multiple correspondence analysis (mca) with factominer (tea … · 2020. 9. 30. · -1.0 -0.5 0.0...
TRANSCRIPT
Multiple Correspondence Analysis (MCA) withFactoMineR (tea dataset)Magalie Houée-Bigot & François Husson
Import data
setwd("C:/Users/houee/Downloads") # select the working directorytea <- read.table("data_MCA_Tea.csv", header=TRUE, sep=";")
header=TRUE : indicates that the file contains the names of the variables
sep=";" : indicates the fields separator (usually “;” or “,” for csv files)
It is important to check that the import is well done
summary(tea)
## breakfast tea.time evening lunch## breakfast :144 Not.tea time:131 evening :103 lunch : 44## Not.breakfast:156 tea time :169 Not.evening:197 Not.lunch:256############ dinner always home work## dinner : 21 always :103 home :291 Not.work:213## Not.dinner:279 Not.always:197 Not.home: 9 work : 87############ tearoom friends resto pub## Not.tearoom:242 friends :196 Not.resto:221 Not.pub:237## tearoom : 58 Not.friends:104 resto : 79 pub : 63############ Tea How sugar how## black : 74 alone:195 No.sugar:155 tea bag :170## Earl Grey:193 lemon: 33 sugar :145 tea bag+unpackaged: 94## green : 33 milk : 63 unpackaged : 36## other: 9######
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## where price age sex## chain store :192 p_branded : 95 Min. :15.00 F:178## chain store+tea shop: 78 p_cheap : 7 1st Qu.:23.00 M:122## tea shop : 30 p_private label: 21 Median :32.00## p_unknown : 12 Mean :37.05## p_upscale : 53 3rd Qu.:48.00## p_variable :112 Max. :90.00#### SPC Sport age_Q frequency## employee :59 Not.sportsman:121 +60 :38 +2/day :127## middle :40 sportsman :179 15-24:92 1 to 2/week: 44## non-worker :64 25-34:69 1/day : 95## other worker:20 35-44:40 3 to 6/week: 34## senior :35 45-59:61## student :70## workman :12## escape.exoticism spirituality healthy## escape-exoticism :142 Not.spirituality:206 healthy :210## Not.escape-exoticism:158 spirituality : 94 Not.healthy: 90############ diuretic friendliness iron.absorption## diuretic :174 friendliness :242 iron absorption : 31## Not.diuretic:126 Not.friendliness: 58 Not.iron absorption:269############ feminine sophisticated slimming## feminine :129 Not.sophisticated: 85 No.slimming:255## Not.feminine:171 sophisticated :215 slimming : 45############ exciting relaxing effect.on.health## exciting :116 No.relaxing:113 effect on health : 66## No.exciting:184 relaxing :187 No.effect on health:234##########
2
Loading FactoMineR
library(FactoMineR)
MCA
res <- MCA(tea, quanti.sup=19, quali.sup=c(20:36))
−2 −1 0 1 2
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MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
breakfast
Not.breakfastNot.tea timetea timeeveningNot.evening
lunch
Not.lunch
dinner
Not.dinneralwaysNot.alwayshomeNot.home
Not.work
work
Not.tearoom
tearoom
friends
Not.friendsNot.resto
resto
Not.pubpub
black
Earl Grey
green
alone
lemon
milk
otherNo.sugar
sugar
tea bag
tea bag+unpackaged
unpackaged
chain store
chain store+tea shop
tea shop
p_brandedp_cheap
p_private label
p_unknown
p_upscale
p_variableF
M
employee
middlenon−workerother workersenior
student
workman
Not.sportsmansportsman
+60
15−24
25−3435−4445−59+2/day1 to 2/week
1/day3 to 6/week
escape−exoticismNot.escape−exoticismNot.spiritualityspiritualityhealthyNot.healthydiureticNot.diureticfriendlinessNot.friendlinessiron absorption
Not.iron absorptionfeminineNot.feminine
Not.sophisticated
sophisticatedNo.slimmingslimming
excitingNo.excitingNo.relaxingrelaxing
effect on healthNo.effect on health
3
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0MCA factor map
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Dim 1 (9.88%)
Dim
2 (
8.10
%)
breakfasttea.time
evening lunchdinner
alwayshome
work
tearoomfriends
resto
pub
Tea
Howsugar
how
whereprice
sexSPC
Sport
age_Q
frequencyescape.exoticismspiritualityhealthydiuretic friendlinessiron.absorptionfemininesophisticated
slimmingexcitingrelaxingeffect.on.health
age
5
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Supplementary variables on the MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%) age
Outputs can be summarized with the function summary.
summary(res, ncp=3, nbelements=Inf) ## fonction summary.MCA
Outputs are given for the first 2 dimensions (by default 3 dimensions are given) and for the 5 first elements.
summary(res, ncp=2, nbelements=5)
#### Call:## MCA(X = tea, quanti.sup = 19, quali.sup = c(20:36))###### Eigenvalues## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6## Variance 0.148 0.122 0.090 0.078 0.074 0.071
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## % of var. 9.885 8.103 6.001 5.204 4.917 4.759## Cumulative % of var. 9.885 17.988 23.989 29.192 34.109 38.868## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11 Dim.12## Variance 0.068 0.065 0.062 0.059 0.057 0.054## % of var. 4.522 4.355 4.123 3.902 3.805 3.628## Cumulative % of var. 43.390 47.745 51.867 55.769 59.574 63.202## Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18## Variance 0.052 0.049 0.048 0.047 0.046 0.040## % of var. 3.462 3.250 3.221 3.127 3.037 2.683## Cumulative % of var. 66.664 69.914 73.135 76.262 79.298 81.982## Dim.19 Dim.20 Dim.21 Dim.22 Dim.23 Dim.24## Variance 0.038 0.037 0.036 0.035 0.031 0.029## % of var. 2.541 2.438 2.378 2.323 2.055 1.915## Cumulative % of var. 84.523 86.961 89.339 91.662 93.717 95.633## Dim.25 Dim.26 Dim.27## Variance 0.027 0.021 0.017## % of var. 1.821 1.407 1.139## Cumulative % of var. 97.454 98.861 100.000#### Individuals (the 5 first)## Dim.1 ctr cos2 Dim.2 ctr cos2## 1 | -0.541 0.658 0.143 | -0.149 0.061 0.011 |## 2 | -0.361 0.293 0.133 | -0.078 0.017 0.006 |## 3 | 0.073 0.012 0.003 | -0.169 0.079 0.018 |## 4 | -0.572 0.735 0.235 | 0.018 0.001 0.000 |## 5 | -0.253 0.144 0.079 | -0.118 0.038 0.017 |#### Categories (the 5 first)## Dim.1 ctr cos2 v.test Dim.2 ctr cos2 v.test## breakfast | 0.166 0.495 0.025 2.756 | -0.166 0.607 0.026 -2.764## Not.breakfast | -0.153 0.457 0.025 -2.756 | 0.154 0.560 0.026 2.764## Not.tea time | -0.498 4.053 0.192 -7.578 | 0.093 0.174 0.007 1.423## tea time | 0.386 3.142 0.192 7.578 | -0.072 0.135 0.007 -1.423## evening | 0.319 1.307 0.053 3.985 | -0.058 0.053 0.002 -0.728#### breakfast |## Not.breakfast |## Not.tea time |## tea time |## evening |#### Categorical variables (eta2)## Dim.1 Dim.2## breakfast | 0.025 0.026 |## tea.time | 0.192 0.007 |## evening | 0.053 0.002 |## lunch | 0.075 0.026 |## dinner | 0.033 0.048 |#### Supplementary categories (the 5 first)## Dim.1 cos2 v.test Dim.2 cos2 v.test## F | 0.151 0.033 3.158 | -0.109 0.017 -2.278 |## M | -0.221 0.033 -3.158 | 0.159 0.017 2.278 |## employee | -0.153 0.006 -1.313 | -0.151 0.006 -1.289 |
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## middle | -0.030 0.000 -0.205 | 0.336 0.017 2.281 |## non-worker | -0.036 0.000 -0.324 | 0.185 0.009 1.666 |#### Supplementary categorical variables (eta2)## Dim.1 Dim.2## sex | 0.033 0.017 |## SPC | 0.032 0.053 |## Sport | 0.001 0.000 |## age_Q | 0.008 0.077 |## frequency | 0.094 0.006 |#### Supplementary continuous variable## Dim.1 Dim.2## age | 0.042 | 0.204 |
Graph of the eigenvalues
barplot(res$eig[,2],main="Eigenvalues", names.arg=1:nrow(res$eig))
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Eigenvalues0
24
68
Graph with some labels
plot(res, label=c("var","quali.sup"), cex=0.7)
9
−2 −1 0 1 2
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01
2MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
breakfast
Not.breakfastNot.tea time
tea timeeveningNot.evening
lunch
Not.lunch
dinner
Not.dinneralways
Not.alwayshomeNot.home
Not.work
work
Not.tearoom
tearoom
friends
Not.friendsNot.resto
resto
Not.pub
pub
black
Earl Grey
green
alone
lemon
milk
other
No.sugar
sugar
tea bag
tea bag+unpackaged
unpackaged
chain store
chain store+tea shop
tea shop
p_brandedp_cheap
p_private label
p_unknown
p_upscale
p_variableF
M
employee
middlenon−worker
other workersenior
student
workman
Not.sportsmansportsman
+60
15−24
25−3435−4445−59+2/day
1 to 2/week
1/day
3 to 6/week
escape−exoticism
Not.escape−exoticismNot.spiritualityspiritualityhealthyNot.healthydiureticNot.diureticfriendliness
Not.friendlinessiron absorptionNot.iron absorptionfeminineNot.feminine
Not.sophisticated
sophisticatedNo.slimming
slimmingexcitingNo.excitingNo.relaxingrelaxing
effect on health
No.effect on health
Graphs with selection of elements
plot(res, invisible=c("var","quali.sup"), cex=0.7)
10
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0MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
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plot(res, invisible=c("ind","quali.sup"),autoLab="y",cex=0.7,title="Active categories")
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2Active categories
Dim 1 (9.88%)
Dim
2 (
8.10
%)
breakfast
Not.breakfastNot.tea time
tea timeevening
Not.evening
lunch
Not.lunch
dinner
Not.dinneralways
Not.always homeNot.home
Not.work
work
Not.tearoom
tearoom
friends
Not.friendsNot.resto
resto
Not.pub
pub
black
Earl Grey
green
alone
lemon
milk
other
No.sugar
sugar
tea bag
tea bag+unpackaged
unpackaged
chain store
chain store+tea shop
tea shop
p_brandedp_cheap
p_private label
p_unknown
p_upscale
p_variable
plot(res, invisible=c("ind","var"),autoLab="y",cex=0.7,title="Supplementary categories")
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Supplementary categories
Dim 1 (9.88%)
Dim
2 (
8.10
%)
F
M
employee
middle
non−worker
other worker
senior
student
workman
Not.sportsman
sportsman
+60
15−24
25−3435−44
45−59
+2/day
1 to 2/week
1/day
3 to 6/week
escape−exoticism
Not.escape−exoticism
Not.spirituality
spiritualityhealthyNot.healthydiuretic
Not.diuretic friendliness
Not.friendliness
iron absorption
Not.iron absorptionfeminine
Not.feminine
Not.sophisticated
sophisticated
No.slimming
slimming
exciting
No.exciting
No.relaxing
relaxing
effect on health
No.effect on health
Selection of some categories
plot(res, invisible="ind",autoLab="y",cex=0.7,selectMod="cos2 10")
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01
2MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
Not.tearoom
tearoomNot.resto
restotea bag
unpackaged
chain store
chain store+tea shop
tea shop
p_upscale
F
M
student
+60
15−24
+2/day
1/dayfriendlinessNot.friendliness
Not.sophisticated
plot(res, invisible="ind",autoLab="y",cex=0.7,selectMod="contrib 20")
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−1
01
2MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
Not.tea time tea time
lunchwork
Not.tearoom
tearoom
friends
Not.friends
resto
pub
green
tea bag
tea bag+unpackaged
unpackaged
chain store
chain store+tea shop
tea shop
p_branded
p_upscale
p_variable
Selection of some individuals
plot(res, invisible=c("var","quali.sup"),autoLab="y",cex=0.7,select="cos2 20")
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50.
00.
51.
0MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
31
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67
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259265
273
283
Selection of some categories and some individuals
plot(res, autoLab="y",cex=0.7, select="cos2 20", selectMod="cos2 10")
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2MCA factor map
Dim 1 (9.88%)
Dim
2 (
8.10
%)
31
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95 100165
168182
187
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200
202
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211227
259265
273
283Not.tearoom
tearoomNot.resto
restotea bag
unpackaged
chain store
chain store+tea shop
tea shop
p_upscale
F
M
student
+60
15−24
+2/day1/day friendliness
Not.friendliness
Not.sophisticated
Graphs of the variables
plot(res, choix="var",xlim=c(0,0.6),ylim=c(0,0.6))
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0.0
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Dim 1 (9.88%)
Dim
2 (
8.10
%)
breakfasttea.time
evening
lunchdinner
alwayshomework
tearoomfriends
resto
pub
Tea
Howsugar
how
where
price
sexSPC
Sport
age_Q
frequencyescape.exoticismspiritualityhealthydiuretic friendlinessiron.absorption
femininesophisticated
slimmingexcitingrelaxingeffect.on.health
age
plot(res, choix="var",xlim=c(0,0.6),ylim=c(0,0.6),invisible=c("quali.sup","quanti.sup"))
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0.0
0.1
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Dim 1 (9.88%)
Dim
2 (
8.10
%)
breakfast tea.timeevening
lunchdinner
alwayshome
worktearoomfriends
resto
pub
Tea
Howsugar
how
where
price
Graphs on dimensions 3 and 4
plot(res,invisible=c("var","quali.sup"),cex=0.7,select="contrib 20",axes=3:4)
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1.0
MCA factor map
Dim 3 (6.00%)
Dim
4 (
5.20
%)
22
44
62
66
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79
127
142
156
191
194
197
198203
204
205
217 222
248
263
plot(res, invisible="ind",autoLab="y",cex=0.7,selectMod="cos2 20",axes=3:4)
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01
MCA factor map
Dim 3 (6.00%)
Dim
4 (
5.20
%)
breakfast
Not.breakfastNot.tea time
tea time evening
Not.evening
dinner
Not.dinner
always
Not.always
home
Not.home
black
Earl Grey
milk
other
No.sugar
sugar
tea bag+unpackaged
unpackaged
middle
non−worker
student
+60
15−2425−34
35−4445−59 +2/day
1 to 2/week
Not.spiritualityspiritualitydiuretic
Not.diuretic
friendliness
Not.friendlinessNo.slimming
slimming
excitingNo.exciting
Confidence ellipses around the categories for the variables 14 to 17
plotellipses(res,keepvar=c(14:17))
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Dim 1 (9.88%)
Dim
2 (
8.1%
)
−0.5
0.0
0.5
1.0
−0.5 0.0 0.5 1.0
tea bagtea bag+unpackaged
unpackaged
how
alonelemon
milkother
How
No.sugarsugar
sugar
−0.5 0.0 0.5 1.0
−0.5
0.0
0.5
1.0
chain storechain store+tea shop
tea shop
where
Description of the dimensions
dimdesc(res)
## $`Dim 1`## $`Dim 1`$quali## R2 p.value## where 0.41793014 1.255462e-35## tearoom 0.37189109 6.082138e-32## how 0.29882863 1.273180e-23## friends 0.24319952 8.616289e-20## resto 0.22646759 2.319804e-18## tea.time 0.19203800 1.652462e-15## price 0.21609382 4.050469e-14
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## pub 0.14722360 5.846592e-12## work 0.11153590 3.000872e-09## How 0.10285191 4.796010e-07## Tea 0.08950330 8.970954e-07## lunch 0.07458227 1.570629e-06## frequency 0.09438792 1.849071e-06## friendliness 0.07132511 2.706357e-06## evening 0.05311759 5.586801e-05## always 0.04479873 2.219503e-04## sex 0.03335969 1.487620e-03## dinner 0.03289362 1.608077e-03## breakfast 0.02539639 5.667604e-03## sugar 0.01527654 3.234986e-02#### $`Dim 1`$category## Estimate p.value## chain store+tea shop 0.33853776 1.344557e-35## tearoom 0.29731072 6.082138e-32## tea bag+unpackaged 0.23457030 1.361423e-21## friends 0.19950832 8.616289e-20## resto 0.20802605 2.319804e-18## tea time 0.17011357 1.652462e-15## pub 0.18137133 5.846592e-12## p_variable 0.27595067 5.956230e-12## work 0.14170406 3.000872e-09## +2/day 0.14855615 7.380937e-07## lunch 0.14862636 1.570629e-06## friendliness 0.13020388 2.706357e-06## other 0.38192443 9.244911e-06## evening 0.09345270 5.586801e-05## always 0.08582336 2.219503e-04## F 0.07158886 1.487620e-03## Not.dinner 0.13685745 1.608077e-03## lemon 0.01223478 3.515252e-03## breakfast 0.06141392 5.667604e-03## senior 0.16802844 8.886876e-03## Earl Grey 0.12203299 1.547110e-02## No.sugar 0.04761975 3.234986e-02## sugar -0.04761975 3.234986e-02## 1 to 2/week -0.10430402 1.829818e-02## p_private label -0.11979263 1.156245e-02## Not.breakfast -0.06141392 5.667604e-03## dinner -0.13685745 1.608077e-03## M -0.07158886 1.487620e-03## alone -0.23140428 2.326233e-04## Not.always -0.08582336 2.219503e-04## 1/day -0.10038745 1.556219e-04## Not.evening -0.09345270 5.586801e-05## Not.friendliness -0.13020388 2.706357e-06## Not.lunch -0.14862636 1.570629e-06## green -0.24569103 1.281162e-07## Not.work -0.14170406 3.000872e-09## p_branded -0.10910793 1.116908e-09## Not.pub -0.18137133 5.846592e-12
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## Not.tea time -0.17011357 1.652462e-15## Not.resto -0.20802605 2.319804e-18## Not.friends -0.19950832 8.616289e-20## tea bag -0.23182447 8.877561e-22## chain store -0.24012436 3.008256e-27## Not.tearoom -0.29731072 6.082138e-32###### $`Dim 2`## $`Dim 2`$quanti## correlation p.value## age 0.2035108 0.0003890693#### $`Dim 2`$quali## R2 p.value## where 0.62550194 4.542155e-64## price 0.56056797 1.837909e-50## how 0.51288621 4.103156e-47## Tea 0.16034278 5.359827e-12## resto 0.05883014 2.165287e-05## age_Q 0.07663110 9.613084e-05## dinner 0.04764166 1.385133e-04## work 0.04334283 2.825934e-04## sugar 0.03078909 2.286813e-03## How 0.04300447 4.565763e-03## lunch 0.02609615 5.035226e-03## breakfast 0.02554407 5.527765e-03## sophisticated 0.02298649 8.531637e-03## tearoom 0.02159669 1.081515e-02## SPC 0.05335498 1.284774e-02## sex 0.01734823 2.250375e-02## friends 0.01527530 3.235693e-02#### $`Dim 2`$category## Estimate p.value## tea shop 0.56623933 3.435386e-58## p_upscale 0.58675674 6.819842e-53## unpackaged 0.47523577 4.876111e-43## green 0.17636551 5.660702e-07## Not.resto 0.09599600 2.165287e-05## black 0.02833892 1.280976e-04## dinner 0.14912299 1.385133e-04## Not.work 0.07997829 2.825934e-04## No.sugar 0.06120846 2.286813e-03## Not.lunch 0.07959849 5.035226e-03## Not.breakfast 0.05576534 5.527765e-03## +60 0.11445238 7.567898e-03## sophisticated 0.05865034 8.531637e-03## tearoom 0.06486865 1.081515e-02## middle 0.09793868 2.228820e-02## M 0.04674127 2.250375e-02## Not.friends 0.04527027 3.235693e-02## friends -0.04527027 3.235693e-02## p_private label -0.13563786 2.301393e-02
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## F -0.04674127 2.250375e-02## Not.tearoom -0.06486865 1.081515e-02## Not.sophisticated -0.05865034 8.531637e-03## p_unknown -0.23171262 7.581675e-03## breakfast -0.05576534 5.527765e-03## lunch -0.07959849 5.035226e-03## p_variable -0.04476924 3.517223e-03## student -0.12977090 2.381679e-03## sugar -0.06120846 2.286813e-03## milk -0.13222339 7.496148e-04## work -0.07997829 2.825934e-04## Not.dinner -0.14912299 1.385133e-04## resto -0.09599600 2.165287e-05## 15-24 -0.16342547 4.501578e-06## p_branded -0.11247568 8.001515e-07## Earl Grey -0.20470443 6.499738e-12## tea bag -0.31755648 2.123707e-18## chain store -0.36891861 5.804094e-23###### $`Dim 3`## $`Dim 3`$quanti## correlation p.value## age -0.3397736 1.530157e-09#### $`Dim 3`$quali## R2 p.value## Tea 0.33178708 9.996725e-27## breakfast 0.21498315 2.138445e-17## sugar 0.21026537 5.278399e-17## How 0.19600156 5.867378e-14## home 0.13440219 5.642852e-11## age_Q 0.14565571 1.852397e-09## evening 0.10637896 7.269113e-09## friends 0.10294629 1.307065e-08## always 0.10133291 1.721112e-08## tea.time 0.05424196 4.636352e-05## frequency 0.06361133 2.167789e-04## pub 0.04311129 2.936636e-04## SPC 0.07625129 6.739742e-04## where 0.04166084 1.801385e-03## exciting 0.02425859 6.872690e-03## dinner 0.02152288 1.095256e-02## spirituality 0.01606168 2.817777e-02## lunch 0.01561039 3.050262e-02## diuretic 0.01302499 4.827448e-02#### $`Dim 3`$category## Estimate p.value## Earl Grey 0.18122366 5.474630e-22## Not.breakfast 0.13921762 2.138445e-17## sugar 0.13764789 5.278399e-17## Not.home 0.32238212 5.642852e-11## evening 0.10304138 7.269113e-09
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## friends 0.10113377 1.307065e-08## always 0.10056783 1.721112e-08## lemon 0.29113799 3.532927e-05## Not.tea time 0.07044079 4.636352e-05## 1 to 2/week 0.13367067 4.787775e-05## 25-34 0.15458550 9.102105e-05## student 0.11762964 1.467086e-04## pub 0.07646920 2.936636e-04## 15-24 0.12278166 4.286711e-04## alone 0.13200504 7.535155e-04## tea shop 0.12875140 1.905017e-03## exciting 0.04797670 6.872690e-03## dinner 0.08625296 1.095256e-02## spirituality 0.04098581 2.817777e-02## lunch 0.05297807 3.050262e-02## unpackaged 0.07670099 3.765383e-02## Not.diuretic 0.03468681 4.827448e-02## diuretic -0.03468681 4.827448e-02## +2/day -0.07763057 3.323605e-02## Not.lunch -0.05297807 3.050262e-02## Not.spirituality -0.04098581 2.817777e-02## chain store+tea shop -0.09887763 2.197901e-02## 35-44 -0.07139235 1.961314e-02## Not.dinner -0.08625296 1.095256e-02## non-worker -0.08793735 8.568111e-03## No.exciting -0.04797670 6.872690e-03## 45-59 -0.07791412 1.331486e-03## +60 -0.12806070 4.108178e-04## Not.pub -0.07646920 2.936636e-04## tea time -0.07044079 4.636352e-05## other -0.33576960 1.254567e-05## milk -0.08737342 7.989362e-08## Not.always -0.10056783 1.721112e-08## Not.friends -0.10113377 1.307065e-08## Not.evening -0.10304138 7.269113e-09## home -0.32238212 5.642852e-11## No.sugar -0.13764789 5.278399e-17## breakfast -0.13921762 2.138445e-17## black -0.22772627 4.313358e-26
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