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

[David Hoaglin <dchoaglin@gmail.com>]

Dear Suryadipta,

I'll have to look at Maarten's Stata tip #87.

In the piece by Michael Rosenfeld the counts in the log-linear model
come from a 2x2 table, which is the usual setting for an odds ratio.
He also says, "all other factors held constant."  That's the part of
the common interpretation of regression coefficients that I urge
people to avoid, because it does not reflect the way regression
actually works.

Lecture 10 by Sharyn O'Halloran deals with multinomial data, which can
be the basis for odds ratios (relative to a reference category).  It
also has the problem of oversimplifying the interpretation by saying
"with the other variables in the model held constant."  It saddens me
to see that flawed interpretation being given to students.  It will
probably lead them to make mistakes later on.

If Trade in your model is "continuous," I do not see a basis for odds ratios.

David Hoaglin

On Mon, Jun 10, 2013 at 1:02 PM, Suryadipta Roy <sroy2138@gmail.com> wrote:
> 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.
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