Heterogeneous choice models are extensions of binary and ordinal regression models that explicitly model the determinants of heteroskedasticity. I show that in many cases moderation (proximity to a choice threshold) will produce empirical results identical to heteroskedasticity in binary heterogeneous choice models, while extremity (a preference for endpoint categories) will produce empirical results identical to heteroskedasticity in ordinal heterogeneous choice models. I show how a simple extension of Williams' user-written oglm command (2006) can create heterogenous ordered choice models that can distinguish between heteroskedasticity, extremity, and moderation.
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