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Last data update: 2014.03.03

R: Correspondence Analysis (CA)

CA	R Documentation

Correspondence Analysis (CA)

Description

Performs Correspondence Analysis (CA) including supplementary row and/or column points.

Usage

CA(X, ncp = 5, row.sup = NULL, col.sup = NULL, 
    quanti.sup=NULL, quali.sup = NULL, graph = TRUE, 
	axes = c(1,2), row.w = NULL, excl=NULL)

Arguments

`X`	a data frame or a table with n rows and p columns, i.e. a contingency table
`ncp`	number of dimensions kept in the results (by default 5)
`row.sup`	a vector indicating the indexes of the supplementary rows
`col.sup`	a vector indicating the indexes of the supplementary columns
`quanti.sup`	a vector indicating the indexes of the supplementary continuous variables
`quali.sup`	a vector indicating the indexes of the categorical supplementary variables
`graph`	boolean, if TRUE a graph is displayed
`axes`	a length 2 vector specifying the components to plot
`row.w`	an optional row weights (by default, a vector of 1 and each row has a weight equals to its margin)
`excl`	numeric vector indicating the indexes of the "junk" columns (default is NULL). Useful for MCA with excl argument.

Value

Returns a list including:

`eig`	a matrix containing all the eigenvalues, the percentage of variance and the cumulative percentage of variance
`col`	a list of matrices with all the results for the column variable (coordinates, square cosine, contributions, inertia)
`row`	a list of matrices with all the results for the row variable (coordinates, square cosine, contributions, inertia)
`col.sup`	a list of matrices containing all the results for the supplementary column points (coordinates, square cosine)
`row.sup`	a list of matrices containing all the results for the supplementary row points (coordinates, square cosine)
`quanti.sup`	if quanti.sup is not NULL, a matrix containing the results for the supplementary continuous variables (coordinates, square cosine)
`quali.sup`	if quali.sup is not NULL, a list of matrices with all the results for the supplementary categorical variables (coordinates of each categories of each variables, v.test which is a criterion with a Normal distribution, square correlation ratio)
`call`	a list with some statistics

Returns the row and column points factor map.
The plot may be improved using the argument autolab, modifying the size of the labels or selecting some elements thanks to the plot.CA function.

Author(s)

Francois Husson Francois.Husson@agrocampus-ouest.fr,Jeremy Mazet

References

Benzecri, J.-P. (1992) Correspondence Analysis Handbook, New-York : Dekker
Benzecri, J.-P. (1980) L'analyse des donn<c3><a9>es tome 2 : l'analyse des correspondances, Paris : Bordas
Greenacre, M.J. (1993) Correspondence Analysis in Practice, London : Academic Press
Husson, F., Le, S. and Pages, J. (2009). Analyse de donnees avec R, Presses Universitaires de Rennes.
Husson, F., Le, S. and Pages, J. (2010). Exploratory Multivariate Analysis by Example Using R, Chapman and Hall.

Examples

data(children)
res.ca <- CA (children, row.sup = 15:18, col.sup = 6:8)
summary(res.ca)
## Ellipses for all the active elements
ellipseCA(res.ca)
## Ellipses around some columns only
ellipseCA(res.ca,ellipse="col",col.col.ell=c(rep("blue",2),rep("transparent",3)),
     invisible=c("row.sup","col.sup"))

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FactoMineR)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FactoMineR/CA.Rd_%03d_medium.png", width=480, height=480)
> ### Name: CA
> ### Title: Correspondence Analysis (CA)
> ### Aliases: CA
> ### Keywords: multivariate
> 
> ### ** Examples
> 
> data(children)
> res.ca <- CA (children, row.sup = 15:18, col.sup = 6:8)
> summary(res.ca)

Call:
CA(X = children, row.sup = 15:18, col.sup = 6:8) 

The chi square of independence between the two variables is equal to 98.80159 (p-value =  9.748064e-05 ).

Eigenvalues
                       Dim.1   Dim.2   Dim.3   Dim.4
Variance               0.035   0.013   0.007   0.006
% of var.             57.043  21.132  11.764  10.061
Cumulative % of var.  57.043  78.175  89.939 100.000

Rows (the 10 first)
                      Iner*1000    Dim.1    ctr   cos2    Dim.2    ctr   cos2  
money               |     3.759 | -0.115  4.550  0.428 |  0.020  0.371  0.013 |
future              |     8.690 |  0.176 17.567  0.716 | -0.098 14.587  0.220 |
unemployment        |     9.151 | -0.212 22.616  0.875 | -0.071  6.779  0.097 |
circumstances       |     3.804 |  0.401  6.274  0.584 |  0.331 11.544  0.398 |
hard                |     1.199 | -0.250  2.994  0.884 |  0.068  0.592  0.065 |
economic            |     8.787 |  0.354 12.005  0.484 |  0.321 26.604  0.397 |
egoism              |     3.287 |  0.060  0.681  0.073 | -0.026  0.338  0.013 |
employment          |     5.648 | -0.137  2.621  0.164 |  0.215 17.555  0.408 |
finances            |     3.576 | -0.237  2.790  0.276 | -0.206  5.690  0.209 |
war                 |     1.025 |  0.217  2.169  0.749 | -0.075  0.694  0.089 |
                     Dim.3    ctr   cos2  
money                0.101 16.884  0.328 |
future              -0.053  7.568  0.064 |
unemployment        -0.004  0.046  0.000 |
circumstances       -0.016  0.046  0.001 |
hard                 0.060  0.845  0.051 |
economic             0.084  3.280  0.027 |
egoism               0.179 29.496  0.655 |
employment          -0.213 30.815  0.398 |
finances            -0.044  0.469  0.010 |
war                 -0.098  2.139  0.152 |

Columns
                      Iner*1000    Dim.1    ctr   cos2    Dim.2    ctr   cos2  
unqualified         |    13.146 | -0.209 25.110  0.676 | -0.081 10.082  0.101 |
cep                 |    10.044 | -0.139 18.297  0.645 |  0.056  8.079  0.105 |
bepc                |     7.670 |  0.109  6.758  0.312 | -0.028  1.251  0.021 |
high_school_diploma |    17.732 |  0.274 37.976  0.758 | -0.121 20.099  0.149 |
university          |    13.468 |  0.231 11.859  0.312 |  0.318 60.488  0.589 |
                     Dim.3    ctr   cos2  
unqualified          0.073 14.659  0.081 |
cep                 -0.018  1.520  0.011 |
bepc                -0.147 59.874  0.570 |
high_school_diploma  0.077 14.407  0.059 |
university           0.094  9.540  0.052 |

Supplementary rows
                      Dim.1  cos2   Dim.2  cos2   Dim.3  cos2  
comfort             | 0.210 0.069 | 0.703 0.775 | 0.071 0.008 |
disagreement        | 0.146 0.131 | 0.119 0.087 | 0.171 0.180 |
world               | 0.523 0.876 | 0.143 0.065 | 0.084 0.023 |
to_live             | 0.308 0.139 | 0.502 0.369 | 0.521 0.397 |

Supplementary columns
                       Dim.1   cos2    Dim.2   cos2    Dim.3   cos2  
thirty              |  0.105  0.138 | -0.060  0.044 | -0.103  0.132 |
fifty               | -0.017  0.011 |  0.049  0.090 | -0.016  0.009 |
more_fifty          | -0.177  0.286 | -0.048  0.021 |  0.101  0.093 |
> ## Ellipses for all the active elements
> ellipseCA(res.ca)
> ## Ellipses around some columns only
> ellipseCA(res.ca,ellipse="col",col.col.ell=c(rep("blue",2),rep("transparent",3)),
+      invisible=c("row.sup","col.sup"))
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>