expansion of the data matrix, so that the levels of all p variables are represented by
dummy binary variables. Such a matrix is called a complete disjunctive table.
MCA is implemented in the function mca() of package MASS and, with more
options, in the function MCA() of package FactoMineR.
5.4.5.1 MCA on the Environmental Variables of the Oribatid Mite
Data Set
As an example, let us compute an MCA on the environmental variables of our
second data set. We have three qualitative variables: Substrate (7 classes), Shrubs
(3 classes) and Microtopography (2 classes). Function MCA() offers the possibility
of projecting supplementary variables into the MCA result. Note that these supplementary variables are not involved in the computation of the MCA itself; they are
added to the result for heuristic purposes only. For more complex, simultaneous
analyses of several data tables, see Chap. 6. Here we shall add two groups of
supplementary variables: (1) the two quantitative environmental variables Substrate
density and Water content, and (2) a 4-group classification of the Hellingertransformed Oribatid mite data submitted to a Ward hierarchical clustering.
The numerical results of the analysis can be accessed by the name of the object
followed by $..., e.g. mite.env.MCA$ind$coord for the site coordinates. The
graphical results are grouped in Fig. 5.9.
# Preparation of supplementary data: mite classification
# into 4 groups
# Hellinger transformation of oribatid mite species data
mite.h <- decostand(mite, "hel")
# Ward clustering of mite data
mite.h.ward <- hclust(dist(mite.h), "ward.D2")
# Cut the dendrogram to 4 groups
mite.h.w.g <- cutree(mite.h.ward, 4)
# Assembly of the data set
mite.envplus <- data.frame(mite.env, mite.h.w.g)
# MCA of qualitative environmental data plus supplementary
# variables:
#
(1) quantitative environmental data,
#
(2) 4-group mite classification.
#
Default: graph=TRUE.
mite.env.MCA <- MCA(mite.envplus, quanti.sup = 1:2, quali.sup = 6)
mite.env.MCA
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5 Unconstrained Ordination
dummy binary variables. Such a matrix is called a complete disjunctive table.
MCA is implemented in the function mca() of package MASS and, with more
options, in the function MCA() of package FactoMineR.
5.4.5.1 MCA on the Environmental Variables of the Oribatid Mite
Data Set
As an example, let us compute an MCA on the environmental variables of our
second data set. We have three qualitative variables: Substrate (7 classes), Shrubs
(3 classes) and Microtopography (2 classes). Function MCA() offers the possibility
of projecting supplementary variables into the MCA result. Note that these supplementary variables are not involved in the computation of the MCA itself; they are
added to the result for heuristic purposes only. For more complex, simultaneous
analyses of several data tables, see Chap. 6. Here we shall add two groups of
supplementary variables: (1) the two quantitative environmental variables Substrate
density and Water content, and (2) a 4-group classification of the Hellingertransformed Oribatid mite data submitted to a Ward hierarchical clustering.
The numerical results of the analysis can be accessed by the name of the object
followed by $..., e.g. mite.env.MCA$ind$coord for the site coordinates. The
graphical results are grouped in Fig. 5.9.
# Preparation of supplementary data: mite classification
# into 4 groups
# Hellinger transformation of oribatid mite species data
mite.h <- decostand(mite, "hel")
# Ward clustering of mite data
mite.h.ward <- hclust(dist(mite.h), "ward.D2")
# Cut the dendrogram to 4 groups
mite.h.w.g <- cutree(mite.h.ward, 4)
# Assembly of the data set
mite.envplus <- data.frame(mite.env, mite.h.w.g)
# MCA of qualitative environmental data plus supplementary
# variables:
#
(1) quantitative environmental data,
#
(2) 4-group mite classification.
#
Default: graph=TRUE.
mite.env.MCA <- MCA(mite.envplus, quanti.sup = 1:2, quali.sup = 6)
mite.env.MCA
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5 Unconstrained Ordination