SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

PLS path models with categorical indicators - a correspondence analytical approach

Jörg Betzin
Technical University of Berlin
Germany

We present an estimation method for path models with categorical manifestvariables. The path model under observation is the usual path model withlinear dependencies between M blocks of manifest variables and correspondinglatent variables and linear relations between the latent variables themselves.

For evaluation of the model the PLS approach is used. In the basic PLS algorithm the latent variables hm (m = 1,...,M) will be estimated by an iteration algorithm of the form

wm
=
amX¢hm-1*
hm
=
bmXwm
with a suitable starting point h0*. Here amand bm are certain constants, X isa (possibly pretreated) data matrix, and hm* is are instrumental variables containing the influence of the other variable blocks.

If the manifest variables are categorical, the linear relations above are meaningless, assuming the latent variables are continuous.Therefore we use correspondence analytical tools for estimation of the latentvariables. The idea of Correspondence Analysis (CorA) is multidimensionalscaling of a set of categorical data, which is, roughly speaking, similar to principal components for categorical data.

One main aspect of CorA is the transformation of the raw data matrix into anindicator matrix G and the analysis of a kind of correlation matrixfor G. If we describe by [(Q)\tilde] a suitabletransformation of G we obtain a decomposition like

~
Q
 
¢
 
~
Q
 
= ~
C
 
~
R
 
(called `transition formulae' in CorA), and we use these decompositionmatrices as transformation matrices in the PLS algorithm