Re: st: RE: RE: RE: Reference group for categorical interactions

[Maarten Buis <maartenlbuis@gmail.com>]

On Thu, Sep 26, 2013 at 1:53 AM, Hussein, Mustafa wrote:
> Though widely used, ORs mask the heterogeneity in the marginal effects across subjects, and their interpretation in the presence of interaction terms is not straightforward. I would suggest sticking to the marginal effects at the means, if that's meaningful, or estimate them at some relevant representative values for other covariates.

A different take on this issue is that a marginal effect is a linear
model estimated on the results of a non-linear (logit) model. If you
need a second model to interpret the results of your original model,
then there is something wrong with your original model. The purpose of
a model is to simplify what you have seen (your data) such that it is
interpretable, and if you think you need to estimate a second model to
interpret the results of your first (logit) model, then your first
model is not doing what it is supposed to be doing.

I would recommend to stick to the interpretation of the model in terms
of its natural parameters in their natural form as the main form of
interpretation, marginal effects can play a useful role as a secondary
interpretation. So you would need to choose your model such that its
natural parameters correspond with what you and your audience are
comfortable with: If you want risk differences you would estimate a
linear probability model, if you want risk ratios you estimate a model
with a log link (e.g. -poisson-), if you want odds ratios you estimate
a logit.

It may be that you will find that a linear probability model or a
Poisson model does not fit the data well, and you will need to move on
to a logit model. That is a good thing: by estimating these models
directly you can easily detect whether your model makes sense. If
instead you had estimated it indirectly by first estimating a logit
model and then estimating marginal effects, you probably would not
have seen that the final model (the marginal effects _not_ the logit)
does not fit the data.

When it comes to the interpretation of interaction terms in a logit model, see:
M.L. Buis (2010) "Stata tip 87: Interpretation of interactions in
non-linear models", The Stata Journal, 10(2), pp. 305-308.
<http://www.maartenbuis.nl/publications/interactions.html>

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------

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