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Re: st: Regression Across Two Groups

From   Richard Williams <[email protected]>
To   [email protected], [email protected]
Subject   Re: st: Regression Across Two Groups
Date   Tue, 13 Dec 2011 15:29:07 -0500

At 01:04 PM 12/13/2011, Maarten Buis wrote:
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

I go over the Pros and Cons of various methods (Allison, Long, My own) in (starting around slide 20.) In logit and probit models that want to examine group differences, radically different interpretations can be consistent with the same empirical results (which I think is what Maarten means when he says "I find it hard to see how one could separate the estimation of the parameters from the estimation of patterns in the residual variance.") Based on theory, you can offer an interpretation, but that interpretation may be wrong.

Long takes a sort of a high-tech descriptive approach that may avoid such issues, but is also somewhat unsatisfying because it doesn't offer a substantive explanation as to why group differences exist.

My own bias is to offer the interpretation I most believe in while conceding the inherent problems that come from working with binary or ordinal dependent variables.

Richard Williams, Notre Dame Dept of Sociology
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