0.014183765  0.0156263575 -0.0041103954  0.0094560690
## 7  -0.07163595 -0.067174065  0.0246928521 -0.0143737732  0.0042116126
## 8  -0.14419260  0.019583128  0.0013727988  0.0086184973  0.0087055285
## 9   0.20787756 -0.005084419 -0.0249802233  0.0035225651 -0.0089361810
## 10 -0.15543413  0.035564192 -0.0108846618 -0.0094923297  0.0074884248
## 11  0.03607073 -0.006328428  0.0260611516  0.0085350796  0.0096236048
## 12  0.19460620  0.015783306  0.0334146931 -0.0042783336  0.0090858147
## 13  0.14263297  0.016218903  0.0289572408  0.0075371273 -0.0022675114
## 14 -0.09123300  0.007260725  0.0160801920  0.0103398205  0.0053093591
## 15 -0.13539383 -0.002077821  0.0065585646 -0.0128632900 -0.0021283435
## 16  0.11580066  0.039470123  0.0158228731 -0.0121975633 -0.0180955952
## 17 -0.02652327  0.039521328 -0.0125754429 -0.0153893622  0.0019185662
## 18  0.19356081  0.001532943 -0.0167615742  0.0139233440  0.0048095048
## 19  0.16502722  0.018593790 -0.0101068790  0.0012837133  0.0040705285
## 20  0.05991629 -0.035071718 -0.0123206319 -0.0007989140  0.0044003454
## 21  0.03032628 -0.017001894 -0.0129755406  0.0146998379  0.0087439286
## 22 -0.20885005  0.023390223 -0.0017845088  0.0044258282 -0.0119167552
## 23  0.03797975  0.032655630 -0.0057543268 -0.0113778047 -0.0079673303
## 24 -0.04264444 -0.018476764  0.0085470991  0.0077033737 -0.0066854494
## 25  0.05861696  0.041284999  0.0094860734 -0.0074534406 -0.0090571311
## 26 -0.13017797 -0.028319194 -0.0190490776 -0.0348051269  0.0002846803
## 27  0.19755143 -0.003204908 -0.0215415753  0.0016830147  0.0008364231
## 28  0.01200446 -0.031942187  0.0302968409  0.0137028438  0.0130784241
## 29 -0.13077958 -0.031422714 -0.0126367087  0.0040885083 -0.0080369561
## 30  0.17713233  0.006785105 -0.0150955134  0.0001343279  0.0076503730
## 31  0.10775830  0.041972202  0.0148983744 -0.0159144489 -0.0141538963
## 32 -0.25032796 -0.027643211 -0.0108538252 -0.0055406632 -0.0116955917
## 33  0.11569554  0.046950029  0.0063046177 -0.0170049515 -0.0123097502
## 34  0.16740483 -0.009807503  0.0290929701  0.0084955406 -0.0278099861
## 35 -0.05570839  0.026564124  0.0004959769 -0.0054131172  0.0065144767
## 36 -0.12441388  0.037784244 -0.0014519909  0.0049994084  0.0109110433
## 37 -0.01997211  0.031322585  0.0048400469 -0.0222074071 -0.0205655179
## 38  0.08791185 -0.001348438 -0.0177395462 -0.0013011323  0.0222544818
## 39 -0.06097907  0.023423817  0.0075083129  0.0040568451  0.0125924618
## 40 -0.16693216 -0.101037066 -0.0074880897 -0.0241850245 -0.0189399876
## 41 -0.17163006  0.039114918 -0.0046719030 -0.0101407206  0.0008107987
## 42 -0.08099393 -0.029073972  0.0232473973 -0.0154935331 -0.0007531510
## 43 -0.09518898 -0.037315019  0.0025524868  0.0233134143 -0.0197076240
## 44 -0.11069222 -0.022216007  0.0081762434  0.0157963399 -0.0048091858
## 45  0.08751127 -0.009132830 -0.0118578118  0.0043207428 -0.0006833211
## 46 -0.25790542  0.016120389 -0.0217594778  0.0068302118 -0.0008179284
## 47 -0.09821000 -0.091146498 -0.0036669551 -0.0251802789  0.0157892923
## 48  0.05038759  0.001902285  0.0164740466  0.0004294256  0.0171988498
## 49 -0.21205882  0.019394101 -0.0213651964  0.0103898587 -0.0015616720
## 50 -0.25708970  0.011721177 -0.0159476809  0.0053901204 -0.0070554055
## 51  0.01504216  0.032940023 -0.0012500395 -0.0048949892  0.0054717411
## 52 -0.08959879  0.006419716  0.0175610731  0.0133010579  0.0062755728
## 53  0.18344690  0.011571630 -0.0171546582 -0.0030149000 -0.0079113512
## 54  0.05742910 -0.022428567 -0.0195999740  0.0099993621  0.0030003543
## 55  0.04814806 -0.027030153 -0.0210009889  0.0104788469 -0.0049097303
## 56 -0.12543517  0.035291028  0.0012175010  0.0108001490  0.0077793083
## 57  0.12704005 -0.003032058  0.0246120979  0.0046642329  0.0090905767
## 58  0.13907450 -0.015293585 -0.0136008603 -0.0057708837 -0.0021082021
## 59 -0.06850883  0.019078997  0.0068309756 -0.0061037875  0.0107565779
## 60  0.09467416  0.036890465  0.0141036217  0.0017254397 -0.0158877771
## 61 -0.05141593 -0.074812741  0.0111424746 -0.0124683091  0.0135507108
## 62 -0.14282022  0.035635168  0.0002401270  0.0020112120  0.0061668610
## 63 -0.03630113 -0.028530568 -0.0105974232 -0.0053486600 -0.0026482893
## 64 -0.06836292 -0.044490756  0.0023810756  0.0062969270 -0.0162197890
## 65  0.10218650 -0.026450000  0.0289939982 -0.0012832369 -0.0125655112
## 66 -0.20736297  0.035067536 -0.0067201641 -0.0054839182 -0.0017825492
## 67 -0.21858936  0.018558322 -0.0020405916  0.0267066786 -0.0140199101
## 68  0.11835187 -0.008471922  0.0171381906 -0.0075890508  0.0006164601
## 69  0.13910658 -0.005697191 -0.0130473521  0.0009644687  0.0105901393
## 70  0.06761672 -0.028088868  0.0030966122 -0.0031198067  0.0044050723
## 71 -0.08010955  0.019394688 -0.0019760418 -0.0027588207  0.0142043981
## 72 -0.14614968  0.034960495  0.0091686873 -0.0072500053  0.0096512269
## 73 -0.15167022  0.027407914 -0.0075379539  0.0050555330  0.0105879021
## 74 -0.06183567 -0.007692716  0.0123485427  0.0207456328 -0.0014951172
##            Dim 6         Dim 7         Dim 8         Dim 9        Dim 10
## 1   7.712087e-03  0.0005893867  2.501359e-03 -5.076129e-04  3.730535e-03
## 2   5.132218e-03  0.0123849633 -6.046837e-03  6.397855e-03  3.109253e-04
## 3   2.598164e-03 -0.0056912054 -1.414568e-02  4.089916e-05 -7.775884e-03
## 4   7.379889e-03 -0.0022015911 -5.429487e-03  5.051901e-03  2.975294e-03
## 5   7.606841e-04  0.0026593567 -2.325575e-03 -2.559932e-04 -8.923743e-03
## 6  -6.926947e-04 -0.0033801611  5.911969e-03  3.610102e-03 -1.848851e-03
## 7  -7.736227e-03  0.0072800646 -1.274670e-02  5.084349e-03 -1.083240e-04
## 8   9.734000e-03  0.0046887323 -4.121253e-03  9.921805e-04  3.091551e-03
## 9   4.574076e-03 -0.0037452655 -3.834707e-03  2.044104e-04 -1.167760e-03
## 10  1.823684e-03  0.0038648277  3.372056e-03  1.796138e-03  4.572545e-03
## 11  1.229221e-03  0.0021535375 -9.411846e-04 -1.196443e-03 -1.070562e-03
## 12  1.536902e-02  0.0041551296  1.178193e-02 -2.073754e-03  9.569149e-04
## 13  5.522114e-03  0.0035424050  8.727955e-03 -7.260960e-03 -8.810982e-03
## 14  3.515490e-03  0.0044145466 -4.292312e-03 -1.117164e-03  3.722278e-03
## 15 -9.223830e-03  0.0072394614  5.484378e-03  2.798288e-03 -1.112812e-02
## 16 -1.527342e-02 -0.0081112299 -2.130402e-03 -1.433011e-03  1.569867e-03
## 17  1.662259e-02 -0.0006184510 -3.874742e-03  6.921625e-03 -3.449915e-03
## 18 -1.945165e-03 -0.0024226369 -1.565864e-02 -6.387004e-03  5.738782e-03
## 19  2.174645e-03  0.0070583995  3.024011e-03 -2.617097e-03 -7.905219e-03
## 20 -7.149919e-04 -0.0185941880  1.054436e-02  5.024476e-04  1.129388e-03
## 21 -2.767247e-03 -0.0018595429 -5.132468e-04  3.010163e-04  4.268996e-03
## 22 -1.086504e-02  0.0122700264  4.615286e-03 -5.780550e-03 -3.211229e-03
## 23  1.213514e-02  0.0011770319 -3.713849e-03 -1.785756e-04  2.904622e-03
## 24  1.886417e-02  0.0028641221  6.555909e-03  6.040571e-03  7.135359e-04
## 25  1.364479e-02 -0.0075477069 -3.057668e-03 -3.622746e-03 -1.982548e-03
## 26 -7.659433e-03  0.0074371771  1.098299e-02 -1.194751e-02  2.160551e-03
## 27 -1.258400e-03  0.0075384871 -2.652325e-03  1.846682e-03 -4.531330e-03
## 28 -1.236925e-03 -0.0001127758 -5.866519e-03 -9.081995e-04  1.744244e-03
## 29  1.297215e-02 -0.0098560080  3.493419e-04 -1.827930e-03 -3.971322e-03
## 30 -4.015520e-03  0.0082949223  3.527403e-04 -3.439390e-03 -2.166143e-03
## 31 -7.186328e-03 -0.0041208712 -4.640794e-04 -2.783965e-03 -1.329843e-03
## 32 -1.417119e-02  0.0124391033 -3.493542e-03  3.878316e-03  7.550145e-03
## 33  1.265205e-02 -0.0131271664 -7.564235e-04  3.683370e-03  3.853748e-03
## 34 -3.024954e-02  0.0070538118 -6.423264e-03 -3.587163e-03  1.776774e-03
## 35 -5.183268e-03 -0.0078242439 -7.306059e-03  9.898603e-03 -2.255733e-03
## 36 -1.836062e-03  0.0007907176 -4.440977e-04 -1.877265e-03  3.975723e-03
## 37  8.313105e-03  0.0004204195 -5.638244e-03 -5.568176e-03 -4.695370e-03
## 38 -6.815904e-03  0.0041354183  5.384019e-03 -5.436468e-03 -2.037019e-03
## 39 -3.540232e-03 -0.0064653657 -8.275811e-03  4.002314e-04 -7.413911e-03
## 40  1.397188e-02 -0.0065169873  3.641521e-03 -3.994261e-03 -3.483317e-05
## 41 -3.645386e-03  0.0145639426  1.118030e-02  5.813762e-03 -1.375390e-03
## 42  1.113601e-03  0.0016289514 -1.198088e-02  4.788098e-03 -1.385699e-03
## 43  5.747819e-03 -0.0037361731 -6.141644e-03 -2.274174e-03 -4.224158e-03
## 44 -1.400553e-03  0.0011452026  3.365855e-03 -3.174352e-03 -3.491870e-03
## 45 -3.894307e-03  0.0099422055 -5.834697e-03 -1.612136e-03  3.478738e-03
## 46 -6.049409e-03 -0.0007614409 -3.229899e-04  7.287470e-03  4.327402e-03
## 47 -6.537334e-03 -0.0070253517  4.735496e-04  1.529730e-03 -2.614638e-03
## 48 -4.675556e-03 -0.0059188988  4.978073e-03  1.890145e-03  5.734929e-05
## 49 -6.565579e-03 -0.0024651121  2.906401e-03  7.056817e-03  1.764148e-03
## 50 -9.877575e-03  0.0064284468  1.276618e-04  6.276036e-03  9.271458e-04
## 51 -1.339422e-02 -0.0176552478 -1.215875e-03  5.083854e-03 -5.581423e-03
## 52  5.455612e-03  0.0057632418  1.425469e-03 -9.934268e-04  2.505034e-03
## 53  1.007618e-02  0.0070648582  3.067823e-03  8.297489e-03  3.016789e-05
## 54 -6.369015e-05 -0.0092470625  2.878429e-03 -4.616584e-03  2.596344e-03
## 55 -1.395020e-03 -0.0102169598  3.032678e-05 -6.193522e-03  8.431076e-05
## 56 -3.132911e-03 -0.0028447094 -3.678135e-03 -1.596590e-03 -9.145012e-04
## 57  6.428115e-04 -0.0003975444  3.954062e-03  1.706299e-03  6.565043e-03
## 58 -1.089042e-02 -0.0016593570  1.288455e-02  4.291591e-03  5.456123e-03
## 59  8.351313e-03 -0.0073778438 -3.330011e-03 -7.956074e-03  3.364940e-03
## 60 -2.845349e-02 -0.0096435159  4.000607e-03 -2.279758e-03  4.669933e-03
## 61 -5.411372e-04  0.0029390556 -1.098469e-02  5.677939e-03 -2.770980e-04
## 62  1.558504e-03 -0.0019007842 -1.325668e-03 -5.910223e-03  3.812063e-03
## 63  8.556322e-03  0.0072732622 -1.940709e-04 -1.065278e-02  1.452570e-03
## 64  8.104206e-03 -0.0022349892  4.564203e-03 -2.935251e-04  1.575122e-03
## 65  2.264836e-03  0.0048839186 -5.638022e-05  2.510100e-03  6.032737e-03
## 66  2.329588e-03  0.0051640102 -7.824931e-04 -9.978609e-03  4.150626e-03
## 67 -1.395234e-03 -0.0105063641  1.402127e-02  5.872687e-03 -4.389138e-03
## 68  1.695739e-03  0.0026125514  9.007654e-03  5.380520e-03  5.952831e-03
## 69 -8.915525e-03  0.0093386661  3.945789e-03  1.821877e-03 -8.665186e-03
## 70 -6.270565e-03 -0.0116750044  1.783974e-03  1.530521e-03  4.607242e-04
## 71  2.404808e-03 -0.0016494522 -4.652304e-03 -3.381176e-03 -7.867110e-04
## 72  9.695883e-04 -0.0096453077 -2.546350e-03 -1.471751e-03  2.038413e-04
## 73  5.107958e-04  0.0067727417 -3.023221e-03  4.357813e-04  4.150763e-03
## 74  1.390106e-02  0.0050460848  6.178636e-03  2.897240e-03  2.018426e-03
##           Dim 11
## 1  -4.691762e-03
## 2  -6.936927e-04
## 3  -1.490110e-03
## 4  -3.096680e-03
## 5   1.884152e-03
## 6  -2.375553e-03
## 7  -1.371146e-03
## 8   2.776853e-03
## 9  -2.868567e-03
## 10 -3.458063e-03
## 11 -1.567051e-04
## 12 -4.918295e-04
## 13  1.046987e-03
## 14  4.592823e-04
## 15  5.007942e-04
## 16  3.934734e-03
## 17  9.197979e-04
## 18  2.055622e-03
## 19  8.445157e-03
## 20  3.391807e-04
## 21  6.065608e-04
## 22  4.558067e-04
## 23 -3.855962e-03
## 24  3.749629e-03
## 25 -4.647617e-04
## 26  3.556525e-03
## 27 -4.993562e-03
## 28 -2.712605e-03
## 29  8.241391e-04
## 30  8.700611e-04
## 31  4.326974e-03
## 32  6.584063e-03
## 33  5.295310e-03
## 34 -4.805064e-03
## 35 -2.105623e-03
## 36 -2.313482e-03
## 37 -4.802925e-03
## 38 -3.659216e-03
## 39  3.524417e-04
## 40 -4.290485e-03
## 41 -4.427189e-03
## 42  1.379444e-03
## 43  3.167553e-03
## 44  4.457306e-03
## 45  3.854518e-04
## 46  5.591919e-05
## 47  5.340268e-03
## 48 -3.071325e-04
## 49  2.223291e-03
## 50 -1.537678e-03
## 51 -1.817802e-03
## 52  2.710817e-03
## 53  6.941893e-03
## 54  1.060832e-03
## 55 -8.206942e-04
## 56 -3.455967e-03
## 57 -2.109475e-03
## 58 -7.651239e-04
## 59  4.924540e-03
## 60  2.579312e-03
## 61 -1.034574e-03
## 62  4.492037e-04
## 63 -7.508471e-03
## 64  7.872872e-04
## 65 -7.686437e-04
## 66 -1.138952e-03
## 67 -5.513158e-03
## 68 -3.618513e-04
## 69  1.805205e-06
## 70  2.617348e-05
## 71  3.292389e-05
## 72 -2.294343e-03
## 73  6.188363e-03
## 74 -2.425415e-03

5.3. Contribution des variables et des individus sur les axes

Interprétation des contributions des variables sur les axes factoriels.

res.temperMax.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
## Tmax_janv 3.458750e+01 10.7098450  5.0023184 18.1734720 13.313255390  5.2878798
## Tmax_fevr 7.323963e+00  9.4667202  2.4083681 22.1844476  1.492398411  3.6241817
## Tmax_mars 2.518809e-06 10.1880114 14.8873129  5.6652626  8.881826469  9.0131174
## Tmax_avri 1.969144e+00  0.5059911 25.9800200  5.5547216  1.375638138  4.8081991
## Tmax_mai  6.099119e-01  1.3408014  0.1864731  2.7970100  0.838695915 16.0181575
## Tmax_juin 4.888499e+00  1.3788270  3.1492198  0.4667534  6.331350895 29.8319183
## Tmax_juil 6.316199e+00  4.1688862 21.1517949  0.2224184  0.324067146  1.0589521
## Tmax_aou  2.016512e+00 16.4438573  3.8501055  0.2923904 14.532157924  6.7141102
## Tmax_sept 4.619059e-01  0.1609036  6.1469011 22.3773733  0.007867379  7.2175531
## Tmax_octo 6.387002e-04  4.1033266  7.2814678 15.2337270 18.633607771  0.2139354
## Tmax_nove 3.369024e+00  2.1021544  6.1618126  4.7415508 31.229303786 14.2235540
## Tmax_dece 3.845670e+01 39.4306756  3.7942057  2.2908728  3.039830777  1.9884414
##                 Dim 7       Dim 8        Dim 9      Dim 10     Dim 11
## Tmax_janv  0.03184938  7.76880193 2.097773e+00  0.03693337  0.1696649
## Tmax_fevr 15.66916894 27.58653250 8.981765e-01  0.96527273  4.0376785
## Tmax_mars 28.02584042  0.06218979 5.315096e-04  0.58233706 16.3883369
## Tmax_avri  6.25831867 16.04461298 1.467398e+01  0.35639270 13.4545365
## Tmax_mai   1.13102434  0.15593631 4.341345e+01 21.77689624  2.3669857
## Tmax_juin  1.41168003  0.35289880 2.200366e+00 12.71374443 25.2324705
## Tmax_juil 16.09940911  2.56693992 2.144942e+01  9.08546650  3.4256931
## Tmax_aou   2.32132194  3.54538222 1.303446e+01 23.94451348  0.3603726
## Tmax_sept 19.95852682  3.91416443 1.336511e-03 16.52665856 11.9041976
## Tmax_octo  5.78718834  5.81332504 1.489745e+00 12.29890745 20.4391010
## Tmax_nove  0.46888365 29.19402262 7.324314e-01  1.65405451  0.3338156
## Tmax_dece  2.83678836  2.99519346 8.327466e-03  0.05882297  1.8871471

Interprétation des contributions des individus sur les axes factoriels.

res.temperMax.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  1.00151934  1.642040525 0.016577786 1.087693e+00 1.204050122 8.586152e-01
## 2  4.83502836  0.268878123 0.429452243 9.518855e-02 1.133900023 5.772960e-01
## 3  0.78569882  0.716935771 0.004329946 1.716529e+00 0.153453547 1.073679e-01
## 4  4.68914998  0.018214090 4.999376424 8.211286e-02 0.297518203 1.165530e+00
## 5  0.75938768  1.810838869 0.017395300 6.807370e+00 1.505651043 1.003772e-02
## 6  0.45103576  0.328222198 1.514388352 1.950409e-01 1.297939065 9.367841e-03
## 7  0.34162581  5.816322107 2.987614387 1.884344e+00 0.203418364 9.231545e-01
## 8  1.46874869  0.524544361 0.009798705 7.188772e-01 0.922266653 1.550856e+00
## 9  4.06907025  0.047132352 4.324799434 1.600767e-01 1.295354239 4.564720e-01
## 10 1.60551659  1.627438046 0.579489112 8.203472e-01 0.641959517 5.120926e-02
## 11 0.10922487  0.065096844 4.196548225 8.378318e-01 1.339343175 2.938997e-02
## 12 3.09921486  0.394721599 6.725223207 2.052191e-01 1.163779755 4.478763e+00
## 13 1.67202764  0.418603782 5.072375173 6.396544e-01 0.072795959 5.806864e-01
## 14 0.60720339  0.074464072 1.388372769 1.068529e+00 0.354257549 2.088956e-01
## 15 1.30573025  0.005954271 0.225510472 1.614693e+00 0.055583239 1.404125e+00
## 16 0.89900840  2.022251704 1.235394808 1.366526e+00 3.781743954 3.623611e+00
## 17 0.04685956  2.014482445 0.775325110 2.161301e+00 0.042237885 4.264504e+00
## 18 3.59093846  0.004360954 1.981965603 2.545601e+00 0.381925383 8.402590e-02
## 19 2.49621739  0.613569285 0.689126164 2.069366e-02 0.261623948 1.004328e-01
## 20 0.30642897  2.032874758 0.953672695 7.463974e-03 0.284720159 1.011043e-02
## 21 0.08541228  0.519796381 1.150870287 2.749396e+00 1.223206998 1.647802e-01
## 22 2.84228557  0.690277672 0.015273176 1.748710e-01 1.594113679 1.782332e+00
## 23 0.08727665  1.249299341 0.147460687 1.073102e+00 0.661643648 2.064481e+00
## 24 0.13266462  0.482212671 0.392248335 5.930923e-01 0.561689275 6.014962e+00
## 25 0.23371184  2.244787375 0.450505871 5.176995e-01 0.961214003 2.934235e+00
## 26 1.24420553  1.140080457 1.960913585 1.218523e+01 0.001025030 9.980165e-01
## 27 3.83217491  0.019528670 3.353770177 3.810578e-02 0.011834277 3.602881e-02
## 28 0.01147150  1.572610362 5.378031722 2.047796e+00 2.345582927 2.821949e-02
## 29 1.21356210  1.356519574 0.833956640 1.624957e-01 0.789532503 2.766515e+00
## 30 2.88690589  0.082017533 1.543213896 2.274572e-04 0.927698516 3.437541e-01
## 31 0.76347545  2.242712896 1.074149589 2.281429e+00 2.269082643 7.867468e-01
## 32 3.72284389  0.879001548 0.515127978 2.498674e-01 1.399926316 2.764369e+00
## 33 0.87275543  2.782835920 0.190752496 2.583094e+00 1.702011501 2.418289e+00
## 34 1.92594915  0.127991831 4.281326501 6.795493e-01 9.156195754 1.457048e+01
## 35 0.22360386  0.984431883 0.001304531 2.892431e-01 0.526746765 4.485107e-01
## 36 1.08860435  1.944063432 0.010913237 2.408240e-01 1.442346631 5.493314e-02
## 37 0.02455619  1.169458433 0.106146478 4.159478e+00 4.485357221 9.857503e-01
## 38 0.74649056  0.003400539 2.237215833 2.240281e-02 8.240795591 1.039690e+00
## 39 0.27999548  0.799947104 0.312440632 1.697838e-01 2.056910361 2.186655e-01
## 40 1.67733848 11.897581008 0.248414036 4.823517e+00 3.719672708 2.722560e+00
## 41 1.89988909  1.910657895 0.103614985 9.086764e-01 0.007304194 1.985893e-01
## 42 0.43439984  1.083802066 2.634066593 2.177789e+00 0.006470734 1.902704e-02
## 43 0.67093246  1.996316231 0.035507972 5.513753e+00 4.954258716 5.668119e-01
## 44 0.89432902  0.697512039 0.359140326 2.495205e+00 0.290811085 3.317339e-02
## 45 0.70133923  0.147899769 0.947769404 2.342325e-01 0.007366388 3.218013e-01
## 46 4.23278117  0.320193442 2.217661197 4.067273e-01 0.007333988 5.395828e-01
## 47 0.65455300 10.916161456 0.067164225 5.895010e+00 2.914495827 6.719890e-01
## 48 0.21542234  0.005944995 1.694874611 2.143629e-03 4.323615835 4.297714e-01
## 49 2.97781259  0.482259220 2.224804514 9.793413e-01 0.027820761 6.613907e-01
## 50 4.09481802  0.164802665 1.159721501 2.465995e-01 0.531268276 1.400533e+00
## 51 0.01731216  1.607442455 0.008799783 2.511682e-01 0.394627052 3.180485e+00
## 52 0.58187492  0.057838032 1.645207964 1.756822e+00 0.491741356 4.998499e-01
## 53 2.94757708  0.227085846 1.897151169 1.090738e-01 0.944387908 2.060457e+00
## 54 0.30242710  0.893133161 2.592752110 1.256120e+00 0.142202222 8.618438e-05
## 55 0.20431975  1.246827207 2.861050959 1.325897e+00 0.365992916 3.974117e-02
## 56 1.10408694  1.692192591 0.007655907 1.121384e+00 0.731562224 1.595836e-01
## 57 1.33906447  0.014769023 3.699225832 2.472924e-01 1.181157321 7.943554e-03
## 58 1.77661125  0.415980093 1.250614813 4.190947e-01 0.070327726 2.524141e+00
## 59 0.34826979  0.522986272 0.254848173 3.787491e-01 1.479025282 1.199111e+00
## 60 0.62651105  1.841834491 1.023341230 2.850988e-02 3.039462176 1.311186e+01
## 61 0.18654150  7.646941064 0.644817399 1.502883e+00 2.232075563 4.787647e-03
## 62 1.39462236  1.681091719 0.000290170 3.788986e-02 0.447930094 3.847868e-02
## 63 0.10964474  1.311369182 0.687767321 3.261127e-01 0.100527092 1.411397e+00
## 64 0.33691100  2.762931262 0.030082486 3.916168e-01 3.267149722 1.097039e+00
## 65 0.82714543  1.073007434 4.901222765 1.787058e-02 2.154566206 9.414467e-02
## 66 2.73632236  1.515206848 0.211523203 2.621905e-01 0.034833138 8.001849e-02
## 67 3.27437574  0.456987638 0.021002744 6.696383e+00 2.320414756 3.090950e-02
## 68 1.09967785  0.109102764 1.697221721 6.194700e-01 0.005139607 5.230707e-02
## 69 1.80242260  0.058538202 1.167076803 1.187046e-02 1.799572376 1.715467e+00
## 70 0.38363415  1.281840968 0.059221054 1.118909e-01 0.280491614 7.644512e-01
## 71 0.46590443  0.528750020 0.020864783 7.570164e-02 2.523356401 9.727841e-02
## 72 1.44284888  1.598588962 0.417958180 4.864429e-01 1.083914064 1.471388e-02
## 73 1.59622355  1.009256559 0.290197327 2.429725e-01 1.340039451 4.194837e-03
## 74 0.28447533  0.085247645 0.835009176 4.386821e+00 0.028649800 3.331116e+00
##           Dim 7        Dim 8        Dim 9       Dim 10       Dim 11
## 1  7.506729e-03 1.803686e-01 1.340237e-02 9.062034e-01 2.420998e+00
## 2  5.032377e+00 1.600291e+00 3.232352e+00 9.557168e-03 8.035080e-02
## 3  7.711611e-01 6.355405e+00 9.585872e-05 4.337799e+00 2.690578e-01
## 4  1.552717e-01 1.259782e+00 1.967863e+00 8.545001e-01 1.563450e+00
## 5  1.836433e-01 1.873446e-01 4.095861e-03 6.230880e+00 4.691653e-01
## 6  3.339073e-01 1.362618e+00 9.167611e-01 3.010150e-01 8.393684e-01
## 7  1.223719e+00 5.004553e+00 1.436641e+00 8.163826e-04 2.209280e-01
## 8  5.386357e-01 5.551387e-01 5.805395e-02 7.056190e-01 9.615288e-01
## 9  4.581080e-01 6.406572e-01 3.284543e-03 1.341971e-01 1.367744e+00
## 10 3.442746e-01 3.496173e-01 1.789742e-01 1.452092e+00 1.402758e+00
## 11 1.350328e-01 3.440667e-02 1.003194e-01 1.005522e-01 3.638925e-03
## 12 4.900385e-01 5.255964e+00 2.937932e-01 7.831430e-02 3.494319e-02
## 13 3.577031e-01 2.896743e+00 3.617267e+00 6.668194e+00 1.590307e-01
## 14 4.930888e-01 6.218623e-01 7.600695e-02 1.056340e+00 2.716342e-02
## 15 1.294765e+00 9.912699e-01 4.656178e-01 9.218394e+00 3.153329e-02
## 16 1.529811e+00 1.407817e-01 1.149291e-01 1.726727e-01 1.832177e+00
## 17 8.836436e-03 4.627121e-01 2.664090e+00 8.285461e-01 9.947723e-02
## 18 1.951068e-01 1.087333e+01 3.264047e+00 3.298896e+00 7.149155e-01
## 19 1.583822e+00 3.878103e-01 5.240826e-01 5.986252e+00 1.153936e+01
## 20 1.023569e+01 4.390985e+00 1.798914e-02 1.137843e-01 1.733394e-02
## 21 1.113825e-01 1.131921e-02 7.025073e-03 1.768845e+00 6.031506e-02
## 22 3.402611e+00 6.422101e-01 1.817715e+00 7.022587e-01 2.389763e-02
## 23 2.907321e-02 3.861212e-01 1.610746e-03 5.334935e-01 1.588014e+00
## 24 2.075563e-01 1.450700e+00 2.222159e+00 3.881664e-02 1.810513e+00
## 25 1.343962e+00 2.942363e-01 7.452444e-01 2.794071e-01 2.593521e-02
## 26 1.408498e+00 4.097696e+00 8.749056e+00 3.581806e-01 1.639320e+00
## 27 1.935424e+00 3.196097e-01 2.795491e-01 2.107135e+00 4.322160e+00
## 28 3.511478e-04 1.267587e+00 5.481340e-02 2.531080e-01 1.033959e+00
## 29 2.390600e+00 4.006497e-03 1.979202e-01 1.169522e+00 8.507033e-02
## 30 2.195757e+00 5.296983e-03 9.086336e-01 4.511980e-01 1.229508e-01
## 31 3.872526e-01 6.551785e-03 4.254122e-01 1.215207e-01 2.172987e+00
## 32 3.188284e+00 3.354823e-01 7.459871e-01 3.539343e+00 4.546100e+00
## 33 3.896943e+00 1.726119e-02 7.384802e-01 1.012003e+00 3.227283e+00
## 34 1.185985e+00 1.311903e+00 7.382442e-01 2.267406e-01 2.800930e+00
## 35 1.529838e+00 1.779451e+00 5.893521e+00 3.831505e-01 5.638899e-01
## 36 1.525099e-02 6.417574e-03 2.069056e-01 1.161771e+00 6.644461e-01
## 37 3.773997e-03 9.054868e-01 1.593411e+00 1.418433e+00 2.506800e+00
## 38 5.729161e-01 1.295460e+00 2.383153e+00 4.188666e-01 2.282972e+00
## 39 1.091687e+00 2.386118e+00 1.006933e-02 4.325538e+00 1.651045e-02
## 40 8.866600e-01 3.693072e-01 8.016824e-01 7.632779e-05 1.955908e+00
## 41 4.744846e+00 3.730182e+00 1.819889e+00 1.275116e-01 2.231478e+00
## 42 6.094297e-02 4.397885e+00 1.267359e+00 1.328858e-01 2.224270e-01
## 43 3.584942e-01 1.292278e+00 3.196995e-01 1.380835e+00 1.311439e+00
## 44 3.320095e-02 3.825916e-01 6.139913e-01 9.301119e-01 2.559782e+00
## 45 3.139701e+00 1.442508e+00 1.986975e-01 1.158243e+00 2.401792e-02
## 46 1.279676e-02 3.071596e-03 2.821288e+00 1.245419e+00 3.512542e-04
## 47 1.161695e+00 7.041186e-03 1.325721e-01 4.848558e-01 3.416288e+00
## 48 1.030975e+00 9.728538e-01 2.530595e-01 2.916457e-04 1.412831e-02
## 49 1.395664e-01 2.588078e-01 2.752906e+00 2.153827e-01 5.777930e-01
## 50 8.879736e-01 4.671634e-04 2.037159e+00 5.565668e-02 2.585777e-01
## 51 8.271827e+00 5.233474e-02 1.650844e+00 2.491019e+00 4.462921e-01
## 52 8.349908e-01 6.814318e-02 5.971534e-02 4.753446e-01 9.402006e-01
## 53 1.516261e+00 3.814050e-01 5.034155e+00 8.330867e-05 7.450669e+00
## 54 2.719486e+00 3.515192e-01 1.631500e+00 6.460068e-01 1.821566e-01
## 55 3.190941e+00 3.750480e-05 2.822390e+00 6.547489e-04 1.047877e-01
## 56 1.969532e-01 4.392394e-01 1.493277e-01 6.133230e-02 1.479445e+00
## 57 4.547934e-03 6.001899e-01 2.016597e-01 3.737243e+00 6.517244e-01
## 58 8.772024e-02 7.055328e+00 1.412287e+00 2.857733e+00 9.491961e-02
## 59 1.400891e+00 3.807110e-01 3.921111e+00 8.780784e-01 3.176500e+00
## 60 2.254547e+00 5.176055e-01 3.032719e-01 1.593100e+00 8.208588e-01
## 61 2.114065e-01 3.939464e+00 1.899111e+00 5.662428e-03 1.333208e-01
## 62 8.567726e-02 5.559404e-02 1.993765e+00 1.038373e+00 2.435336e-02
## 63 1.526612e+00 1.449939e-03 7.882468e+00 1.834753e-01 8.280290e+00
## 64 1.248957e-01 6.948407e-01 5.185055e-03 1.869212e-01 7.887425e-02
## 65 6.553214e-01 1.165010e-04 4.166445e-01 3.012865e+00 8.261139e-02
## 66 5.885749e-01 1.802799e-02 5.289734e+00 1.145745e+00 1.457172e-01
## 67 2.623603e+00 6.233421e+00 1.973027e+00 1.379701e+00 3.676768e+00
## 68 1.858522e-01 2.947271e+00 1.897373e+00 2.907491e+00 1.814557e-02
## 69 2.817434e+00 6.709813e-01 2.581000e-01 7.309255e+00 5.358084e-07
## 70 3.966851e+00 1.235571e-01 1.640878e-01 1.861432e-02 1.014675e-04
## 71 6.850628e-02 7.270192e-01 6.928716e-01 4.695856e-02 1.389139e-04
## 72 2.179616e+00 2.026481e-01 1.221470e-01 2.933362e-03 6.276777e-01
## 73 1.103938e+00 2.934367e-01 1.100067e-02 1.249410e+00 4.690721e+00
## 74 6.570497e-01 1.314114e+00 5.213440e-01 3.167730e-01 7.725625e-01

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.temperMax.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
## Tmax_janv 9.753708e-01 0.015598297 0.001916587 0.0037407473 2.179366e-03
## Tmax_fevr 8.996470e-01 0.060057742 0.004019347 0.0198904471 1.064158e-03
## Tmax_mars 2.648487e-06 0.553267831 0.212679424 0.0434802977 5.421259e-02
## Tmax_avri 7.889839e-01 0.010470729 0.141428408 0.0162451143 3.199559e-03
## Tmax_mai  7.142740e-01 0.081097149 0.002967020 0.0239090123 5.701610e-03
## Tmax_juin 9.391320e-01 0.013680575 0.008219789 0.0006544983 7.060619e-03
## Tmax_juil 9.133717e-01 0.031135458 0.041557135 0.0002347645 2.720333e-04
## Tmax_aou  6.533015e-01 0.275143990 0.016946973 0.0006914264 2.732992e-02
## Tmax_sept 5.519742e-01 0.009930579 0.099799452 0.1951840563 5.457462e-05
## Tmax_octo 1.089642e-03 0.361548310 0.168776643 0.1896980576 1.845351e-01
## Tmax_nove 8.625939e-01 0.027797798 0.021434701 0.0088612024 4.641517e-02
## Tmax_dece 9.471288e-01 0.050155050 0.001269593 0.0004118204 4.345920e-04
##                  Dim 6        Dim 7        Dim 8        Dim 9       Dim 10
## Tmax_janv 0.0006435833 2.589577e-06 0.0004735035 7.086311e-05 9.965830e-07
## Tmax_fevr 0.0019213595 5.549441e-03 0.0073238883 1.321596e-04 1.134541e-04
## Tmax_mars 0.0409025357 8.496469e-02 0.0001413319 6.694602e-07 5.858966e-04
## Tmax_avri 0.0083146823 7.229788e-03 0.0138943551 7.042870e-03 1.366354e-04
## Tmax_mai  0.0809623145 3.818976e-03 0.0003946967 6.090221e-02 2.440269e-02
## Tmax_juin 0.0247346028 7.819242e-04 0.0001465277 5.063573e-04 2.337053e-03
## Tmax_juil 0.0006609076 6.712418e-03 0.0008022802 3.715510e-03 1.257138e-03
## Tmax_aou  0.0093880200 2.168331e-03 0.0024825302 5.058446e-03 7.422717e-03
## Tmax_sept 0.0372244214 6.876558e-02 0.0101093438 1.913150e-06 1.889706e-02
## Tmax_octo 0.0015752232 2.846635e-02 0.0214353210 3.044457e-03 2.007693e-02
## Tmax_nove 0.0157174871 3.461344e-04 0.0161552937 2.246365e-04 4.052249e-04
## Tmax_dece 0.0002113598 2.014379e-04 0.0001594338 2.456750e-07 1.386207e-06
##                 Dim 11
## Tmax_janv 2.710488e-06
## Tmax_fevr 2.809718e-04
## Tmax_mars 9.762083e-03
## Tmax_avri 3.053967e-03
## Tmax_mai  1.570357e-03
## Tmax_juin 2.746097e-03
## Tmax_juil 2.806372e-04
## Tmax_aou  6.614083e-05
## Tmax_sept 8.058802e-03
## Tmax_octo 1.975394e-02
## Tmax_nove 4.841880e-05
## Tmax_dece 2.632981e-05

Interprétation des COS2 des variables quantitatives supplémentaires sur les axes factoriels.

res.temperMax.ca$col.sup$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        Dim 6
## lat  0.55942746 0.10428973 0.04968068 0.07020953 0.102357262 0.0001057031
## long 0.04516227 0.08457691 0.43743646 0.08093739 0.001452151 0.0109937037
##            Dim 7       Dim 8       Dim 9      Dim 10       Dim 11
## lat  0.003113198 0.011014263 0.002916216 0.003594508 5.453055e-06
## long 0.115358067 0.001503865 0.007617375 0.004185784 8.471592e-06

Interprétation des COS2 des variables qualitatives supplémentaires sur les axes factoriels.

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

##                                           Dim 1        Dim 2        Dim 3
## reg_admin. Occitanie                  0.7945879 1.132521e-03 0.0849367036
## reg_admin.Auvergne-Rhone-Alpes        0.8569479 1.269663e-01 0.0018068318
## reg_admin.Bourgogne-Franche-Comte     0.9774923 8.227131e-05 0.0061667930
## reg_admin.Bretagne                    0.8747406 7.672667e-02 0.0163382141
## reg_admin.Centre-Val de Loire         0.9514385 2.296822e-02 0.0064847685
## reg_admin.Corse                       0.9893627 4.173513e-06 0.0086448743
## reg_admin.Grand-Est                   0.9903416 3.648280e-03 0.0026700930
## reg_admin.Hauts-de-France             0.9479858 4.558184e-02 0.0003415250
## reg_admin.Ile-de-France               0.9278374 6.617481e-02 0.0002571179
## reg_admin.Normandie                   0.3995142 4.083696e-01 0.0041971676
## reg_admin.Nouvelle-Aquitaine          0.8645602 1.620741e-03 0.1184775298
## reg_admin.Occitanie                   0.7125262 2.709105e-01 0.0015687167
## reg_admin.Pays-de-la-Loire            0.5025532 3.474148e-01 0.0023105232
## reg_admin.Picardie                    0.9380626 4.910944e-02 0.0046001176
## reg_admin.Provence-Alpes-Cotes-d'Azur 0.9573224 3.717675e-03 0.0271611078
## reg_clim.Climat de montagne           0.6618652 3.218625e-01 0.0016701344
## reg_clim.Climat mediterraneen         0.9816400 3.835101e-03 0.0138948765
## reg_clim.Climat nord-ouest            0.9103959 5.336141e-02 0.0005539288
## reg_clim.Climat oceanique aquitain    0.8961886 4.486064e-03 0.0875572747
## reg_clim.Climat oceanique Aquitain    0.5926396 1.824200e-02 0.3093626843
## reg_clim.Climat oceanique degrade     0.9784601 1.743015e-02 0.0013281760
## reg_clim.Climat oceanique nord-ouest  0.4509095 4.479412e-01 0.0191363655
## reg_clim.Climat semi-continental      0.9922350 6.191492e-07 0.0014905429
##                                              Dim 4        Dim 5        Dim 6
## reg_admin. Occitanie                  5.771261e-05 0.0925749811 6.841658e-03
## reg_admin.Auvergne-Rhone-Alpes        2.324859e-03 0.0072761091 3.812430e-03
## reg_admin.Bourgogne-Franche-Comte     1.184776e-02 0.0008238631 1.533949e-03
## reg_admin.Bretagne                    3.402350e-03 0.0191485316 6.415578e-03
## reg_admin.Centre-Val de Loire         1.877548e-03 0.0123094006 1.136567e-03
## reg_admin.Corse                       3.260686e-04 0.0002199334 1.649967e-04
## reg_admin.Grand-Est                   1.271841e-03 0.0005155529 9.095962e-04
## reg_admin.Hauts-de-France             2.667909e-03 0.0004763954 1.419797e-04
## reg_admin.Ile-de-France               3.846889e-04 0.0038219143 2.099807e-05
## reg_admin.Normandie                   9.922830e-02 0.0215447040 3.958790e-02
## reg_admin.Nouvelle-Aquitaine          1.027157e-05 0.0075090428 5.991628e-03
## reg_admin.Occitanie                   7.766983e-04 0.0034968724 1.329341e-03
## reg_admin.Pays-de-la-Loire            1.905862e-03 0.0304921879 2.506622e-02
## reg_admin.Picardie                    3.498523e-03 0.0021773087 1.291333e-04
## reg_admin.Provence-Alpes-Cotes-d'Azur 4.212160e-04 0.0035124996 3.262642e-04
## reg_clim.Climat de montagne           1.054093e-02 0.0025749391 3.530168e-04
## reg_clim.Climat mediterraneen         3.464796e-04 0.0001953920 2.737618e-05
## reg_clim.Climat nord-ouest            1.079714e-03 0.0286224878 8.203942e-04
## reg_clim.Climat oceanique aquitain    7.750856e-05 0.0095241807 7.568596e-04
## reg_clim.Climat oceanique Aquitain    3.318149e-02 0.0421848281 6.882417e-04
## reg_clim.Climat oceanique degrade     4.572670e-04 0.0016436236 1.307873e-04
## reg_clim.Climat oceanique nord-ouest  3.489024e-02 0.0297257688 1.778770e-03
## reg_clim.Climat semi-continental      3.038867e-03 0.0024524618 1.614014e-04
##                                              Dim 7        Dim 8        Dim 9
## reg_admin. Occitanie                  1.096419e-02 7.755636e-03 1.118111e-03
## reg_admin.Auvergne-Rhone-Alpes        1.491950e-05 4.147482e-05 8.724113e-05
## reg_admin.Bourgogne-Franche-Comte     1.105170e-03 5.338167e-06 8.701841e-05
## reg_admin.Bretagne                    2.487997e-03 1.550300e-04 2.110557e-04
## reg_admin.Centre-Val de Loire         2.503406e-04 2.591508e-03 6.539731e-04
## reg_admin.Corse                       1.255938e-04 1.016105e-03 4.336568e-05
## reg_admin.Grand-Est                   2.139146e-04 1.031037e-04 2.536573e-04
## reg_admin.Hauts-de-France             1.559708e-03 6.269170e-04 7.794401e-05
## reg_admin.Ile-de-France               5.746454e-04 2.044015e-04 3.749240e-04
## reg_admin.Normandie                   6.922666e-04 2.003425e-02 7.510589e-05
## reg_admin.Nouvelle-Aquitaine          1.051792e-04 7.234613e-04 9.106623e-04
## reg_admin.Occitanie                   6.278758e-03 1.976929e-03 2.899789e-04
## reg_admin.Pays-de-la-Loire            5.215212e-02 1.396354e-02 1.159498e-02
## reg_admin.Picardie                    5.799617e-04 4.414978e-04 1.252617e-04
## reg_admin.Provence-Alpes-Cotes-d'Azur 5.705472e-03 5.942769e-04 9.069948e-04
## reg_clim.Climat de montagne           3.754665e-05 8.309516e-04 4.800464e-07
## reg_clim.Climat mediterraneen         3.761884e-05 6.596655e-07 1.952355e-05
## reg_clim.Climat nord-ouest            3.859590e-04 3.070421e-03 1.621800e-03
## reg_clim.Climat oceanique aquitain    3.707633e-06 1.277721e-03 3.268037e-06
## reg_clim.Climat oceanique Aquitain    2.112446e-03 4.034877e-04 6.520261e-04
## reg_clim.Climat oceanique degrade     2.612452e-04 2.377282e-04 1.843730e-05
## reg_clim.Climat oceanique nord-ouest  1.297661e-02 2.624786e-03 6.191872e-06
## reg_clim.Climat semi-continental      8.719029e-05 1.568598e-04 3.389597e-04
##                                             Dim 10       Dim 11
## reg_admin. Occitanie                  1.029321e-06 2.952204e-05
## reg_admin.Auvergne-Rhone-Alpes        7.050974e-04 1.681494e-05
## reg_admin.Bourgogne-Franche-Comte     3.356546e-05 8.219640e-04
## reg_admin.Bretagne                    1.500042e-04 2.239208e-04
## reg_admin.Centre-Val de Loire         2.812681e-04 7.881824e-06
## reg_admin.Corse                       8.915046e-06 8.330631e-05
## reg_admin.Grand-Est                   4.494936e-05 2.740501e-05
## reg_admin.Hauts-de-France             1.524227e-04 3.875467e-04
## reg_admin.Ile-de-France               1.609720e-04 1.880824e-04
## reg_admin.Normandie                   4.749677e-03 2.006910e-03
## reg_admin.Nouvelle-Aquitaine          9.993810e-07 9.025445e-05
## reg_admin.Occitanie                   8.291288e-04 1.688426e-05
## reg_admin.Pays-de-la-Loire            1.191500e-02 6.315229e-04
## reg_admin.Picardie                    8.118113e-04 4.643065e-04
## reg_admin.Provence-Alpes-Cotes-d'Azur 1.836196e-04 1.485071e-04
## reg_clim.Climat de montagne           1.800953e-04 8.411317e-05
## reg_clim.Climat mediterraneen         1.886992e-07 2.793462e-06
## reg_clim.Climat nord-ouest            8.779953e-05 1.537744e-07
## reg_clim.Climat oceanique aquitain    1.925432e-05 1.056073e-04
## reg_clim.Climat oceanique Aquitain    5.220410e-04 1.118529e-05
## reg_clim.Climat oceanique degrade     2.818396e-05 4.325151e-06
## reg_clim.Climat oceanique nord-ouest  1.008096e-05 4.077106e-07
## reg_clim.Climat semi-continental      1.611074e-06 3.651556e-05

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

res.temperMax.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        Dim 6
## 1  0.90401976 7.655012e-02 2.033067e-04 7.166296e-03 6.308970e-03 3.344952e-03
## 2  0.98948416 2.841900e-03 1.194074e-03 1.421885e-04 1.347038e-03 5.098953e-04
## 3  0.91687521 4.320936e-02 6.865043e-05 1.462094e-02 1.039505e-03 5.407557e-04
## 4  0.98251428 1.971041e-04 1.423204e-02 1.255815e-04 3.618709e-04 1.054000e-03
## 5  0.82651167 1.017908e-01 2.572314e-04 5.407976e-02 9.512728e-03 4.715127e-05
## 6  0.89610254 3.367892e-02 4.087809e-02 2.828410e-03 1.496912e-02 8.032651e-05
## 7  0.47598624 4.185387e-01 5.655550e-02 1.916346e-02 1.645240e-03 5.551250e-03
## 8  0.96799557 1.785466e-02 8.774072e-05 3.458203e-03 3.528399e-03 4.411335e-03
## 9  0.98179202 5.873363e-04 1.417741e-02 2.819177e-04 1.814296e-03 4.753473e-04
## 10 0.93806264 4.910944e-02 4.600118e-03 3.498523e-03 2.177309e-03 1.291333e-04
## 11 0.59263957 1.824200e-02 3.093627e-01 3.318149e-02 4.218483e-02 6.882417e-04
## 12 0.95308379 6.269223e-03 2.809912e-02 4.606457e-04 2.077521e-03 5.944429e-03
## 13 0.93500451 1.208974e-02 3.853792e-02 2.610872e-03 2.363050e-04 1.401472e-03
## 14 0.94205414 5.966668e-03 2.926539e-02 1.210035e-02 3.190481e-03 1.398761e-03
## 15 0.97258057 2.290573e-04 2.282157e-03 8.778735e-03 2.403318e-04 4.513884e-03
## 16 0.83717619 9.725944e-02 1.563023e-02 9.288401e-03 2.044281e-02 1.456355e-02
## 17 0.23321683 5.178079e-01 5.242666e-02 7.851395e-02 1.220279e-03 9.160156e-02
## 18 0.97824767 6.135724e-05 7.335734e-03 5.061754e-03 6.039691e-04 9.879312e-05
## 19 0.97597327 1.238975e-02 3.660672e-03 5.905583e-05 5.937838e-04 1.694742e-04
## 20 0.65860368 2.256568e-01 2.784840e-02 1.170939e-04 3.552286e-03 9.378569e-05
## 21 0.54108064 1.700663e-01 9.905460e-02 1.271302e-01 4.498181e-02 4.505256e-03
## 22 0.97658695 1.224928e-02 7.129830e-05 4.385619e-04 3.179493e-03 2.643045e-03
## 23 0.49387973 3.651179e-01 1.133721e-02 4.432349e-02 2.173415e-02 5.042044e-02
## 24 0.65061396 1.221379e-01 2.613581e-02 2.123051e-02 1.599041e-02 1.273133e-01
## 25 0.60945505 3.023289e-01 1.596129e-02 9.853911e-03 1.455045e-02 3.302392e-02
## 26 0.85946412 4.067378e-02 1.840351e-02 6.143831e-02 4.110244e-06 2.975404e-03
## 27 0.98505331 2.592570e-04 1.171263e-02 7.149492e-05 1.765840e-05 3.997026e-05
## 28 0.05791367 4.100393e-01 3.688849e-01 7.546014e-02 6.873960e-02 6.148693e-04
## 29 0.91869193 5.303681e-02 8.577446e-03 8.978831e-04 3.469551e-03 9.038859e-03
## 30 0.98633189 1.447240e-03 7.163466e-03 5.672311e-07 1.839893e-03 5.068868e-04
## 31 0.82084812 1.245331e-01 1.569058e-02 1.790377e-02 1.416163e-02 3.650693e-03
## 32 0.97612660 1.190322e-02 1.835072e-03 4.782015e-04 2.130747e-03 3.128240e-03
## 33 0.81322921 1.339219e-01 2.414889e-03 1.756833e-02 9.206153e-03 9.725261e-03
## 34 0.90818109 3.117119e-03 2.742917e-02 2.338937e-03 2.506329e-02 2.965337e-02
## 35 0.75142881 1.708589e-01 5.956205e-05 7.094822e-03 1.027557e-02 6.505100e-03
## 36 0.90617455 8.357871e-02 1.234247e-04 1.463226e-03 6.969582e-03 1.973553e-04
## 37 0.15976379 3.929575e-01 9.382738e-03 1.975268e-01 1.693986e-01 2.767942e-02
## 38 0.89021549 2.094412e-04 3.624811e-02 1.950039e-04 5.704732e-02 5.351151e-03
## 39 0.79511783 1.173235e-01 1.205465e-02 3.519222e-03 3.390714e-02 2.679991e-03
## 40 0.70798908 2.593630e-01 1.424586e-03 1.486071e-02 9.113934e-03 4.959706e-03
## 41 0.93460904 4.854317e-02 6.925177e-04 3.262728e-03 2.085784e-05 4.216288e-04
## 42 0.78463892 1.011052e-01 6.464182e-02 2.871216e-02 6.784675e-05 1.483283e-04
## 43 0.78725502 1.209788e-01 5.660687e-04 4.722303e-02 3.374509e-02 2.870438e-03
## 44 0.93229677 3.755364e-02 5.086601e-03 1.898598e-02 1.759799e-03 1.492517e-04
## 45 0.94964734 1.034297e-02 1.743587e-02 2.315001e-03 5.790074e-05 1.880592e-03
## 46 0.98679951 3.855307e-03 7.024330e-03 6.921119e-04 9.925185e-06 5.429175e-04
## 47 0.50818541 4.377143e-01 7.084709e-04 3.340657e-02 1.313518e-02 2.251709e-03
## 48 0.79458793 1.132521e-03 8.493670e-02 5.771261e-05 9.257498e-02 6.841658e-03
## 49 0.97700337 8.171893e-03 9.917385e-03 2.345323e-03 5.298623e-05 9.365466e-04
## 50 0.99023079 2.058304e-03 3.810326e-03 4.352753e-04 7.457805e-04 1.461732e-03
## 51 0.11786748 5.652252e-01 8.139940e-04 1.248180e-02 1.559642e-02 9.345631e-02
## 52 0.92557463 4.751588e-03 3.555570e-02 2.039762e-02 4.540606e-03 3.431580e-03
## 53 0.97741085 3.889068e-03 8.547134e-03 2.639990e-04 1.817849e-03 2.948819e-03
## 54 0.74663846 1.138805e-01 8.696756e-02 2.263554e-02 2.037940e-03 9.183133e-07
## 55 0.61504853 1.938424e-01 1.170122e-01 2.913257e-02 6.395390e-03 5.163121e-04
## 56 0.91450868 7.238987e-02 8.615646e-05 6.779672e-03 3.517476e-03 5.704865e-04
## 57 0.95355977 5.431773e-04 3.579018e-02 1.285367e-03 4.882581e-03 2.441372e-05
## 58 0.96062658 1.161658e-02 9.187395e-03 1.654033e-03 2.207415e-04 5.890450e-03
## 59 0.85471933 6.628900e-02 8.497592e-03 6.784677e-03 2.107068e-02 1.270106e-02
## 60 0.76408187 1.160126e-01 1.695658e-02 2.537912e-04 2.151807e-02 6.901574e-02
## 61 0.29814702 6.312279e-01 1.400227e-02 1.753276e-02 2.070900e-02 3.302553e-05
## 62 0.93708564 5.833880e-02 2.648998e-06 1.858299e-04 1.747142e-03 1.115875e-04
## 63 0.51119829 3.157694e-01 4.356620e-02 1.109786e-02 2.720696e-03 2.840033e-02
## 64 0.66234152 2.805306e-01 8.035023e-04 5.619505e-03 3.728474e-02 9.308113e-03
## 65 0.85491707 5.727806e-02 6.882610e-02 1.348189e-04 1.292699e-02 4.199625e-04
## 66 0.96718395 2.766032e-02 1.015796e-03 6.764390e-04 7.147098e-05 1.220688e-04
## 67 0.96659191 6.967268e-03 8.423591e-05 1.442862e-02 3.976267e-03 3.938033e-05
## 68 0.96031665 4.920715e-03 2.013697e-02 3.948564e-03 2.605399e-05 1.971433e-04
## 69 0.97107234 1.628838e-03 8.542815e-03 4.668018e-05 5.628071e-03 3.988872e-03
## 70 0.81919766 1.413673e-01 1.718123e-03 1.743958e-03 3.476855e-03 7.045209e-03
## 71 0.91039593 5.336141e-02 5.539288e-04 1.079714e-03 2.862249e-02 8.203942e-04
## 72 0.93193891 5.332696e-02 3.667803e-03 2.293340e-03 4.064029e-03 4.101724e-05
## 73 0.95608316 3.122101e-02 2.361576e-03 1.062255e-03 4.659238e-03 1.084400e-05
## 74 0.80613984 1.247647e-02 3.214872e-02 9.073725e-02 4.712840e-04 4.074067e-02
##           Dim 7        Dim 8        Dim 9       Dim 10       Dim 11
## 1  1.953649e-05 3.518828e-04 1.449143e-05 7.826872e-04 1.237992e-03
## 2  2.969342e-03 7.078274e-04 7.923911e-04 1.871471e-06 9.315477e-06
## 3  2.594637e-03 1.602935e-02 1.339976e-07 4.843592e-03 1.778709e-04
## 4  9.380249e-05 5.705039e-04 4.939134e-04 1.713172e-04 1.855811e-04
## 5  5.762858e-04 4.407023e-04 5.340006e-06 6.489015e-03 2.892787e-04
## 6  1.912713e-03 5.851124e-03 2.181795e-03 5.722409e-04 9.447228e-04
## 7  4.915898e-03 1.507050e-02 2.397746e-03 1.088382e-06 1.743811e-04
## 8  1.023525e-03 7.907622e-04 4.583199e-05 4.449796e-04 3.589990e-04
## 9  3.186908e-04 3.340940e-04 9.493152e-07 3.098213e-05 1.869538e-04
## 10 5.799617e-04 4.414978e-04 1.252617e-04 8.118113e-04 4.643065e-04
## 11 2.112446e-03 4.034877e-04 6.520261e-04 5.220410e-04 1.118529e-05
## 12 4.344971e-04 3.493417e-03 1.082261e-04 2.304435e-05 6.087612e-06
## 13 5.767270e-04 3.501054e-03 2.423048e-03 3.567980e-03 5.037978e-05
## 14 2.205688e-03 2.085232e-03 1.412557e-04 1.568157e-03 2.387433e-05
## 15 2.780612e-03 1.595815e-03 4.154443e-04 6.570090e-03 1.330597e-05
## 16 4.107412e-03 2.833465e-04 1.282018e-04 1.538582e-04 9.665526e-04
## 17 1.267991e-04 4.977270e-03 1.588261e-02 3.945685e-03 2.804726e-04
## 18 1.532465e-04 6.402092e-03 1.065144e-03 8.599109e-04 1.103318e-04
## 19 1.785415e-03 3.277128e-04 2.454519e-04 2.239518e-03 2.555890e-03
## 20 6.342913e-02 2.039740e-02 4.631438e-05 2.340026e-04 2.110555e-05
## 21 2.034399e-03 1.549802e-04 5.330938e-05 1.072199e-02 2.164574e-04
## 22 3.370798e-03 4.769128e-04 7.481351e-04 2.308789e-04 4.651608e-06
## 23 4.743440e-04 4.722429e-03 1.091846e-05 2.888659e-03 5.090757e-03
## 24 2.934821e-03 1.537674e-02 1.305433e-02 1.821504e-04 5.030082e-03
## 25 1.010474e-02 1.658349e-03 2.327935e-03 6.971760e-04 3.831384e-05
## 26 2.805234e-03 6.117781e-03 7.239489e-03 2.367455e-04 6.415115e-04
## 27 1.434392e-03 1.775632e-04 8.607629e-05 5.182636e-04 6.293907e-04
## 28 5.111263e-06 1.383112e-02 3.314811e-04 1.222674e-03 2.957122e-03
## 29 5.217856e-03 6.555281e-06 1.794771e-04 8.471497e-04 3.648304e-05
## 30 2.162978e-03 3.911448e-06 3.718693e-04 1.475033e-04 2.379726e-05
## 31 1.200437e-03 1.522460e-05 5.478841e-04 1.250149e-04 1.323518e-03
## 32 2.410269e-03 1.901163e-04 2.343008e-04 8.879694e-04 6.752668e-04
## 33 1.046940e-02 3.476240e-05 8.242717e-04 9.022904e-04 1.703580e-03
## 34 1.612442e-03 1.337051e-03 4.170026e-04 1.023060e-04 7.482296e-04
## 35 1.482284e-02 1.292448e-02 2.372436e-02 1.232032e-03 1.073514e-03
## 36 3.660303e-05 1.154599e-05 2.063123e-04 9.253510e-04 3.133333e-04
## 37 7.079396e-05 1.273263e-02 1.241813e-02 8.830190e-03 9.239365e-03
## 38 1.969877e-03 3.338977e-03 3.404348e-03 4.779589e-04 1.542327e-03
## 39 8.938323e-03 1.464505e-02 3.425250e-05 1.175343e-02 2.656100e-05
## 40 1.079047e-03 3.369086e-04 4.053398e-04 3.082709e-08 4.676913e-04
## 41 6.729785e-03 3.965979e-03 1.072402e-03 6.001990e-05 6.218697e-04
## 42 3.173811e-04 1.716891e-02 2.742149e-03 2.296692e-04 2.276003e-04
## 43 1.212819e-03 3.277263e-03 4.493551e-04 1.550324e-03 8.717457e-04
## 44 9.978946e-05 8.620070e-04 7.667084e-04 9.277608e-04 1.511697e-03
## 45 1.225744e-02 4.221540e-03 3.222833e-04 1.500645e-03 1.842361e-05
## 46 8.601622e-06 1.547696e-06 7.878827e-04 2.778193e-04 4.639056e-08
## 47 2.600441e-03 1.181522e-05 1.232936e-04 3.601919e-04 1.502577e-03
## 48 1.096419e-02 7.755636e-03 1.118111e-03 1.029321e-06 2.952204e-05
## 49 1.320252e-04 1.835247e-04 1.081935e-03 6.761663e-05 1.073930e-04
## 50 6.191262e-04 2.441682e-07 5.901168e-04 1.287844e-05 3.542403e-05
## 51 1.623758e-01 7.701074e-04 1.346356e-02 1.622795e-02 1.721341e-03
## 52 3.829489e-03 2.342733e-04 1.137834e-04 7.234930e-04 8.472418e-04
## 53 1.449650e-03 2.733487e-04 1.999630e-03 2.643298e-08 1.399627e-03
## 54 1.935770e-02 1.875674e-03 4.824894e-03 1.526057e-03 2.547650e-04
## 55 2.769460e-02 2.440082e-07 1.017717e-02 1.885896e-06 1.786959e-04
## 56 4.703542e-04 7.863292e-04 1.481617e-04 4.860912e-05 6.942061e-04
## 57 9.337656e-06 9.237483e-04 1.720191e-04 2.546489e-03 2.629150e-04
## 58 1.367538e-04 8.245139e-03 9.147370e-04 1.478522e-03 2.907523e-05
## 59 9.912639e-03 2.019397e-03 1.152731e-02 2.061983e-03 4.416332e-03
## 60 7.927710e-03 1.364359e-03 4.430517e-04 1.859081e-03 5.671327e-04
## 61 9.742057e-04 1.360851e-02 3.635938e-03 8.659677e-06 1.207140e-04
## 62 1.659837e-04 8.073643e-05 1.604751e-03 6.676055e-04 9.270147e-06
## 63 2.052143e-02 1.461066e-05 4.402252e-02 8.185084e-04 2.187017e-02
## 64 7.079321e-04 2.952369e-03 1.221044e-05 3.516166e-04 8.784299e-05
## 65 1.952872e-03 2.602498e-07 5.158446e-04 2.979654e-03 4.837122e-05
## 66 5.998199e-04 1.377234e-05 2.239684e-03 3.875020e-04 2.917815e-05
## 67 2.233007e-03 3.977037e-03 6.976840e-04 3.897118e-04 6.148737e-04
## 68 4.679440e-04 5.562725e-03 1.984782e-03 2.429469e-03 8.976864e-06
## 69 4.376490e-03 7.813111e-04 1.665690e-04 3.768010e-03 1.635345e-10
## 70 2.442276e-02 5.702399e-04 4.197193e-04 3.803318e-05 1.227449e-07
## 71 3.859590e-04 3.070421e-03 1.621800e-03 8.779953e-05 1.537744e-07
## 72 4.059045e-03 2.828967e-04 9.450623e-05 1.812910e-06 2.296722e-04
## 73 1.906444e-03 3.798700e-04 7.892819e-06 7.160625e-04 1.591646e-03
## 74 5.368356e-03 8.048546e-03 1.769707e-03 8.589303e-04 1.240236e-03

6. Aide à l’interprétation

6.1. Graphiques de la contribution

des variables

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

des individus

          fviz_ca_row(res.temperMax.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.temperMax.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.temperMax.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.temperMax.ca,
                      select.row = list(contrib = 5), 
                      #select.col = list(contrib = 5), # si on veut toutes les variables
                      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 ds coordonnées.

### fonction dimdesc() [in FactoMineR]

res.desc <- dimdesc(res.temperMax.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
## 46 -0.2579054
## 50 -0.2570897
## 32 -0.2503280
## 67 -0.2185894

– Pour les colonnes (pour nous, les variables)

### Description de la dimension 1 pour 4 colonnes

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

##                 coord
## long      -0.24529634
## lat       -0.13864262
## Tmax_juil -0.08928686
## Tmax_juin -0.08508948

Aide sur l’axe 2