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st: Question on constraining estimates


From   "Narasimhan Sowmyanarayanan" <narasimhan.sowmyanarayanan@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Question on constraining estimates
Date   Fri, 28 Mar 2008 10:49:02 -0400

Hi Statalisters:

First of all I apologize if this question does not relate entirely to
a software problem in stata. However, I am a little confused about
some results that stata is throwing up.

I am trying to run some simple OLS models across two different groups.
Group A and Group B. My regression equation is of the simple form

y=a+a1 *x1 +e

However, the variable x1 is measured across two different groups. My
objectives were to examine the following.

a) examine possible invariance of the equation across the two groups
b) test for significant differences in the regression coefficients
across the groups.

For testing both I started with creating a group dummy variable and
the interaction terms for each of the independent variable as in

http://www.ats.ucla.edu/stat/stata/faq/compreg3.htm

I created 1 interaction term. For testing a) I used a constrained
regression with the coefficient of the interaction variables to be
constrained to 0 and comparing the two regression equations using with
a change in F value between the constrained and free models. For
testing (b)  I used the suest procedure in stata, and the alternative
equivalent procedure I understood is that i can test for the
interaction coefficients to be zero is to use the test procedure.

I am finding that despite  getting a significant improvement in the
model fit (Decrease in F values) when releasing the parameters (each
one of them) as opposed to a fully constrained regression equation (as
in (a) -- suggesting that substantively the impact of the IV's on the
models is different), I find none of the slopes are significantly
different when I test for the coefficient of the interaction variable
to be zero. My expectation was, given the significant changes in the
model F values on changing each parameter, I should find significant
differences in regression coefficients across the models ? Is this a
reasonable expectation ? I was curious to understand how these are
implemented

Thanks

Narsi
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