Capítulo 6: Análisis factorial de datos mixtos en R
#install.packages(c("FactoMineR", "factoextra"))
library("FactoMineR")
## Warning: package 'FactoMineR' was built under R version 4.2.3
library("factoextra")
## Warning: package 'factoextra' was built under R version 4.2.3
## Loading required package: ggplot2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library("FactoMineR")
data(wine)
df <- wine[,c(1,2, 16, 22, 29, 28, 30,31)]
head(df[, 1:7], 4)
## Label Soil Plante Acidity Harmony Intensity Overall.quality
## 2EL Saumur Env1 2.000 2.107 3.143 2.857 3.393
## 1CHA Saumur Env1 2.000 2.107 2.964 2.893 3.214
## 1FON Bourgueuil Env1 1.750 2.179 3.143 3.074 3.536
## 1VAU Chinon Env2 2.304 3.179 2.038 2.462 2.464
str(df)
## 'data.frame': 21 obs. of 8 variables:
## $ Label : Factor w/ 3 levels "Saumur","Bourgueuil",..: 1 1 2 3 1 2 2 1 3 1 ...
## $ Soil : Factor w/ 4 levels "Reference","Env1",..: 2 2 2 3 1 1 1 2 2 3 ...
## $ Plante : num 2 2 1.75 2.3 1.76 ...
## $ Acidity : num 2.11 2.11 2.18 3.18 2.57 ...
## $ Harmony : num 3.14 2.96 3.14 2.04 3.64 ...
## $ Intensity : num 2.86 2.89 3.07 2.46 3.64 ...
## $ Overall.quality: num 3.39 3.21 3.54 2.46 3.74 ...
## $ Typical : num 3.25 3.04 3.18 2.25 3.44 ...
library(FactoMineR)
res.famd <- FAMD(df, graph = FALSE)
print(res.famd)
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues and inertia"
## 2 "$var" "Results for the variables"
## 3 "$ind" "results for the individuals"
## 4 "$quali.var" "Results for the qualitative variables"
## 5 "$quanti.var" "Results for the quantitative variables"
library("factoextra")
eig.val <- get_eigenvalue(res.famd)
head(eig.val)
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 4.8315174 43.922886 43.92289
## Dim.2 1.8568797 16.880724 60.80361
## Dim.3 1.5824794 14.386176 75.18979
## Dim.4 1.1491200 10.446546 85.63633
## Dim.5 0.6518053 5.925503 91.56183
fviz_screeplot(res.famd)
var <- get_famd_var(res.famd)
var
## FAMD results for variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
# Coordinates of variables
head(var$coord)
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Plante 0.7344160 0.060551966 0.105902048 0.004011299 0.0010340559
## Acidity 0.1732738 0.491118153 0.126394029 0.115376784 0.0045862935
## Harmony 0.8943968 0.023628146 0.040124469 0.003653813 0.0086624633
## Intensity 0.6991811 0.134639254 0.065382234 0.023214984 0.0064730431
## Overall.quality 0.9115699 0.005246728 0.009336677 0.005445276 0.0007961880
## Typical 0.7808611 0.027094327 0.001549791 0.083446627 0.0005912942
# Cos2: quality of representation on the factore map
head(var$cos2)
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Plante 0.53936692 3.666541e-03 1.121524e-02 1.609052e-05 1.069272e-06
## Acidity 0.03002381 2.411970e-01 1.597545e-02 1.331180e-02 2.103409e-05
## Harmony 0.79994566 5.582893e-04 1.609973e-03 1.335035e-05 7.503827e-05
## Intensity 0.48885427 1.812773e-02 4.274836e-03 5.389355e-04 4.190029e-05
## Overall.quality 0.83095973 2.752815e-05 8.717353e-05 2.965103e-05 6.339153e-07
## Typical 0.60974400 7.341026e-04 2.401853e-06 6.963340e-03 3.496288e-07
# Contributions to the dimensions
head(var$contrib)
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Plante 15.200526 3.2609526 6.69215972 0.3490757 0.15864490
## Acidity 3.586323 26.4485720 7.98708850 10.0404466 0.70362936
## Harmony 18.511716 1.2724651 2.53554453 0.3179662 1.32899551
## Intensity 14.471254 7.2508336 4.13163258 2.0202401 0.99309457
## Overall.quality 18.867156 0.2825562 0.59000304 0.4738648 0.12215119
## Typical 16.161818 1.4591321 0.09793437 7.2617850 0.09071638
# Plot of variables
fviz_famd_var(res.famd, repel = TRUE)
# Contribution to the first dimension
fviz_contrib(res.famd, "var", axes = 1)
# Contribution to the second dimension
fviz_contrib(res.famd, "var", axes = 2)
quanti.var <- get_famd_var(res.famd, "quanti.var")
quanti.var
## FAMD results for quantitative variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
fviz_famd_var(res.famd, "quanti.var", repel = TRUE,
col.var = "black")
fviz_famd_var(res.famd, "quanti.var", col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
# Color by cos2 values: quality on the factor map
fviz_famd_var(res.famd, "quanti.var", col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
quali.var <- get_famd_var(res.famd, "quali.var")
quali.var
## FAMD results for qualitative variable categories
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
fviz_famd_var(res.famd, "quali.var", col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
)
ind <- get_famd_ind(res.famd)
ind
## FAMD results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
fviz_famd_ind(res.famd, col.ind = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
fviz_mfa_ind(res.famd,
habillage = "Label", # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, ellipse.type = "confidence",
repel = TRUE # Avoid text overlapping
)
fviz_ellipses(res.famd, c("Label", "Soil"), repel = TRUE)
## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## ℹ Please use `gather()` instead.
## ℹ The deprecated feature was likely used in the factoextra package.
## Please report the issue at <]8;;https://github.com/kassambara/factoextra/issueshttps://github.com/kassambara/factoextra/issues]8;;>.
fviz_ellipses(res.famd, 1:2, geom = "point")
Capítulo 7: análisis de factores múltiples
#install.packages(c("FactoMineR", "factoextra"))
library("FactoMineR")
library("factoextra")
library("FactoMineR")
data(wine)
colnames(wine)
## [1] "Label" "Soil"
## [3] "Odor.Intensity.before.shaking" "Aroma.quality.before.shaking"
## [5] "Fruity.before.shaking" "Flower.before.shaking"
## [7] "Spice.before.shaking" "Visual.intensity"
## [9] "Nuance" "Surface.feeling"
## [11] "Odor.Intensity" "Quality.of.odour"
## [13] "Fruity" "Flower"
## [15] "Spice" "Plante"
## [17] "Phenolic" "Aroma.intensity"
## [19] "Aroma.persistency" "Aroma.quality"
## [21] "Attack.intensity" "Acidity"
## [23] "Astringency" "Alcohol"
## [25] "Balance" "Smooth"
## [27] "Bitterness" "Intensity"
## [29] "Harmony" "Overall.quality"
## [31] "Typical"
library(FactoMineR)
data(wine)
res.mfa <- MFA(wine,
group = c(2, 5, 3, 10, 9, 2),
type = c("n", "s", "s", "s", "s", "s"),
name.group = c("origin","odor","visual", "odor.after.shaking", "taste", "overall"),
num.group.sup = c(1, 6),
graph = FALSE)
print(res.mfa)
## **Results of the Multiple Factor Analysis (MFA)**
## The analysis was performed on 21 individuals, described by 31 variables
## *Results are available in the following objects :
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$separate.analyses" "separate analyses for each group of variables"
## 3 "$group" "results for all the groups"
## 4 "$partial.axes" "results for the partial axes"
## 5 "$inertia.ratio" "inertia ratio"
## 6 "$ind" "results for the individuals"
## 7 "$quanti.var" "results for the quantitative variables"
## 8 "$quanti.var.sup" "results for the quantitative supplementary variables"
## 9 "$quali.var.sup" "results for the categorical supplementary variables"
## 10 "$summary.quanti" "summary for the quantitative variables"
## 11 "$summary.quali" "summary for the categorical variables"
## 12 "$global.pca" "results for the global PCA"
library("factoextra")
eig.val <- get_eigenvalue(res.mfa)
head(eig.val)
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 3.4619504 49.378382 49.37838
## Dim.2 1.3667683 19.494446 68.87283
## Dim.3 0.6154291 8.777969 77.65080
## Dim.4 0.3721997 5.308747 82.95954
## Dim.5 0.2703825 3.856511 86.81605
## Dim.6 0.2024033 2.886912 89.70297
fviz_screeplot(res.mfa)
group <- get_mfa_var(res.mfa, "group")
group
## Multiple Factor Analysis results for variable groups
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
## 4 "$correlation" "Correlation between groups and principal dimensions"
# Coordinates of groups
head(group$coord)
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## odor 0.7820738 0.61977283 0.37353451 0.17260092 0.08553276
## visual 0.8546846 0.04014481 0.01438360 0.04550736 0.02966750
## odor.after.shaking 0.9247734 0.46892047 0.18009116 0.10139051 0.11589439
## taste 0.9004187 0.23793016 0.04741982 0.05270088 0.03928784
# Cos2: quality of representation on the factore map
head(group$cos2)
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## odor 0.3799491 0.238613517 0.0866745169 0.018506155 0.0045445922
## visual 0.7284016 0.001607007 0.0002062976 0.002065011 0.0008776492
## odor.after.shaking 0.6245535 0.160582210 0.0236855692 0.007507471 0.0098089810
## taste 0.7222292 0.050429542 0.0020031144 0.002474125 0.0013749986
# Contributions to the dimensions
head(group$contrib)
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## odor 22.59055 45.345861 60.694972 46.37321 31.63399
## visual 24.68795 2.937207 2.337166 12.22660 10.97242
## odor.after.shaking 26.71250 34.308703 29.262699 27.24089 42.86313
## taste 26.00900 17.408230 7.705163 14.15930 14.53047
fviz_mfa_var(res.mfa, "group")
# Contribution to the first dimension
fviz_contrib(res.mfa, "group", axes = 1)
# Contribution to the second dimension
fviz_contrib(res.mfa, "group", axes = 2)
quanti.var <- get_mfa_var(res.mfa, "quanti.var")
quanti.var
## Multiple Factor Analysis results for quantitative variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
# Coordinates
head(quanti.var$coord)
## Dim.1 Dim.2 Dim.3 Dim.4
## Odor.Intensity.before.shaking 0.5908036 0.66723783 -0.02326175 0.3287015
## Aroma.quality.before.shaking 0.8352510 -0.07539908 -0.35417877 0.1414425
## Fruity.before.shaking 0.7160259 -0.15069626 -0.53748761 0.2517063
## Flower.before.shaking 0.4387181 -0.40937751 0.63731284 0.4029075
## Spice.before.shaking 0.0380525 0.86501993 0.12795122 -0.1822298
## Visual.intensity 0.8811873 0.23833245 0.14099033 -0.2128871
## Dim.5
## Odor.Intensity.before.shaking 0.05786231
## Aroma.quality.before.shaking 0.04992114
## Fruity.before.shaking 0.18981578
## Flower.before.shaking 0.12200773
## Spice.before.shaking 0.36741971
## Visual.intensity -0.17676282
# Cos2: quality on the factore map
head(quanti.var$cos2)
## Dim.1 Dim.2 Dim.3 Dim.4
## Odor.Intensity.before.shaking 0.349048863 0.445206325 0.000541109 0.10804466
## Aroma.quality.before.shaking 0.697644264 0.005685021 0.125442602 0.02000597
## Fruity.before.shaking 0.512693037 0.022709361 0.288892928 0.06335608
## Flower.before.shaking 0.192473567 0.167589944 0.406167661 0.16233443
## Spice.before.shaking 0.001447992 0.748259477 0.016371514 0.03320769
## Visual.intensity 0.776491025 0.056802358 0.019878273 0.04532093
## Dim.5
## Odor.Intensity.before.shaking 0.003348047
## Aroma.quality.before.shaking 0.002492121
## Fruity.before.shaking 0.036030029
## Flower.before.shaking 0.014885886
## Spice.before.shaking 0.134997242
## Visual.intensity 0.031245096
# Contributions to the dimensions
head(quanti.var$contrib)
## Dim.1 Dim.2 Dim.3 Dim.4
## Odor.Intensity.before.shaking 4.49733206 14.5296787 0.03921898 12.948424
## Aroma.quality.before.shaking 8.98882147 0.1855354 9.09194110 2.397581
## Fruity.before.shaking 6.60581103 0.7411389 20.93864000 7.592798
## Flower.before.shaking 2.47993227 5.4694372 29.43858302 19.454686
## Spice.before.shaking 0.01865671 24.4200703 1.18658923 3.979718
## Visual.intensity 7.91221841 1.4660681 1.13941864 4.295418
## Dim.5
## Odor.Intensity.before.shaking 0.5523351
## Aroma.quality.before.shaking 0.4111309
## Fruity.before.shaking 5.9439566
## Flower.before.shaking 2.4557588
## Spice.before.shaking 22.2708049
## Visual.intensity 4.0764862
fviz_mfa_var(res.mfa, "quanti.var", palette = "jco",
col.var.sup = "violet", repel = TRUE)
fviz_mfa_var(res.mfa, "quanti.var", palette = "jco",
col.var.sup = "violet", repel = TRUE,
geom = c("point", "text"), legend = "bottom")
# Contributions to dimension 1
fviz_contrib(res.mfa, choice = "quanti.var", axes = 1, top = 20,
palette = "jco")
# Contributions to dimension 2
fviz_contrib(res.mfa, choice = "quanti.var", axes = 2, top = 20,
palette = "jco")
fviz_mfa_var(res.mfa, "quanti.var", col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
col.var.sup = "violet", repel = TRUE,
geom = c("point", "text"))
# Color by cos2 values: quality on the factor map
fviz_mfa_var(res.mfa, col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
col.var.sup = "violet", repel = TRUE)
fviz_cos2(res.mfa, choice = "quanti.var", axes = 1)
ind <- get_mfa_ind(res.mfa)
ind
## Multiple Factor Analysis results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates"
## 2 "$cos2" "Cos2, quality of representation"
## 3 "$contrib" "Contributions"
## 4 "$coord.partiel" "Partial coordinates"
## 5 "$within.inertia" "Within inertia"
## 6 "$within.partial.inertia" "Within partial inertia"
fviz_mfa_ind(res.mfa, col.ind = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE)
fviz_mfa_ind(res.mfa,
habillage = "Label", # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, ellipse.type = "confidence",
repel = TRUE # Avoid text overlapping
)
fviz_ellipses(res.mfa, c("Label", "Soil"), repel = TRUE)
fviz_mfa_ind(res.mfa, partial = "all")
fviz_mfa_ind(res.mfa, partial = c("1DAM", "1VAU", "2ING"))
fviz_mfa_axes(res.mfa)
Capítulo 8: Agrupación jerárquica en componentes principales
Caso 1: Variables continuas
Caso 2: Agrupación en datos categóricos
Caso 3: Agrupación en clústeres en datos mixtos
#install.packages(c("FactoMineR", "factoextra"))
library(factoextra)
library(FactoMineR)
library(FactoMineR)
# Compute PCA with ncp = 3
res.pca <- PCA(USArrests, ncp = 3, graph = FALSE)
# Compute hierarchical clustering on principal components
res.hcpc <- HCPC(res.pca, graph = FALSE)
fviz_dend(res.hcpc,
cex = 0.7, # Label size
palette = "jco", # Color palette see ?ggpubr::ggpar
rect = TRUE, rect_fill = TRUE, # Add rectangle around groups
rect_border = "jco", # Rectangle color
labels_track_height = 0.8 # Augment the room for labels
)
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
## Please report the issue at <]8;;https://github.com/kassambara/factoextra/issueshttps://github.com/kassambara/factoextra/issues]8;;>.
fviz_cluster(res.hcpc,
repel = TRUE, # Avoid label overlapping
show.clust.cent = TRUE, # Show cluster centers
palette = "jco", # Color palette see ?ggpubr::ggpar
ggtheme = theme_minimal(),
main = "Factor map"
)
# Principal components + tree
plot(res.hcpc, choice = "3D.map")
head(res.hcpc$data.clust, 10)
## Murder Assault UrbanPop Rape clust
## Alabama 13.2 236 58 21.2 3
## Alaska 10.0 263 48 44.5 4
## Arizona 8.1 294 80 31.0 4
## Arkansas 8.8 190 50 19.5 3
## California 9.0 276 91 40.6 4
## Colorado 7.9 204 78 38.7 4
## Connecticut 3.3 110 77 11.1 2
## Delaware 5.9 238 72 15.8 2
## Florida 15.4 335 80 31.9 4
## Georgia 17.4 211 60 25.8 3
res.hcpc$desc.var$quanti
## $`1`
## v.test Mean in category Overall mean sd in category Overall sd
## UrbanPop -3.898420 52.07692 65.540 9.691087 14.329285
## Murder -4.030171 3.60000 7.788 2.269870 4.311735
## Rape -4.052061 12.17692 21.232 3.130779 9.272248
## Assault -4.638172 78.53846 170.760 24.700095 82.500075
## p.value
## UrbanPop 9.682222e-05
## Murder 5.573624e-05
## Rape 5.076842e-05
## Assault 3.515038e-06
##
## $`2`
## v.test Mean in category Overall mean sd in category Overall sd
## UrbanPop 2.793185 73.87500 65.540 8.652131 14.329285
## Murder -2.374121 5.65625 7.788 1.594902 4.311735
## p.value
## UrbanPop 0.005219187
## Murder 0.017590794
##
## $`3`
## v.test Mean in category Overall mean sd in category Overall sd
## Murder 4.357187 13.9375 7.788 2.433587 4.311735
## Assault 2.698255 243.6250 170.760 46.540137 82.500075
## UrbanPop -2.513667 53.7500 65.540 7.529110 14.329285
## p.value
## Murder 1.317449e-05
## Assault 6.970399e-03
## UrbanPop 1.194833e-02
##
## $`4`
## v.test Mean in category Overall mean sd in category Overall sd
## Rape 5.352124 33.19231 21.232 6.996643 9.272248
## Assault 4.356682 257.38462 170.760 41.850537 82.500075
## UrbanPop 3.028838 76.00000 65.540 10.347798 14.329285
## Murder 2.913295 10.81538 7.788 2.001863 4.311735
## p.value
## Rape 8.692769e-08
## Assault 1.320491e-05
## UrbanPop 2.454964e-03
## Murder 3.576369e-03
res.hcpc$desc.axes$quanti
## $`1`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.1 -5.175764 -1.964502 -5.639933e-16 0.6192556 1.574878
## p.value
## Dim.1 2.269806e-07
##
## $`2`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.2 3.585635 0.7428712 -5.369316e-16 0.6137936 0.9948694
## p.value
## Dim.2 0.0003362596
##
## $`3`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.1 2.058338 1.0610731 -5.639933e-16 0.5146613 1.5748783
## Dim.3 2.028887 0.3965588 3.535366e-17 0.3714503 0.5971291
## Dim.2 -4.536594 -1.4773302 -5.369316e-16 0.5750284 0.9948694
## p.value
## Dim.1 3.955769e-02
## Dim.3 4.246985e-02
## Dim.2 5.717010e-06
##
## $`4`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.1 4.986474 1.892656 -5.639933e-16 0.6126035 1.574878
## p.value
## Dim.1 6.149115e-07
res.hcpc$desc.ind$para
## Cluster: 1
## Idaho South Dakota Maine Iowa New Hampshire
## 0.3674381 0.4993032 0.5012072 0.5533105 0.5891145
## ------------------------------------------------------------
## Cluster: 2
## Ohio Oklahoma Pennsylvania Kansas Indiana
## 0.2796100 0.5047549 0.5088363 0.6039091 0.7100820
## ------------------------------------------------------------
## Cluster: 3
## Alabama South Carolina Georgia Tennessee Louisiana
## 0.3553460 0.5335189 0.6136865 0.8522640 0.8780872
## ------------------------------------------------------------
## Cluster: 4
## Michigan Arizona New Mexico Maryland Texas
## 0.3246254 0.4532480 0.5176322 0.9013514 0.9239792
Caso de variables categóricas
# Loading data
library(FactoMineR)
data(tea)
# Performing MCA
res.mca <- MCA(tea,
ncp = 20, # Number of components kept
quanti.sup = 19, # Quantitative supplementary variables
quali.sup = c(20:36), # Qualitative supplementary variables
graph=FALSE)
# Dendrogram
fviz_dend(res.hcpc, show_labels = FALSE)
# Individuals facor map
fviz_cluster(res.hcpc, geom = "point", main = "Factor map")
# Description by variables
res.hcpc$desc.var$test.chi2
## p.value df
## where 8.465616e-79 4
## how 3.144675e-47 4
## price 1.862462e-28 10
## tearoom 9.624188e-19 2
## pub 8.539893e-10 2
## friends 6.137618e-08 2
## resto 3.537876e-07 2
## How 3.616532e-06 6
## Tea 1.778330e-03 4
## sex 1.789593e-03 2
## frequency 1.973274e-03 6
## work 3.052988e-03 2
## tea.time 3.679599e-03 2
## lunch 1.052478e-02 2
## dinner 2.234313e-02 2
## always 3.600913e-02 2
## sugar 3.685785e-02 2
## sophisticated 4.077297e-02 2
# Description by variable categories
res.hcpc$desc.var$category
## $`1`
## Cla/Mod Mod/Cla Global p.value
## where=chain store 85.937500 93.750000 64.000000 2.094419e-40
## how=tea bag 84.117647 81.250000 56.666667 1.478564e-25
## tearoom=Not.tearoom 70.661157 97.159091 80.666667 1.082077e-18
## price=p_branded 83.157895 44.886364 31.666667 1.631861e-09
## pub=Not.pub 67.088608 90.340909 79.000000 1.249296e-08
## friends=Not.friends 76.923077 45.454545 34.666667 2.177180e-06
## resto=Not.resto 64.705882 81.250000 73.666667 4.546462e-04
## price=p_private label 90.476190 10.795455 7.000000 1.343844e-03
## tea.time=Not.tea time 67.938931 50.568182 43.666667 4.174032e-03
## How=alone 64.102564 71.022727 65.000000 9.868387e-03
## work=Not.work 63.380282 76.704545 71.000000 1.036429e-02
## sugar=sugar 66.206897 54.545455 48.333333 1.066744e-02
## always=Not.always 63.959391 71.590909 65.666667 1.079912e-02
## price=p_unknown 91.666667 6.250000 4.000000 1.559798e-02
## frequency=1 to 2/week 75.000000 18.750000 14.666667 1.649092e-02
## frequency=1/day 68.421053 36.931818 31.666667 1.958790e-02
## age_Q=15-24 68.478261 35.795455 30.666667 2.179803e-02
## price=p_cheap 100.000000 3.977273 2.333333 2.274539e-02
## lunch=Not.lunch 61.328125 89.204545 85.333333 2.681490e-02
## SPC=senior 42.857143 8.522727 11.666667 4.813710e-02
## lunch=lunch 43.181818 10.795455 14.666667 2.681490e-02
## always=always 48.543689 28.409091 34.333333 1.079912e-02
## sugar=No.sugar 51.612903 45.454545 51.666667 1.066744e-02
## work=work 47.126437 23.295455 29.000000 1.036429e-02
## tea.time=tea time 51.479290 49.431818 56.333333 4.174032e-03
## How=lemon 30.303030 5.681818 11.000000 5.943089e-04
## resto=resto 41.772152 18.750000 26.333333 4.546462e-04
## How=other 0.000000 0.000000 3.000000 2.952904e-04
## price=p_variable 44.642857 28.409091 37.333333 1.595638e-04
## frequency=+2/day 45.669291 32.954545 42.333333 9.872288e-05
## friends=friends 48.979592 54.545455 65.333333 2.177180e-06
## how=unpackaged 19.444444 3.977273 12.000000 4.328211e-07
## pub=pub 26.984127 9.659091 21.000000 1.249296e-08
## where=tea shop 6.666667 1.136364 10.000000 4.770573e-10
## price=p_upscale 18.867925 5.681818 17.666667 9.472539e-11
## how=tea bag+unpackaged 27.659574 14.772727 31.333333 1.927326e-13
## tearoom=tearoom 8.620690 2.840909 19.333333 1.082077e-18
## where=chain store+tea shop 11.538462 5.113636 26.000000 1.133459e-23
## v.test
## where=chain store 13.307475
## how=tea bag 10.449142
## tearoom=Not.tearoom 8.826287
## price=p_branded 6.030764
## pub=Not.pub 5.692859
## friends=Not.friends 4.736242
## resto=Not.resto 3.506146
## price=p_private label 3.206448
## tea.time=Not.tea time 2.864701
## How=alone 2.580407
## work=Not.work 2.563432
## sugar=sugar 2.553408
## always=Not.always 2.549133
## price=p_unknown 2.418189
## frequency=1 to 2/week 2.397866
## frequency=1/day 2.334149
## age_Q=15-24 2.293869
## price=p_cheap 2.277684
## lunch=Not.lunch 2.214202
## SPC=senior -1.976156
## lunch=lunch -2.214202
## always=always -2.549133
## sugar=No.sugar -2.553408
## work=work -2.563432
## tea.time=tea time -2.864701
## How=lemon -3.434198
## resto=resto -3.506146
## How=other -3.619397
## price=p_variable -3.775692
## frequency=+2/day -3.893709
## friends=friends -4.736242
## how=unpackaged -5.053925
## pub=pub -5.692859
## where=tea shop -6.226471
## price=p_upscale -6.475138
## how=tea bag+unpackaged -7.353743
## tearoom=tearoom -8.826287
## where=chain store+tea shop -10.029275
##
## $`2`
## Cla/Mod Mod/Cla Global p.value
## where=tea shop 90.000000 84.375 10.00000 3.703402e-30
## how=unpackaged 66.666667 75.000 12.00000 5.346850e-20
## price=p_upscale 49.056604 81.250 17.66667 2.392655e-17
## Tea=green 27.272727 28.125 11.00000 4.436713e-03
## sophisticated=sophisticated 13.488372 90.625 71.66667 8.080918e-03
## sex=M 16.393443 62.500 40.66667 9.511848e-03
## resto=Not.resto 13.122172 90.625 73.66667 1.587879e-02
## dinner=dinner 28.571429 18.750 7.00000 1.874042e-02
## escape.exoticism=Not.escape-exoticism 14.556962 71.875 52.66667 2.177458e-02
## how=tea bag+unpackaged 5.319149 15.625 31.33333 3.876799e-02
## escape.exoticism=escape-exoticism 6.338028 28.125 47.33333 2.177458e-02
## dinner=Not.dinner 9.318996 81.250 93.00000 1.874042e-02
## resto=resto 3.797468 9.375 26.33333 1.587879e-02
## Tea=Earl Grey 7.253886 43.750 64.33333 1.314753e-02
## sex=F 6.741573 37.500 59.33333 9.511848e-03
## sophisticated=Not.sophisticated 3.529412 9.375 28.33333 8.080918e-03
## where=chain store+tea shop 2.564103 6.250 26.00000 3.794134e-03
## price=p_variable 3.571429 12.500 37.33333 1.349384e-03
## age_Q=15-24 2.173913 6.250 30.66667 6.100227e-04
## price=p_branded 2.105263 6.250 31.66667 4.024289e-04
## how=tea bag 1.764706 9.375 56.66667 5.537403e-09
## where=chain store 1.562500 9.375 64.00000 1.664577e-11
## v.test
## where=tea shop 11.410559
## how=unpackaged 9.156781
## price=p_upscale 8.472945
## Tea=green 2.845318
## sophisticated=sophisticated 2.648670
## sex=M 2.593088
## resto=Not.resto 2.411690
## dinner=dinner 2.350655
## escape.exoticism=Not.escape-exoticism 2.294277
## how=tea bag+unpackaged -2.066641
## escape.exoticism=escape-exoticism -2.294277
## dinner=Not.dinner -2.350655
## resto=resto -2.411690
## Tea=Earl Grey -2.479748
## sex=F -2.593088
## sophisticated=Not.sophisticated -2.648670
## where=chain store+tea shop -2.894789
## price=p_variable -3.205264
## age_Q=15-24 -3.427119
## price=p_branded -3.538486
## how=tea bag -5.830161
## where=chain store -6.732775
##
## $`3`
## Cla/Mod Mod/Cla Global p.value
## where=chain store+tea shop 85.897436 72.826087 26.00000 5.730651e-34
## how=tea bag+unpackaged 67.021277 68.478261 31.33333 1.382641e-19
## tearoom=tearoom 77.586207 48.913043 19.33333 1.252051e-16
## pub=pub 63.492063 43.478261 21.00000 1.126679e-09
## friends=friends 41.836735 89.130435 65.33333 1.429181e-09
## price=p_variable 51.785714 63.043478 37.33333 1.572243e-09
## resto=resto 54.430380 46.739130 26.33333 2.406386e-07
## How=other 100.000000 9.782609 3.00000 1.807938e-05
## frequency=+2/day 41.732283 57.608696 42.33333 4.237330e-04
## tea.time=tea time 38.461538 70.652174 56.33333 8.453564e-04
## work=work 44.827586 42.391304 29.00000 9.079377e-04
## sex=F 37.078652 71.739130 59.33333 3.494245e-03
## lunch=lunch 50.000000 23.913043 14.66667 3.917102e-03
## How=lemon 51.515152 18.478261 11.00000 8.747530e-03
## sugar=No.sugar 36.129032 60.869565 51.66667 3.484061e-02
## home=home 31.615120 100.000000 97.00000 3.506563e-02
## home=Not.home 0.000000 0.000000 3.00000 3.506563e-02
## sugar=sugar 24.827586 39.130435 48.33333 3.484061e-02
## price=p_private label 9.523810 2.173913 7.00000 2.370629e-02
## how=unpackaged 13.888889 5.434783 12.00000 1.645107e-02
## How=alone 25.128205 53.260870 65.00000 5.300881e-03
## lunch=Not.lunch 27.343750 76.086957 85.33333 3.917102e-03
## sex=M 21.311475 28.260870 40.66667 3.494245e-03
## Tea=green 9.090909 3.260870 11.00000 2.545816e-03
## frequency=1 to 2/week 11.363636 5.434783 14.66667 1.604219e-03
## work=Not.work 24.882629 57.608696 71.00000 9.079377e-04
## tea.time=Not.tea time 20.610687 29.347826 43.66667 8.453564e-04
## where=tea shop 3.333333 1.086957 10.00000 1.466234e-04
## price=p_branded 14.736842 15.217391 31.66667 2.746948e-05
## resto=Not.resto 22.171946 53.260870 73.66667 2.406386e-07
## friends=Not.friends 9.615385 10.869565 34.66667 1.429181e-09
## pub=Not.pub 21.940928 56.521739 79.00000 1.126679e-09
## how=tea bag 14.117647 26.086957 56.66667 1.082059e-12
## tearoom=Not.tearoom 19.421488 51.086957 80.66667 1.252051e-16
## where=chain store 12.500000 26.086957 64.00000 1.711522e-19
## v.test
## where=chain store+tea shop 12.150084
## how=tea bag+unpackaged 9.053653
## tearoom=tearoom 8.278053
## pub=pub 6.090345
## friends=friends 6.052158
## price=p_variable 6.036775
## resto=resto 5.164845
## How=other 4.287379
## frequency=+2/day 3.524844
## tea.time=tea time 3.337500
## work=work 3.317602
## sex=F 2.920541
## lunch=lunch 2.884762
## How=lemon 2.621767
## sugar=No.sugar 2.110206
## home=home 2.107600
## home=Not.home -2.107600
## sugar=sugar -2.110206
## price=p_private label -2.261856
## how=unpackaged -2.398752
## How=alone -2.788157
## lunch=Not.lunch -2.884762
## sex=M -2.920541
## Tea=green -3.017842
## frequency=1 to 2/week -3.155139
## work=Not.work -3.317602
## tea.time=Not.tea time -3.337500
## where=tea shop -3.796720
## price=p_branded -4.193490
## resto=Not.resto -5.164845
## friends=Not.friends -6.052158
## pub=Not.pub -6.090345
## how=tea bag -7.119644
## tearoom=Not.tearoom -8.278053
## where=chain store -9.030332
res.hcpc$desc.axes
##
## Link between the cluster variable and the quantitative variables
## ================================================================
## Eta2 P-value
## Dim.2 0.66509105 2.828937e-71
## Dim.1 0.63497903 1.009707e-65
## Dim.4 0.11231020 2.073924e-08
## Dim.14 0.03141943 8.732913e-03
## Dim.6 0.02358138 2.890373e-02
##
## Description of each cluster by quantitative variables
## =====================================================
## $`1`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.6 2.647552 0.03433626 -2.721637e-17 0.2655618 0.2671712
## Dim.2 -7.796641 -0.13194656 -6.207419e-17 0.1813156 0.3486355
## Dim.1 -12.409741 -0.23196088 -1.678981e-16 0.2143767 0.3850642
## p.value
## Dim.6 8.107689e-03
## Dim.2 6.357699e-15
## Dim.1 2.314001e-35
##
## $`2`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.2 13.918285 0.81210870 -6.207419e-17 0.2340345 0.3486355
## Dim.4 4.350620 0.20342610 7.249699e-19 0.3700048 0.2793822
## Dim.14 2.909073 0.10749165 4.512196e-17 0.2161509 0.2207818
## Dim.13 2.341566 0.08930402 1.266782e-17 0.1606616 0.2278809
## Dim.3 2.208179 0.11087544 -4.161891e-17 0.2449710 0.3000159
## Dim.11 -2.234447 -0.08934293 6.504924e-17 0.2066708 0.2389094
## p.value
## Dim.2 4.905356e-44
## Dim.4 1.357531e-05
## Dim.14 3.625025e-03
## Dim.13 1.920305e-02
## Dim.3 2.723180e-02
## Dim.11 2.545367e-02
##
## $`3`
## v.test Mean in category Overall mean sd in category Overall sd
## Dim.1 13.485906 0.45155993 -1.678981e-16 0.2516544 0.3850642
## Dim.6 -2.221728 -0.05161581 -2.721637e-17 0.2488566 0.2671712
## Dim.4 -4.725270 -0.11479621 7.249699e-19 0.2924881 0.2793822
## p.value
## Dim.1 1.893256e-41
## Dim.6 2.630166e-02
## Dim.4 2.298093e-06
res.hcpc$desc.ind$para
## Cluster: 1
## 285 152 166 143 71
## 0.5884476 0.6242123 0.6242123 0.6244176 0.6478185
## ------------------------------------------------------------
## Cluster: 2
## 31 95 53 182 202
## 0.6620553 0.7442013 0.7610437 0.7948663 0.8154826
## ------------------------------------------------------------
## Cluster: 3
## 172 33 233 18 67
## 0.7380497 0.7407711 0.7503006 0.7572188 0.7701598