title: Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials.
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.
authors: Economics Department, Second University of Naples, Corso Gran Priorato di Malta, 81043 , Capua, CE, Italy. rosaria.lombardo@unina2.it.
authors: Rosaria
authors: R
authors: Lombardo
authors: School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, 2308, Australia.
authors: Eric J
authors: EJ
authors: Beh
authors: Faculty of Social and Behavioural Sciences, Leiden University, Wassenaarseweg 52, 2333 AK, Leiden, The Netherlands.
authors: Pieter M
authors: PM
authors: Kroonenberg
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D006304:Health Status; D006801:Humans; D008875:Middle Aged; D015233:Models, Statistical; D011594:Psychometrics; D013223:Statistics as Topic; D055815:Young Adult
keywords: bivariate moment decomposition; generalized singular value decomposition; hybrid decomposition; polynomial biplots; symmetric and non-symmetric correspondence analysis