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st: Poisson model with interaction term


From   agostino@unical.it
To   statalist@hsphsun2.harvard.edu
Subject   st: Poisson model with interaction term
Date   Mon, 25 Feb 2008 14:41:29 +0100

Dear all,
I’m estimating a Poisson model, which includes an interaction term as follows:

(ln)Y=a+b1x1+b2x2+b12x1*x2
and I need to compute the impact (marginal effect) of x1 on lnY.


I have found on SJ an article “Computing interaction effects and standard 
errors in Logit and Probit models”, by Norton, Wang and Ai (2004), who warn 
that for nonlinear models:“ First, the interaction effect could be nonzero even 
if b12 = 0. (…) Second, the statistical significance of the interaction effect 
cannot be tested with a simple t-test on the coefficient of the interaction 
term b12. Thirdly, the interaction effect is conditional on the independent 
variables, unlike the interaction effect in linear models. (It is well known 
that the marginal effect of a single uninteracted variable in a nonlinear model 
is conditional on the independent variables). Fourthly, the interaction effect 
may have different signs for different values of covariates. Therefore, the 
sign of b12 does not necessarily indicate the sign of the interaction effect” 
(page 156).
 Please notice that my interest is  computing the effect of x1 on lnY ,  I’m 
not interested in the marginal effect of the interaction term, nor in the 
effect of  x1 on E(Y), because my dependent variable is not a count.
  Since there is the interaction I cannot conclude that the impact of x1 on lnY 
is just b1.
In a linear model I could apply the following formula:
 marginal effect of x1= b1+ b12*x2, 
and compute the relative standard errors sqrt(varb1+var b12*x22+2x2covb1b12)
However, according to Norton et al. (2004),  I cannot employ the STATA 
estimates in this way,  as the interaction effect may have different signs for 
different values of covariates. 

How can I then compute (and possibly graph) the impact of x1 across the values 
of x2 using STATA?

I would really appreciate any assistance with this issue 

Maria


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