Re: st: Heteroskedastic Probit Model

[Richard Williams <Williams.NDA@comcast.net>]

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

http://www.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf

(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.


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Richard Williams, Notre Dame Dept of Sociology
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