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From |
Cameron McIntosh <cnm100@hotmail.com> |

To |
STATA LIST <statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: Regression Across Two Groups |

Date |
Tue, 13 Dec 2011 14:40:27 -0500 |

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 > -------------------------- > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Regression Across Two Groups***From:*Robson Glasscock <glasscockrc@vcu.edu>

**References**:**st: Regression Across Two Groups***From:*Muhammad Anees <anees@aneconomist.com>

**RE: st: Regression Across Two Groups***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: st: Regression Across Two Groups***From:*Muhammad Anees <anees@aneconomist.com>

**RE: st: Regression Across Two Groups***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: st: Regression Across Two Groups***From:*Muhammad Anees <anees@aneconomist.com>

**RE: st: Regression Across Two Groups***From:*Cameron McIntosh <cnm100@hotmail.com>

**Re: st: Regression Across Two Groups***From:*Maarten Buis <maartenlbuis@gmail.com>

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