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st: logit with interaction and transformation


From   "Pabst Alexander" <Pabst@ift.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: logit with interaction and transformation
Date   Fri, 31 Jul 2009 16:15:56 +0200

Hi,

I'd like to estimate a logistic regression model with an interaction
term between a continuous predictor (X1) and another but ln-transformed
continuous predictor (X2):

Y(0;1) = _b0 + _b1*X1 + _b2*(ln)X2 + _b3*X1(ln)*X2 + ...covariates... 

The interpretation of the interaction in the case of untransformed
predictors should usually be this way:
sum X1
global m  = r(mean)
global sd = r(sd)
lincom x2 + ($m+$sd)*X2*X1  /* Slope 1: high X1 */
lincom x2 + ($m-$sd)*X2*X1  /* Slope 2: low X1*/

I wonder how to interpret the interaction, i.e. the slopes when one
variable is transformed. That means, I would like to say "Given an
increase of 1 unit in X2, the odds ratio associated with Y is ...[OR]...
for X1 one SD above and ...[OR]... for X1 one SD below the mean."

Can I do this with nlcom like this: nlcom exp(x2) + ($m+$sd)*X2*X1 ? But
what about the product term?
Or is there another way?
Thanks for any help!

Alex
 


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