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st: RE: Comparing models across ethnic groups


From   "Maarten Buis" <M.Buis@fsw.vu.nl>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Comparing models across ethnic groups
Date   Tue, 20 Jun 2006 13:29:51 +0200

---- Stephen Soldz wrote:
<snip>
> In particular, our question concerns ethnic group similarities and
> differences in predictive models.We are willing to view whites as a
> reference group and examine differences in models for other groups 1 by 1.
>
> As I see it, this is essentially an interaction of ethnicity X predictor.
> The problem is that we have multple predictors and want to ultimately do a
> multivariate model including a number of precdictors. HYet, models with many
> interactions are essentially impossible to interpret.
>
> I can only see looking at interactions one predictor at a time, to see which
> predictors differ by ethnic group. Then constructing a model separately for
> each ethnic group. Not that satisfactory.
> 
> Questions:
> 
> A. If we use my strategy, is there any reasonable way to compare the final
> models as a whole? If so, can we compare particular paths.
> 
> B. Is there a better alternative?
>
> C. How might one estimate power, to at least have something to put in a
> "power" section of the grant? BTW, at this point, we can find no info on
> design effects in the sample.


Separate models for different ethnic groups is equivalent to a single model
with interaction terms between all variables and ethnic background. So the 
separate models can be seen as a representation of the interaction model 
that you find more easily interpretable. You could give two tables: one 
showing the different models for different groups and one testing the 
differences versus white like the table below. "Predictor # for white" is 
the main effect of predictor #, and "dif. black vs white" is the interaction
effect of predictor # X black. 

--------------------------------------------------
                              b        t       p   
--------------------------------------------------         
predictor 1 for white
     dif. black vs white
     dif. hispanic vs white
     dif. native vs white

predictor 2 for white
     dif. black vs white
     dif. hispanic vs white
     dif. native vs white
--------------------------------------------------

This way you would look at the same model twice: saying that the effect of 
of predictor x is 3 for whites and 2 for blacks is the same as saying that
the effect of predictor x is 3 for whites and 1 less for blacks. But that 
isn't a bad thing if it helps interpretation of the model.

Also you don't necessarily need to look at differences versus whites, you 
could also look at differences versus the grand mean, or other contrasts. 
Look at -findit xi3- for various pre-programmed options. Another option 
would be to leave the main effect for predictor 2 out of the model and add 
the interaction between predictor 2 and all ethnic dummies (including 
white). In that case the parameters for the interactions are the same as 
those you would get if you estimated separate models of the different 
ethnic groups. If you are uncomfortable with using this kind of "tricks" 
using different coding schemes, you can also calculate the effect of 
predictor 2 for blacks and its standard  error and confidence interval 
using -lincom-: the effect of predictor 2 for blacks is the main effect of 
predictor 2 and the interaction term of predictor 2 with the black dummy. 

In general, models with many interactions are not "essentially impossible to
interpret". It just requires a lot of careful thought about how to construct
tables (and/or graps) and which contrasts to use. 

As for power, my experience is that interactions devour lots and lots of 
power, especially if some of the groups are relatively small. But that 
statement is probably not precise enough for you.

HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology 
Vrije Universiteit Amsterdam 
Boelelaan 1081 
1081 HV Amsterdam 
The Netherlands

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z214 

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------



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