ANALYSIS OF DISCRETE DATA USING LOG-MULTIPLICATIVE MODELS AND OTHER LOG-NONLINEAR MODELS (CONTINGENCY TABLES, FREQUENCY DATA, ASSOCIATION MODELS)

This work extends the association models of Goodman, Clogg, and Agresti and Kezouh. New models are formulated for the analysis of conditional association and for the analysis of partial association. In many situations these models facilitate the parsimonious modelling of seemingly complex cross-classifications of discrete data. Most of the usual log-linear models used in the analysis of discrete data are special cases of models introduced here.;Computational procedures for fitting the models with the method of maximum likelihood are discussed. A cyclic ascent algorithm is given particular emphasis, due to its ease of implementation and generally good performance in the examples considered in this thesis. This procedure is equivalent to the iterative proportional fitting algorithm when applied to log-linear models. Procedures for obtaining initial parameter estimates and enforcing identifiability constraints are also discussed.;Some results on the use of multiplicative interaction models in the analysis of discretized bivariate normal data are also given. An approximate relationship between the odds ratio and the tetrachoric correlation is derived, conditions under which a particular association model and the discretized bivariate normal model are indistinguishable are given, and a general association model for I x J tables is shown to have an interesting interpretation from the point of view of fitted correlations.;For most of the models, the maximum likelihood estimates of the multiplicative interaction parameters can be interpreted as fitting product-moment correlations. These maximum likelihood estimates can also be made to satisfy the same constraints as the canonical scores in a canonical correlation model.