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From |
"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu> |

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

Subject |
RE: st: Differences in regression slopes |

Date |
Thu, 21 Feb 2008 08:39:01 -0800 |

The 3.29 appears to be pi^2/3 which is the standard deviation of a standard logistic distribution. Tony Peter A. Lachenbruch Department of Public Health Oregon State University Corvallis, OR 97330 Phone: 541-737-3832 FAX: 541-737-4001 -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard Williams Sent: Wednesday, February 20, 2008 2:17 PM To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu Subject: Re: st: Differences in regression slopes 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. ------------------------------------------- Richard Williams, Notre Dame Dept of Sociology OFFICE: (574)631-6668, (574)631-6463 HOME: (574)289-5227 EMAIL: Richard.A.Williams.5@ND.Edu WWW: http://www.nd.edu/~rwilliam * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: Differences in regression slopes***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**References**:**st: Differences in regression slopes***From:*"Barth Riley" <BarthRiley@comcast.net>

**Re: st: Differences in regression slopes***From:*"E. Paul Wileyto" <epw@mail.med.upenn.edu>

**Re: st: Differences in regression slopes***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

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