facto_summarize - Subset and summarize the output of factor analyses - R software and data mining


Description

Subset and summarize the results of Principal Component Analysis (PCA), Correspondence Analysis (CA) and Multiple Correspondence Analysis (MCA) functions from several packages.

The function facto_summarize() [in factoextra package] is used.

Install and load factoextra

The package devtools is required for the installation as factoextra is hosted on github.

# install.packages("devtools")
devtools::install_github("kassambara/factoextra")

Load factoextra :

library("factoextra")

Usage

facto_summarize(X, element, result = c("coord", "cos2", "contrib"),
                axes = 1:2, select = NULL)

Arguments

Argument Description
X an object of class PCA, CA and MCA [FactoMineR]; prcomp and princomp [stats]; dudi, pca, coa and acm [ade4]; ca [ca package].
element allowed values are “row” and “col” for CA; “var” and “ind” for PCA or MCA.
result the result to be extracted for the element. Possible values are the combination of c(“cos2”, “contrib”, “coord”).
axes a numeric vector specifying the axes of interest. Default values are 1:2 for axes 1 and 2.
select

a selection of variables. Allowed values are NULL or a list containing the arguments name, cos2 or contrib. Default is list(name = NULL, cos2 = NULL, contrib = NULL):

  • name: is a character vector containing variable names to be selected
  • cos2: if cos2 is in [0, 1], ex: 0.6, then variables with a cos2 > 0.6 are selected. if cos2 > 1, ex: 5, then the top 5 variables with the highest cos2 are selected
  • contrib: if contrib > 1, ex: 5, then the top 5 variables with the highest contrib are selected.

Details

If length(axes) > 1, then the columns contrib and cos2 correspond to the total contributions and total cos2 of the axes. In this case, the column coord is calculated as x^2 + y^2 + …+; x, y, … are the coordinates of the points on the specified axes.

Value

A data frame containing the (total) coord, cos2 and the contribution for the axes.

Examples

Principal component analysis

A principal component analysis (PCA) is performed using the built-in R function prcomp() and the decathlon2 [in factoextra] data

data(decathlon2)
decathlon2.active <- decathlon2[1:23, 1:10]
res.pca <- prcomp(decathlon2.active,  scale = TRUE)
# Summarize variables on axes 1:2
facto_summarize(res.pca, "var", axes = 1:2)[,-1]
                    Dim.1       Dim.2     coord      cos2  contrib
X100m        -0.850625692  0.17939806 0.7557477 0.7557477 75.57477
Long.jump     0.794180641 -0.28085695 0.7096035 0.7096035 70.96035
Shot.put      0.733912733 -0.08540412 0.5459218 0.5459218 54.59218
High.jump     0.610083985  0.46521415 0.5886267 0.5886267 58.86267
X400m        -0.701603377 -0.29017826 0.5764507 0.5764507 57.64507
X110m.hurdle -0.764125197  0.02474081 0.5844994 0.5844994 58.44994
Discus        0.743209016 -0.04966086 0.5548258 0.5548258 55.48258
Pole.vault   -0.217268042 -0.80745110 0.6991827 0.6991827 69.91827
Javeline      0.428226639 -0.38610928 0.3324584 0.3324584 33.24584
X1500m        0.004278487 -0.78448019 0.6154275 0.6154275 61.54275
# Select the top 5 contributing variables
facto_summarize(res.pca, "var", axes = 1:2,
           select = list(contrib = 5))[,-1]
                  Dim.1      Dim.2     coord      cos2  contrib
X100m      -0.850625692  0.1793981 0.7557477 0.7557477 75.57477
Long.jump   0.794180641 -0.2808570 0.7096035 0.7096035 70.96035
Pole.vault -0.217268042 -0.8074511 0.6991827 0.6991827 69.91827
X1500m      0.004278487 -0.7844802 0.6154275 0.6154275 61.54275
High.jump   0.610083985  0.4652142 0.5886267 0.5886267 58.86267
# Select variables with cos2 >= 0.6
facto_summarize(res.pca, "var", axes = 1:2,
           select = list(cos2 = 0.6))[,-1]
                  Dim.1      Dim.2     coord      cos2  contrib
X100m      -0.850625692  0.1793981 0.7557477 0.7557477 75.57477
Long.jump   0.794180641 -0.2808570 0.7096035 0.7096035 70.96035
Pole.vault -0.217268042 -0.8074511 0.6991827 0.6991827 69.91827
X1500m      0.004278487 -0.7844802 0.6154275 0.6154275 61.54275
# Select by names
facto_summarize(res.pca, "var", axes = 1:2,
     select = list(name = c("X100m", "Discus", "Javeline")))[,-1]
              Dim.1       Dim.2     coord      cos2  contrib
X100m    -0.8506257  0.17939806 0.7557477 0.7557477 75.57477
Discus    0.7432090 -0.04966086 0.5548258 0.5548258 55.48258
Javeline  0.4282266 -0.38610928 0.3324584 0.3324584 33.24584
# Summarize individuals on axes 1:2
facto_summarize(res.pca, "ind", axes = 1:2)[,-1]
                 Dim.1      Dim.2      coord      cos2   contrib
SEBRLE       0.1912074 -1.5541282  2.4518746 0.5050034 10.660324
CLAY         0.7901217 -2.4204156  6.4827039 0.5057178 28.185669
BERNARD     -1.3292592 -1.6118687  4.3650507 0.4871654 18.978481
YURKOV      -0.8694134  0.4328779  0.9432630 0.1199355  4.101143
ZSIVOCZKY   -0.1057450  2.0233632  4.1051806 0.5779938 17.848611
McMULLEN     0.1185550  0.9916237  0.9973729 0.1543704  4.336404
MARTINEAU   -2.3923532  1.2849234  7.3743818 0.5205607 32.062530
HERNU       -1.8910497 -1.1784614  4.9648401 0.5543447 21.586261
BARRAS      -1.7744575  0.4125321  3.3188820 0.6495490 14.429922
NOOL        -2.7770058  1.5726757 10.1850700 0.6469840 44.282913
BOURGUIGNON -4.4137335 -1.2635770 21.0776704 0.9301572 91.642045
Sebrle       3.4514485 -1.2169193 13.3933893 0.7593400 58.232127
Clay         3.3162243 -1.6232908 13.6324164 0.8523470 59.271375
Karpov       4.0703560  0.7983510 17.2051623 0.8138146 74.805053
Macey        1.8484623  2.0638828  7.6764252 0.8165181 33.375762
Warners      1.3873514 -0.2819083  2.0042163 0.2662078  8.713984
Zsivoczky    0.4715533  0.9267436  1.0812163 0.2190667  4.700940
Hernu        0.2763118  1.1657260  1.4352654 0.4666709  6.240284
Bernard      1.3672590  1.4780354  4.0539857 0.6274807 17.626025
Schwarzl    -0.7102777 -0.6584251  0.9380181 0.2170229  4.078340
Pogorelov   -0.2143524 -0.8610557  0.7873639 0.1337231  3.423321
Schoenbeck  -0.4953166 -1.3000530  1.9354762 0.5291161  8.415114
Barras      -0.3158867  0.8193681  0.7711485 0.1466237  3.352820

Correspondence Analysis

The function CA() in FactoMineR package is used:

# Install and load FactoMineR to compute CA
# install.packages("FactoMineR")
library("FactoMineR")
data("housetasks")
res.ca <- CA(housetasks, graph = FALSE)
# Summarize row variables on axes 1:2
facto_summarize(res.ca, "row", axes = 1:2)[,-1]
                Dim.1      Dim.2     coord      cos2   contrib
Laundry    -0.9918368  0.4953220 1.2290841 0.9245395 12.403601
Main_meal  -0.8755855  0.4901092 1.0068569 0.9739621  8.833091
Dinner     -0.6925740  0.3081043 0.5745869 0.9303433  3.558222
Breakfeast -0.5086002  0.4528038 0.4637054 0.9051733  3.722406
Tidying    -0.3938084 -0.4343444 0.3437401 0.9748275  2.404604
Dishes     -0.1889641 -0.4419662 0.2310416 0.7642703  1.497001
Shopping   -0.1176813 -0.4033171 0.1765136 0.8113088  1.214543
Official    0.2266324  0.2536132 0.1156819 0.1194711  0.636781
Driving     0.7417696  0.6534143 0.9771724 0.7672477  7.788243
Finances    0.2707669 -0.6178684 0.4550760 0.9973464  2.948600
Insurance   0.6470759 -0.4737832 0.6431778 0.8848140  5.126245
Repairs     1.5287787  0.8642647 3.0841176 0.9326072 29.178865
Holidays    0.2524863 -1.4350066 2.1229933 0.9921522 19.477003
# Summarize column variables on axes 1:2
facto_summarize(res.ca, "col", axes = 1:2)[,-1]
                  Dim.1      Dim.2      coord      cos2  contrib
Wife        -0.83762154  0.3652207 0.83499601 0.9543242 28.72693
Alternating -0.06218462  0.2915938 0.08889388 0.1098815  1.29467
Husband      1.16091847  0.6019199 1.71003929 0.9795683 37.35808
Jointly      0.14942609 -1.0265791 1.07619274 0.9979998 31.40952

Multiple Correspondence Analysis

The function MCA() in FactoMineR package is used:

library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2,
              quali.sup = 3:4, graph=FALSE)
# Summarize variables on axes 1:2
res <- facto_summarize(res.mca, "var", axes = 1:2)
head(res)
             name      Dim.1       Dim.2      coord      cos2   contrib
Nausea_n Nausea_n  0.2673909  0.12139029 0.08623348 0.3090033 0.6128991
Nausea_y Nausea_y -0.9581506 -0.43498187 1.10726185 0.3090033 2.1962218
Vomit_n   Vomit_n  0.4790279 -0.40919465 0.39690803 0.5953620 2.1649529
Vomit_y   Vomit_y -0.7185419  0.61379197 0.89304306 0.5953620 3.2474293
Abdo_n     Abdo_n  1.3180221 -0.03574501 1.73845988 0.8457372 5.1722773
Abdo_y     Abdo_y -0.6411999  0.01738946 0.41143974 0.8457372 2.5162430
# Summarize individuals on axes 1:2
res <- facto_summarize(res.mca, "ind", axes = 1:2)
head(res)
  name      Dim.1       Dim.2     coord       cos2   contrib
1    1 -0.4525811 -0.26415072 0.2746052 0.46457063 0.4992822
2    2  0.8361700 -0.03193457 0.7002000 0.55670644 1.2730909
3    3 -0.4481892  0.13538726 0.2192032 0.59815656 0.3985513
4    4  0.8803694 -0.08536230 0.7823370 0.75476958 1.4224310
5    5 -0.4481892  0.13538726 0.2192032 0.59815656 0.3985513
6    6 -0.3594324 -0.43604390 0.3193260 0.06143111 0.5805927

Infos

This analysis has been performed using R software (ver. 3.1.2) and factoextra (ver. 1.0.2)


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