Fitting Heterogeneous Choice Models with Oglm

Abstract

When a binary or ordinal regression model incorrectly assumes that error variances are the same for all cases, the standard errors are wrong and (unlike ordinary least squares regression) the parameter estimates are biased. Heterogeneous choice models (also known as location–scale models or heteroskedastic ordered models) explicitly specify the determinants of heteroskedasticity in an attempt to correct for it. Such models are also useful when the variance itself is of substantive interest. This article illustrates how the author's Stata program oglm (ordinal generalized linear models) can be used to fit heterogeneous choice and related models. It shows that two other models that have appeared in the literature (Allison's model for group comparisons and Hauser and Andrew's logistic response model with proportionality constraints) are special cases of a heterogeneous choice model and alternative parameterizations of it. The article further argues that heterogeneous choice models may sometimes be an attractive alternative to other ordinal regression models, such as the generalized ordered logit model fit by gologit2. Finally, the article offers guidelines on how to interpret, test, and modify heterogeneous choice models.