Fitting Multinomial Models in R: A Program Based on Bock’s Multinomial Response Relation Model

Abstract

Bock’s model for multinomial responses considered contingency tables as consisting of two kinds of variables, sampling variables (that defined groups) and response variables. Contrasts among response variables were specified, and these were modeled as functions of contrasts among categories defined by the sampling variables. This neat separation into independent and dependent variables was not captured by general log-linear model programs, but fits well within the framework that most social scientists are familiar with. The model is framed to parallel the usual multivariate analysis of variance (MANOVA) model, so those familiar with MANOVA will find the multinomial model very natural. This chapter describes an R function to fit this model, and provides several examples.