CAIV {CoCoAn}R Documentation

Function to perform correspondence analysis with (or without) respect to instrumental variables

Description

Multivariate analysis. This function perform correspondence analysis or constrained correspondence analysis. This latter is better known under the name of canonical correspondence analysis. This analysis finds coefficients of variables to obtain a row score of unit variance. This row score is used to compute by weighted averaging a column score of maximized variance.

Usage

CAIV(L, E=diag(1, dim(L)[1], dim(L)[1]), normE=TRUE)

Arguments

L a (i,j) matrix of non-negative number
E an (i,p) optional matrix of p external variables
normE TRUE to normalize variables in matrix E, FALSE otherwise

Details

This function compute correspondence analysis (enter L) or constrained correspondence analysis (enter L and E). The function return the coefficient (B) to compute a row score of unit variance (R) that maximize the between-column inertia (column score in F obtained by weighting averaging). D contains the intra-set covariance (correlation if normE=TRUE). For correspondence analysis, CAIV(t(L)) gives a column score of unit variance that maximize the between-rows inertia. Note that this function does not use convenient rescaling and so is a little bit different of ter Braak's CCA. (We use the algorithm of Chessel et al.)

Value

A list with components

ev a vector containing eigenvalues
B coefficients of variables of E (only in constrained analysis)
D covariance matrix between external variables and row scores (only in constrained analysis)
R row coordinates of unit variance
F column coordinates of variance ev[i]

Author(s)

Stephane DRAY dray@biomserv.univ-lyon1.fr

References

ter Braak (1986): Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67(5), 1167–1179.

Chessel, Lebreton and Yoccoz (1987): Propriétés de l'analyse canonique des correspondances; une illustration en hydrobiologie. Revue de Statistique Appliquée 35(4) 55–72.

See Also

CAIV.plot

Examples

##correspondence analysis
L <- matrix(c(4,2,0,2,0,5,1,3,2,4,0,2,2,0,3,1),4,4)
CAIV(L)
CAIV(t(L))
##canonical correspondence analysis
E <-matrix(c(1.5,2.3,2,1.6,0.9,0.8,1.2,1.5),4,2)
CAIV(L,E)

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