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Re: st: Heteroskedastic Probit Model

From   Richard Williams <>
Subject   Re: st: Heteroskedastic Probit Model
Date   Sat, 24 Apr 2010 01:07:49 -0500

At 02:54 PM 4/22/2010, Richard Williams wrote:
True, but if you just throw up your hands and say you will assume no hetero, that has problems too. You may get estimates that are misleading, particularly if, say, you are interested in things like group comparisons of effects. If you have a theoretically plausible model, you can test whether the variables in the variance equation have significant effects. Alas, if the model is wrong that can also lead to incorrect conclusions. But you're taking a risk whatever you do, so you should think about what makes most sense while realizing that other things may make sense too.

Also, the rough information becomes less rough if you have ordinal variables, because ordinal variables convey more information about the underlying latent variable.

I tossed this out quickly the other day and i thought I should elaborate. Binary dependent variables have been shown to have lots of problems in a heteroskedastic probit model, even if the model is correctly specified. As Maarten says, such variables convey only limited information about the underlying Y*. Simulation studies, however, indicate that ordinal variables convey more information and fare much better in a heteroskedastic model. For a discussion, see

(or else go to the May 2009 Sociological Methods and Research where the final paper was published). The paper also elaborates on why a bad hetero model can be worse than a model that just ignores heteroskedasticity.

Richard Williams, Notre Dame Dept of Sociology
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