Contingency Table Analysis: The WLS Approach

Abstract

This chapter introduces the weighted least squares (WLS) method of categorical data analysis, also known as the GSK approach, developed by Grizzle, Starmer, and Koch. We begin with a definition and several examples of contingency tables and then discuss different functions of the contingency table frequencies that we may form. Next we present the variance-covariance matrix of a function and then show its use in applying the linear model to categorical data. Note that the development of the linear model to categorical data follows closely the presentation in Appendix B. The next sections define additive and multiplicative association; this discussion is followed by a demonstration that the hypothesis of no multiplicative association is equivalent to the hypothesis of independence of rows and columns in two-way tables. We begin with a discussion of the contingency table.