Re: st: Regression Across Two Groups

[Robson Glasscock <glasscockrc@vcu.edu>]

Like Nick, I was also surprised. The original example given seems like
a case where a dummy variable for foreign and an interaction term
would allow Muhammad to test what he wants. Are you sure you want to
test this with a limited dependent variable model, Muhammad?

best,
Robson Glasscock

On Tue, Dec 13, 2011 at 2:40 PM, Cameron McIntosh <cnm100@hotmail.com> wrote:
> Maarten,
> Thanks for your comments. My understanding is that the residual variance difference term is only identifiable for situations with groups (or time points) > 1. Essentially, the term is fixed in the first group but left free in the second, so the first group becomes a "reference category", and the estimate of epsilon_squared for the second group is actually the difference in unobserved residual variation (the same approach is taken in multiple group factor analysis for estimating latent means). I seem to recall that this is somewhat similar in motivation to a more complicated work-around proposed by Allison (1999) in his classic paper I cited earlier in this thread. Unfortunately, I know of no detailed documentation on Muthen/Asparouhov's approach, other than what is mentioned in the manual and occasionally on the Mplus discussion list (www.statmodel.com), but I have been assuming that given the originators' reputations, it's kosher.
> Best regards,
> Cam
> ----------------------------------------
>> Date: Tue, 13 Dec 2011 19:04:26 +0100
>> Subject: Re: st: Regression Across Two Groups
>> From: maartenlbuis@gmail.com
>> To: statalist@hsphsun2.harvard.edu
>>
>> On Tue, Dec 13, 2011 at 6:44 PM, Cameron McIntosh wrote:
>> > I will note that one of the easiest ways to do this is via the Mplus package (www.statmodel.com), which through a special THETA parameterization allows the difference in residual variance to be directly estimated for the multi-group case in both logit and probit models. Thus, cross-group differences in residual variation will not be absorbed by the model coefficients, and not confound the comparison.
>>
>> I find that rather suspect: The residuals we are talking here about
>> are the differences between the latent (and thus unobserved) variable
>> and the predicted probability. The only information in the data
>> concerning any patterns in the variance of these residuals is in the
>> form the fit of a model with a more complex functional form for the
>> relationship between the explanatory variables on the probability of
>> success. So I find it hard to see how one could separate the
>> estimation of the parameters from the estimation of patterns in the
>> residual variance. As a consequence, these models tend to be very
>> (i.e. way too) sensitive to model specification. Moreover, the
>> difference between the complex functional form and the "regular"
>> functional form are really subtle, which means that there is very
>> little information from the data that these models can use. In
>> essence, the problem is real and it cannot be solved.
>>
>> -- Maarten
>>
>> --------------------------
>> Maarten L. Buis
>> Institut fuer Soziologie
>> Universitaet Tuebingen
>> Wilhelmstrasse 36
>> 72074 Tuebingen
>> Germany
>>
>>
>> http://www.maartenbuis.nl
>> --------------------------
>>
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