Simple Correspondence Analysis of Ordinal Cross‐Classifications Using Orthogonal Polynomials

Abstract

A method is developed that caters for the application of correspondence analysis to two-way contingency tables with one and two ordered sets of categories. The method involves calculating orthogonal polynomials of the type described by EMERSON (1968). and partitioning the chi-square statistic using the method described in LANCASTER (1953). The method has all the features of simple correspondence analysis, although allows for additional information about the structure and association of the data to be made by isolating location, dispersion and higher order components of the rows and columns.

A Non-Iterative Alternative to Ordinal Log-Linear Models

“…The RC bivariate correlation model for a doubly ordinal two-way crossclassifications has been discussed by Rayner and Best [24] and Beh [3]. These authors demonstrate that p ij can be reconstituted by the saturated model…”

“…The polynomials used as those considered by Beh [3,4], Beh and Davy [6,7], and Rayner and Best [24].…”

“…See for example Gilula [14], Gilula and Haberman [15,16], and Gilula and Ritov [17]. In this section we consider the correlation models for two-way ordinal cross -classifications as seen in Beh [3], Beh and Davy [6,7], Rayner and Best [24] and Best and Rayner [8].…”

“…Authors such as Best and Rayner [8], Beh [3,4] and Weller and Romney [29] have cited this example in their analyses. The parental socio-economic status is designated A through to F in a sequence from highest to lowest position.…”

Approximating Exact Test of Mutual Independence in Multiway Contingency Tables via Stochastic Approximation Monte Carlo

“…The data classifies 1517 people according to their reported happiness, number of completed years of schooling, and number of siblings. Beh and Davy (1997) discussed partitioning the chi-squared statistic for a partially ordered three-way contingency table with a generalized linear model, where happiness is regarded as a response variable and schooling and siblings as the explanatory variables.…”