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

[<S.Jenkins@lse.ac.uk>]

The debate about the relative usefulness of odds ratios and marginal effects will run and run, and for some good reasons.

Nonetheless, for some strongly expressed views that are counter to Maarten's, and which I have some sympathy with, have a look at:

"Log Odds and Ends", by Edward C. Norton, NBER Working Paper No. 18252, http://www.nber.org/papers/w18252
Inter alia, Norton states in his abstract " There is no one odds ratio ..."

Stephen
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Stephen P. Jenkins <s.jenkins@lse.ac.uk>
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Date: Thu, 26 Sep 2013 09:36:32 +0200
From: Maarten Buis <maartenlbuis@gmail.com>
Subject: Re: st: RE: RE: RE: Reference group for categorical interactions

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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