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Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials

Published online by Cambridge University Press:  01 January 2025

Rosaria Lombardo ,
Eric J. Beh  and
Pieter M. Kroonenberg
Rosaria Lombardo*
Affiliation:
Second University of Naples
Eric J. Beh
Affiliation:
University of Newcastle
Pieter M. Kroonenberg
Affiliation:
Leiden University
*
Correspondence should be made to Rosaria Lombardo, Economics Department, Second University of Naples, Corso Gran Priorato di Malta, 81043 Capua, CE Italy. Email: rosaria.lombardo@unina2.it
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Abstract

The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display—the polynomial biplot.

Keywords

symmetric and non-symmetric correspondence analysisgeneralized singular value decompositionbivariate moment decompositionhybrid decompositionpolynomial biplots
Type
Article
Information
Psychometrika , Volume 81 , Issue 2 , June 2016 , pp. 325 - 349
Copyright
Copyright © 2015 The Psychometric Society

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