Loglinear Models for Reciprocal and Other Simultaneous Effects

Abstract

This paper presents new models for simultaneous relationships among endogenous categorical variables. Previous investigators have argued that the loglinearllogit framework is insufficiently rich for the development of simultaneous equation models and that only models that postulate latent continuous variables (e.g. multivariate probit models) can represent simultaneous relationships among categorical variables. This paper shows that by using latent class methods, we can develop loglinear models for simultaneous effects that are analogous to linear models in simultaneous equation theory. These models, which are extensions of conventional loglinear and logit models for cross-classified data, are suitable when an independent variable is jointly determined with the dependent variable in a single-equation logit model or when there are reciprocal effects between two endogenous categorical variables. The models proposed here are extensions of recently developed