Posted by
JOHN ANTONAKIS on
Sep 08, 2006; 8:25pm
URL: http://spssx-discussion.165.s1.nabble.com/regression-with-interaction-of-group-variable-tp1070835p1070841.html
Hi:
Comments below
> Hi All -
>
> Any comments/advice appreciated!
>
> I have a situation with 2 groups, and 3 continuous
> predictor variables. THe research question is mostly
> regarding whether the predictors differ across the groups.
> I created product vectors of (group x predictor) for all
> crossings of group and predictors. Does it make sense to
> run a regression with just the product vectors as
> predictors (ignoring the vectors of predictor variables?)
>
No. The cross-products are scaled-on the main effects and
the two-way effects. You MUST control for main and two-way
effects before you can use the three-way effects to predict
Y. See, for example,
Evans, M. G. 1991. The problem of analyzing multiplicative
composites. American Psychologist, 46: 6-15.
Any short of doing what I have suggested, will result in
"profoundly and fatally flawed" results (to quote from
Evans).
> Another note: I am using path analysis on this data as
> well, modeling the relationships for the groups separately
> to adress certain predictions regarding the relationships
> between predictors and outcomes in the groups, but I want
> the regression as an omnibus test of differences in the
> predictors. Am I correctly interpreting significant
> coefficients in the regression of the product vectors as
> answering this question?
It is not exactly the same thing, but it will give you
similar results. In the multiple group situation you have
two equations (using one predictor here to keep things
simple):
y(G1)=b0 + b1x + e
y(G2)=b0 + b1x + e
If you estimate a model in which b1 is constrained to be
equal, you notice that the error terms are still
independent. If you pool the data and estimate the following
equation (where z is a grouping dummy variable) you have:
y=b0 + b1x + b2z + b3xz + e
The e term here is now pooled. Here, if b3 is significantly
different from zero it is the same as saying that b1 is
different in both groups. However, the t-statistic will not
be precisely the same because of the way in which the error
term is handled.
HTH,
John.
___________________________________
Prof. John Antonakis
School of Management and Economics
University of Lausanne
Internef #527
CH-1015 Lausanne-Dorigny
Switzerland
Tel: ++41 (0)21 692-3438
Fax: ++41 (0)21 692-3305
http://www.hec.unil.ch/jantonakis___________________________________