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st: RE: RE: comparing coefficients

From   "Hoetker, Glenn" <[email protected]>
To   <[email protected]>
Subject   st: RE: RE: comparing coefficients
Date   Mon, 30 Aug 2004 15:02:56 -0500

In response to Ricardo Ovaldia's question about comparing coefficients
across groups in logit models, I'd note that comparing coefficients
across logit models is actually significantly trickier than the
literature would suggest.  The heart of the issue is that logit/probit
coefficients are scaled by the unobserved heterogeneity in the sample.
Thus, apparent differences in coefficients across groups can reflect
"real" differences or differences in unobserved heterogeneity. 

The canonical reference on the topic is 

Allison, Paul D. Comparing logit and probit coefficients across groups.
SMR/Sociological Methods & Research. 1999; 28(2):186-208.

Ken Train also discusses this from the economics viewpoint on pages
44-46 of 

Train, Kenneth E. Discrete choice methods with simulation. Cambridge :
Cambridge University Press; 2004.

The interaction technique (logit y x_male x cigs_male cigs) is
particularly susceptible to yielding false results.  Even in a linear
model, it will result in apparent NON-significance of the interaction
term if the two groups have different variances (see Gujarati, Damodar.
Basic econometrics. 2nd ed. New York: McGraw-Hill; 1988).

I have a working paper that uses Monte Carlo simulations to test the
methods suggested by the Allison piece, finding them to be a significant
improvement over existing practice, although not a panacea. Simulations
show that the interaction technique performs particularly poorly for
logit, frequently yielding significant results of the _incorrect_ sign!
The paper suggests a few alternatives that might also be helpful.  The
simulations also show that even fairly small differences in unobserved
heterogeneity across groups can cause problems. If you think the paper
might be useful to you, you can find it ("Confounded coefficients...")
in the working papers section of

Best wishes!


Glenn Hoetker
Assistant Professor of Strategy
College of Business
University of Illinois at Urbana-Champaign
[email protected]

-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Nichols,
Sent: Monday, August 30, 2004 2:34 PM
To: '[email protected]'
Subject: st: RE: comparing coefficients

One way is
.  gen x_male=x*male
.  gen cigs_male=cigs*male
.  logit y x_male x cigs_male cigs
.  test cigs_male

-----Original Message-----
From: Ricardo Ovaldia [mailto:[email protected]]
Sent: Monday, August 30, 2004 3:25 PM
To: [email protected]
Subject: st: comparing coefficients

This question may have been asked and answered before,
but I could not find it in the archives.

If I fit two logistic models, less say one for males
and one for females, than include the same 5
covariates and one exposure variable, less say number
of cigarettes smoked per day. How can I test if the
odd ratios (coefficients) for the exposure variable
(number smoked)are the same in the two models?

Thank you in advance,


Ricardo Ovaldia, MS
Oklahoma City, OK

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