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st: RE: Test for similarity among subsamples


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Test for similarity among subsamples
Date   Tue, 1 Apr 2008 15:34:44 -0400

P.M.J. Stromberg wrote:

>>I want to run probit estimations on three sub samples (representing
one 
ethnic group each), with the same variables (Y and X). But first I need
to 
know if this is justified: is there a way to test if the difference
among 
the sub samples is statistically significant (such as log likelihood
ratio 
test)?<<

There may be some super-clever econometric test I'm unaware of for this,
but it seems to me that you have a classic "multi-group analysis"
problem. This sort of thing shows up in a lot of psychometric
applications a lot (see "factorial invariance"). In general, the
resulting models are interactions of the group variables with all the
other predictors. You would test these as a block. 

Let's say you have an outcome (y) three predictors (u, v, w) and one
group membership (g).

     probit y u v w                         //assumes no group effect at
all. 
     xi: probit y u v w i.g                 //assumes group effect
shifts intercepts only. 
     xi: probit y i.g*u i.g*v i.g.w i.g     //makes group interactions 

Likelihood ratio tests among these models will tell you whether you need
the group interactions. Of course, such tests are unlikely to have good
power if you have many groups and/or many predictors. 

Jay

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