Interpreting and using heterogeneous choice and generalized ordered logit models

The assumptions of the ordered logit/probit models estimated by ologit and oprobit are often violated. When an 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, which can be estimated with the user-written program oglm, explicitly specify the determinants of heteroskedasticity in an attempt to correct for it. Further, these models can be used when the variance/variability of underlying attitudes is itself of substantive interest. In other instances, the parallel lines assumption of the ordered logit/probit model is violated; in such cases, a generalized ordered logit/probit model (estimated via gologit2) may be called for. This paper talks about how to interpret and use the models that are estimated by oglm and gologit2. We talk about key assumptions behind the models, when each type of model may be appropriate, when the models may be problematic, and how to interpret the results and make them easier to understand.