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RE: st: Regression Across Two Groups

From   Cameron McIntosh <>
Subject   RE: st: Regression Across Two Groups
Date   Tue, 13 Dec 2011 14:40:27 -0500

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 (, but I have been assuming that given the originators' reputations, it's kosher.
Best regards,
> Date: Tue, 13 Dec 2011 19:04:26 +0100
> Subject: Re: st: Regression Across Two Groups
> From:
> To:
> 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 (, 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
> --------------------------
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