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


From   Suryadipta Roy <sroy2138@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 13:02:56 -0400

Dear David,

Thank you so much for the insightful comments! I have tried to be very
careful with -margins- and -marginsplot- to derive conclusions about
predictions and marginal effects. As regards the log-odds
interpretation, I was under the impression that interactions in a
broad category of non-linear models with multiplicative effects (e.g.
poisson, nbreg, log-linear, etc) can be given a log-odds
interpretation. My impressions are based on the readings of Maarten
Buis's Stata tip # 87: Interpretation of interactions in non-linear
models) as well as the following link:
http://www.stanford.edu/~mrosenfe/soc_388_notes/soc_388_2002/Interpreting%20the%20coefficients%20of%20loglinear%20models.pdf

I believe that I should have been more careful about the "odds ratio
remaining constant" statement. I completely understand that it would
change for interaction terms when any one of the associated variables
changes. However, I was wondering if things will be different in the
absence of interactions as stated here in this link (on pp. 8):
http://www.columbia.edu/~so33/SusDev/Lecture_10.pdf
I will change some of my variables to check for the effects on the
odds ratio. Once gain, thank you very much for the help!

Sincerely,
Suryadipta.

On Mon, Jun 10, 2013 at 11:18 AM, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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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