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Re: st: Interpretation of interaction term in log linear (non linear) model


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpretation of interaction term in log linear (non linear) model
Date   Mon, 10 Jun 2013 11:18:39 -0400

Dear Suryadipta,

I have little experience with -margins-, but it seems that one has be
careful in using it.  For example, I would not want it to evaluate the
model only at the means of the other predictors unless I had checked
that that combination of values was supported by the data.

Your model is not a logistic regression, so it does not involve
log-odds, and none of the coefficients have an interpretation as
log-odds-ratios.

What is the basis for your statement that the odds ratio is constant
(does not depend on the values of the other predictor variables)?
When a logistic regression involves other predictors, each odds ratio
is an adjusted odds ratio (i.e., the odds ratio is adjusted for the
contributions of the other predictors).  To calculate predicted
probabilities from such a model, one has to supply values of all the
predictors, and each combination of those values should be supported
by the data (the idea is to avoid extrapolating outside the region of
"predictor space" covered by the data).

The adjustment for the contributions of the other predictors (in the
data at hand) is part of the interpretation of a regression
coefficient in all types of regression models.

David Hoaglin

On Mon, Jun 10, 2013 at 9:37 AM, Suryadipta Roy <sroy2138@gmail.com> wrote:
> Dear David,
> Thank you very much for the wonderful suggestions! I would make sure
> that the writeup reflects them! In fact, I have used -margins- to
> reflect the contribution of x1 in the two groups as well. A related
> question was if the coefficient of the interaction term in the
> log-linear model can be interpreted as a log-odds ratio, and that an
> important property of odds ratios is that it is constant, i.e. does
> not matter what values the other independent variables take on. I
> believe that your suggestions (and my query here) is relevant for
> Poisson/NB models as well.
>
> Sincerely,
> Suryadipta.
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