Description Usage Arguments Details Value Author(s) References See Also Examples
Performs multiple factor analysis to analyze a set of individuals (observations) described by several groups of variables. Variables within a group can be a mixture of quantitative and qualitative variables.
1 2 
data 
a data frame with 
groups 
a vector which gives the groups of the columns in 
name.groups 
a vector of size 
ndim 
number of dimensions kept in the results (by default 5). 
rename.level 
boolean, if TRUE all the levels of the qualitative variables are renamed as follows: "variable_name=level_name". This prevents to have identical names for the levels. 
graph 
boolean, if TRUE the following graphics are displayed for the first two dimensions of PCAmix: plot of the individuals coordinates, plot of the squared loadings of variables, plot of the partial axes, plot of the correlation circle (if quantitative variables are available), plot of the levels component map (if qualitative variables are available). 
axes 
a length 2 vector specifying the axes to plot. 
Multiple Factor Analysis (MFA) developed by Escofier and Pages in 1983 is a method of factorial analysis to deal with multiple groups of variables collected on the same observations. The main idea of MFA is to normalize each group by dividing all the variables belonging to this group by the first eigenvalue coming from the Principal Component Analysis (PCA) of this group. Then, a usual PCA on all the weighted variables taken together is applied. Initially this method has been developed for groups only containing quantitative variables. Afterwards this method has been improved to deal simultaneously with groups of qualitative variables and groups of quantitative variables. The MFAmix
method allows to perform MFA method for groups containing a mixture of quantitative and qualitative variables
One of the outputs available in the MFAmix method are the squared loadings (sqload
). Squared loadings for a qualitative variable are correlation ratios between the variable and the principal components. For a quantitative variable, squared loadings are the squared correlation between the variable and the principal components.
Some others outputs are specific to MFA:
Coordinates of groups are the sum of the absolute contributions of variables belonging to the groups,
Partial individuals coordinates are factor coordinates of individuals according to a specific group. The partial coordinates can be achieved by projecting the data set of each group onto the principal component space of MFAmix,
Partial axes of a group are correlation between each principal components of the separated analyses of the group and the principal components of MFAmix.
eig 
a matrix containing the eigenvalues, the percentages of variance and the cumulative percentages of variance. 
ind 
a list containing the results for the individuals (observations):

quanti 
a list containing the results for the quantitative variables:

levels 
a list containing the results for the levels of the qualitative variables:

quali 
a list containing the results for the qualitative variables:

sqload 
a matrix of dimension ( 
coef 
the coefficients of the linear combinations used to construct the principal components of MFAmix, and to predict coordinates (scores) of new observations in the function 
eig.separate 
a matrix containing the 
separate.analyses 
the results for the separated analyses of each group. 
groups 
a list containing the results for the groups:

partial.axes 
a matrix containing the coordinates of the partial axes. 
ind.partial 
a list of 
listvar.group 
list the variables in each group. It is usefull to check the adequacy between the vector 
global.pca 
an object of class 
Amaury Labenne [email protected], Marie Chavent, Vanessa Kuentz, Benoit Liquet, Jerome Saracco
Chavent M., KuentzSimonet V., Labenne A., Saracco J., Multivariate analysis of mixed data: The PCAmixdata R package, arXiv:1411.4911 [stat.CO].
Escofier, B. and Pages, J. (1994). Multiple factor analysis (afmult package). Computational statistics & data analysis, 18(1):121140.
Le, S., Josse, J., and Husson, F. (2008). Factominer: an r package for multivariate analysis. Journal of statistical software, 25(1):118.
print.MFAmix
, summary.MFAmix
, predict.MFAmix
, plot.MFAmix
1 2 3 4 5 6 7 8 9 10 11 12  data(gironde)
class.var<c(rep(1,9),rep(2,5),rep(3,9),rep(4,4))
names < c("employment","housing","services","environment")
dat<cbind(gironde$employment[1:20,],gironde$housing[1:20,],
gironde$services[1:20,],gironde$environment[1:20,])
res<MFAmix(data=dat,groups=class.var,
name.groups=names, rename.level=TRUE, ndim=3,graph=FALSE)
summary(res)

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