st: Date: Sat, 28 Sep 2013 11:24:34 +0200

[Pieter Tuytens <pietertuytens@hotmail.be>]

Dear statalist,


I am considering to use a heteroscedastic probit model since, by using Williams (2010) oglm's stepwise selection procedure, my model showed heteroskedasticity issues.  

A colleague has however following comment and I wonder if these are true and if it is better to refrain from using heteroskedastic models. 

 

...a result from basic statistics,is that there is a specific and special reason for the ordered probit with heteroscedasticity. Basu’s theorem (and Cochran’s theorem) states that a two-parameter distribution with those parameters representing mean and variance has separable parameters if and only if the distribution is normal. The normal distribution has many qualities that are unique and this is one of them. Indeed, this is even more troublesome because the latent variable conceptualization of ordered regression models (the fact that parameters are identified to scale) is even more vexing because Basu’s theorem implies that the mean and variance of the underlying logistic regression cannot be separated. Making an argument in favor of a model that not only has bad properties in Monte Carlo evidence, but that makes no logical sense in the first place is something I would not do. Indeed, I still don’t understand why a simple logistic regression does not better measure these c!
 laims.....

References:

Williams, R. 2010. “Fitting heterogeneous choice models with oglm” Stata Journal Volume 10( 4): 540-567.

Many thanks,

Pieter 		 	   		  
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