Estimating Heterogeneous Choice Models with Stata
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 OLS regression) the parameter estimates are biased. Heterogeneous choice/ location-scale models explicitly specify the determinants of heteroskedasticity in an attempt to correct for it. These models are also useful when the variability of underlying attitudes is itself of substantive interest. This paper illustrates how Williams’ user-written routine oglm (Ordinal Generalized Linear Models) can be used to estimate heterogeneous choice and related models. It further shows how two other models that have appeared in the literature – Allison’s (1999) model for comparing logit and probit coefficients across groups, and Hauser and Andrew’s (2006) logistic response model with partial proportionality constraints (LRPPC) – are special cases of the heterogenous choice model and/or algebraically equivalent to it, and can also be estimated with oglm. Other key features of oglm that are illustrated include support for linear constraints, the use of prefix commands such as svy and stepwise, and the computation of predicted probabilities and marginal effects.
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