Analyse Factorielle Multiple
Husson et al.
05/09/2018
1. Importer les données
QteVie <- read.table("https://r-stat-sc-donnees.github.io/QteVie.csv", header = TRUE, sep = ";", quote = "", check.names = FALSE, row.names = 1, fileEncoding = "latin1")
summary(QteVie) Logements sans sanitaires Coût logement Nb pièces par personne Revenu ménages
Min. : 0.000 Min. :11.00 Min. :0.900 Min. :11664
1st Qu.: 0.200 1st Qu.:19.75 1st Qu.:1.350 1st Qu.:18532
Median : 0.800 Median :21.00 Median :1.650 Median :23941
Mean : 2.533 Mean :20.83 Mean :1.661 Mean :24122
3rd Qu.: 3.825 3rd Qu.:22.00 3rd Qu.:1.925 3rd Qu.:28896
Max. :15.100 Max. :26.00 Max. :2.500 Max. :41355
Patrimoine financier Taux emploi Sécurité emploi Chômage longue durée
Min. : 3251 Min. :49.00 Min. : 2.400 Min. : 0.010
1st Qu.: 14254 1st Qu.:61.00 1st Qu.: 4.250 1st Qu.: 1.325
Median : 31413 Median :67.00 Median : 5.150 Median : 1.940
Mean : 40273 Mean :66.39 Mean : 5.672 Mean : 3.535
3rd Qu.: 56322 3rd Qu.:72.00 3rd Qu.: 6.025 3rd Qu.: 3.908
Max. :145769 Max. :82.00 Max. :17.800 Max. :18.390
Revenus moyens activité Horaires travail lourds Qualité réseau social
Min. :16193 Min. : 0.160 Min. :72.00
1st Qu.:22517 1st Qu.: 3.640 1st Qu.:87.00
Median :35982 Median : 6.850 Median :90.00
Mean :36054 Mean : 9.156 Mean :89.64
3rd Qu.:47713 3rd Qu.:12.363 3rd Qu.:94.00
Max. :56340 Max. :40.860 Max. :96.00
Satisfaction sur la vie Temps aux loisirs et à soi Pollution atmosphérique
Min. :4.800 Min. :13.42 Min. : 9.00
1st Qu.:5.975 1st Qu.:14.58 1st Qu.:14.50
Median :6.850 Median :14.94 Median :18.00
Mean :6.583 Mean :14.88 Mean :19.89
3rd Qu.:7.300 3rd Qu.:15.11 3rd Qu.:24.50
Max. :7.500 Max. :16.06 Max. :46.00
Qualité eau Espérance de vie Auto-évaluation état de santé Taux agression
Min. :56.00 Min. :70.20 Min. :30.00 Min. : 1.30
1st Qu.:76.00 1st Qu.:78.58 1st Qu.:63.75 1st Qu.: 2.55
Median :85.00 Median :81.00 Median :69.00 Median : 3.75
Mean :82.69 Mean :79.74 Mean :67.92 Mean : 4.05
3rd Qu.:91.25 3rd Qu.:81.58 3rd Qu.:76.25 3rd Qu.: 5.00
Max. :97.00 Max. :83.20 Max. :90.00 Max. :12.80
Taux homicides Niveau instruction Compétences élèves Années scolarité
Min. : 0.300 Min. :34.00 Min. :402.0 Min. :14.40
1st Qu.: 0.575 1st Qu.:71.75 1st Qu.:483.5 1st Qu.:16.40
Median : 0.900 Median :80.00 Median :498.5 Median :17.55
Mean : 2.831 Mean :75.36 Mean :494.1 Mean :17.49
3rd Qu.: 1.425 3rd Qu.:86.50 3rd Qu.:515.2 3rd Qu.:18.40
Max. :25.500 Max. :94.00 Max. :542.0 Max. :19.80
Région
Am Nord : 3
Am Sud : 2
Asie : 3
Europe Est : 7
Europe Nord : 5
Europe Ouest:14
Océanie : 2 2 et 3. Choisir les groupes de variables
library(FactoMineR)
afm <- MFA(QteVie, group = c(5,5,3,6,3,1), type = c(rep("s",5),"n"), name.group = c("Bien-être matériel","Emploi","Satisfaction","Santé et sécurité","Enseignement","Région"), num.group.sup = 6)
4. Choisir le nombre d’axes
barplot(afm$eig[,2], names = paste("Dim", 1:nrow(afm$eig)))
5. Analyser les résultats
summary(afm, nbelement = 10, nb.dec = 2, ncp = 2)
Call:
MFA(base = QteVie, group = c(5, 5, 3, 6, 3, 1), type = c(rep("s",
5), "n"), name.group = c("Bien-être matériel", "Emploi",
"Satisfaction", "Santé et sécurité", "Enseignement", "Région"),
num.group.sup = 6)
Eigenvalues
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7 Dim.8 Dim.9 Dim.10 Dim.11
Variance 3.37 1.29 1.04 0.78 0.51 0.40 0.39 0.25 0.23 0.16 0.13
% of var. 37.04 14.20 11.38 8.55 5.57 4.39 4.30 2.69 2.52 1.79 1.46
Cumulative % of var. 37.04 51.24 62.62 71.17 76.74 81.13 85.43 88.12 90.64 92.43 93.89
Dim.12 Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18 Dim.19 Dim.20 Dim.21 Dim.22
Variance 0.10 0.10 0.09 0.07 0.06 0.04 0.03 0.03 0.02 0.02 0.00
% of var. 1.13 1.06 1.02 0.72 0.61 0.46 0.38 0.31 0.21 0.17 0.03
Cumulative % of var. 95.02 96.09 97.11 97.83 98.44 98.90 99.28 99.58 99.80 99.97 100.00
Groups
Dim.1 ctr cos2 Dim.2 ctr cos2
Bien-être matériel | 0.76 22.46 0.47 | 0.10 7.79 0.01 |
Emploi | 0.62 18.33 0.28 | 0.68 52.27 0.34 |
Satisfaction | 0.61 18.20 0.29 | 0.30 23.01 0.07 |
Santé et sécurité | 0.84 24.77 0.52 | 0.12 9.01 0.01 |
Enseignement | 0.55 16.24 0.25 | 0.10 7.92 0.01 |
Supplementary group
Dim.1 cos2 Dim.2 cos2
Région | 0.47 0.04 | 0.34 0.02 |
Individuals (the 10 first)
Dim.1 ctr cos2 Dim.2 ctr cos2
Allemagne | 1.74 2.50 0.80 | 0.15 0.05 0.01 |
Australie | 1.83 2.75 0.53 | 0.65 0.91 0.07 |
Autriche | 0.76 0.48 0.22 | 0.83 1.48 0.25 |
Belgique | 1.37 1.55 0.36 | -0.39 0.33 0.03 |
Brésil | -2.71 6.04 0.39 | 1.41 4.29 0.11 |
Canada | 1.90 2.97 0.52 | 0.69 1.03 0.07 |
Chili | -2.70 6.01 0.60 | 1.09 2.53 0.10 |
Corée | -1.29 1.37 0.11 | 0.38 0.32 0.01 |
Danemark | 2.07 3.51 0.55 | -0.42 0.38 0.02 |
Espagne | -0.11 0.01 0.00 | -2.96 18.78 0.53 |
Continuous variables (the 10 first)
Dim.1 ctr cos2 Dim.2 ctr cos2
Logements sans sanitaires | -0.70 5.06 0.49 | 0.26 1.84 0.07 |
Coût logement | 0.16 0.26 0.02 | -0.32 2.82 0.10 |
Nb pièces par personne | 0.79 6.40 0.62 | 0.09 0.24 0.01 |
Revenu ménages | 0.82 6.94 0.67 | 0.19 0.96 0.04 |
Patrimoine financier | 0.61 3.81 0.37 | 0.27 1.94 0.07 |
Taux emploi | 0.68 5.35 0.46 | 0.53 8.52 0.28 |
Sécurité emploi | -0.19 0.43 0.04 | -0.71 15.13 0.50 |
Chômage longue durée | -0.21 0.51 0.04 | -0.88 23.24 0.77 |
Revenus moyens activité | 0.87 8.80 0.76 | 0.17 0.89 0.03 |
Horaires travail lourds | -0.53 3.24 0.28 | 0.39 4.48 0.15 |
Supplementary categories
Dim.1 cos2 v.test Dim.2 cos2 v.test
Am Nord | -0.37 0.03 -0.36 | 1.49 0.50 2.33 |
Am Sud | -2.71 0.61 -2.11 | 1.25 0.13 1.58 |
Asie | -1.74 0.37 -1.69 | 0.45 0.03 0.71 |
Europe Est | -1.01 0.37 -1.60 | -0.30 0.03 -0.77 |
Europe Nord | 1.85 0.74 2.40 | 0.11 0.00 0.23 |
Europe Ouest | 0.45 0.25 1.15 | -0.56 0.39 -2.31 |
Océanie | 1.66 0.55 1.29 | 0.51 0.05 0.65 |round(afm$group$RV, 2) Bien-être matériel Emploi Satisfaction Santé et sécurité Enseignement Région
Bien-être matériel 1.00 0.39 0.32 0.56 0.20 0.22
Emploi 0.39 1.00 0.46 0.35 0.26 0.23
Satisfaction 0.32 0.46 1.00 0.34 0.15 0.25
Santé et sécurité 0.56 0.35 0.34 1.00 0.51 0.30
Enseignement 0.20 0.26 0.15 0.51 1.00 0.24
Région 0.22 0.23 0.25 0.30 0.24 1.00
MFA 0.71 0.71 0.65 0.79 0.60 0.36
MFA
Bien-être matériel 0.71
Emploi 0.71
Satisfaction 0.65
Santé et sécurité 0.79
Enseignement 0.60
Région 0.36
MFA 1.00plot(afm, partial = c("France","Autriche"), invisible = "quali")
plot(afm, invisible = "quali", partial = "all", xlim = c(-5,5),
ylim = c(-5,5),
palette = palette(c("black", "transparent", "transparent", "blue", "transparent", "transparent")),
title = "Graphe des points partiels sur la satisfaction")
Factoshiny
library(Factoshiny)
res.shiny <- MFAshiny(QteVie)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