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Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials

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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.

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Acknowledgments

The authors are very grateful for the comments made by the associate editor and referees during the preparation of this paper. Their comments and insights have greatly improved the paper.

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Authors and Affiliations

  1. Economics Department, Second University of Naples, Corso Gran Priorato di Malta, 81043 , Capua, CE, Italy

    Rosaria Lombardo

  2. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, 2308, Australia

    Eric J. Beh

  3. Faculty of Social and Behavioural Sciences, Leiden University, Wassenaarseweg 52, 2333 AK, Leiden, The Netherlands

    Pieter M. Kroonenberg

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  1. Rosaria Lombardo
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  2. Eric J. Beh
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  3. Pieter M. Kroonenberg
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Correspondence to Rosaria Lombardo.

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Lombardo, R., Beh, E.J. & Kroonenberg, P.M. Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials. Psychometrika 81, 325–349 (2016). https://doi.org/10.1007/s11336-015-9448-y

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