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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 13:48:53 -0400

Dear David,
The dependent variable in my regression is indeed a continuous
variable, highly skewed with a lot of zeros (bilateral imports between
countries). I will refrain from using an odds ratio interpretation as
you have suggested. Here is a link to Maarten's Stata tip # 87:
http://www.maartenbuis.nl/publications/interactions.pdf

Best regards,
Suryadipta.

On Mon, Jun 10, 2013 at 1:34 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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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