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Re: st: Differences in regression slopes


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: Differences in regression slopes
Date   Wed, 20 Feb 2008 17:17:23 -0500

At 12:14 PM 2/20/2008, E. Paul Wileyto wrote:
Responses so far have sent you this way and that. Just look up -test- in STATA help.

To get to the point of using -test- for your purpose, you would need to specify a model that has group-specific slopes, or combine two regressions, one for each group, using -suest-.

Paul
Without going into all the gory details, in logit and probit models such comparisons have much the same problem as you have in OLS if you try to compare standardized coefficients across groups. In OLS, the problem with comparing standardized coefficients is that, unless the means and standard deviations of variables are the same across populations, the variables will get standardized differently across populations (e.g. in one population the variable gets divided by 3 while in the other it gets divided by 4) so the coefficients are not comparable.

In logit and probit models, the coefficients are inherently standardized, albeit in a different way. In order to identify the coefficients, in a logit model, the residual variance is typically fixed at pi^2/3, or about 3.29. In probit, the residual variance is typically fixed at one. BUT, if residual variability differs across populations, the coefficients in the two populations get standardized differently and hence are not directly comparable.

For a much more detailed and probably clearer discussion, see

Allison, Paul. 1999. "Comparing Logit and Probit Coefficients Across Groups." Sociological Methods and Research 28(2): 186-208.

Incidentally, a little exercise I use to help my students see this: Run a logit model. Then run Long and Freese's -fitstat- command. The error variance will be reported as 3.29. Now, add some variables to the model. Or, if you prefer, drop some variables. Or, just use entirely different variables. No matter what you do, the error variance is always 3.29. It is very different from the way we are used to seeing things in OLS.


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Richard Williams, Notre Dame Dept of Sociology
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