Re: st: marginal effects of interaction variables after clogit

[Maarten Buis <maartenlbuis@gmail.com>]

On Mon, Mar 26, 2012 at 4:51 PM, Ori Katz wrote:
> clogit choice1 c.m_inc12_jman i(1
> 3/8)bn.ethnic_origin_ussr#c.m_inc12_jman, or group(id)
>
> you can see that I omit ethnic origin 2 (there are 8 categories).

the easy way to do so is to type -ib2.ethnic_origin- instead of  -i(1
3/8)bn.ethnic_origin-.

> after the regression I try to run marginal effects, by using the
> command:
> margins, dydx(*) predict(xb)

This not meaningfull, it just shows the "effect" on the linear
predictor, which is a beast without substantive interpretation in a
-clogit-.

> I run into two problems in the results from the margins command:
>
> 1. the results table include m_inc12_jman and ethnic_origin_ussr, but
> not the interaction between them.

Marginal effects of interaction terms in non-linear models are hard
and Stata won't calculate them. My take on that is that marginal
effects get so tricky with interaction terms that they are no longer
useful. Instead you should learn how to interpret (and explain to your
audience) the interaction in the natural metric of the model.

In case of a -clogit- they are odds ratios and ratios of odds ratios.
These have an unjust (or at least exaggerated) reputation of being
hard to interpret, but they are actually quite easy: see for example:
M.L. Buis (2010) "Stata tip 87: Interpretation of interactions in
non-linear models", The Stata Journal, 10(2), pp. 305-308.

Alternatively, you can start with choosing the metric of interest as
linear additive on the probability, which is typically what one ends
up with when reporting marginal effects, and look for a model in which
that is the natural metric. This is just the linear probability model.

I would typically prefer a logit over a linear probability model and
interpret my results in terms of odds, odds ratios, and ratios of odds
ratios. However, I would consider a linear probability more "honest"
than fitting a logit and report only one (average) marginal effect per
variable. The latter gives your audience only one additive effect per
variable, which is just a straight line. So is in essence marginal
effects used like that are just a linear model fitted on top of a
non-linear model. If you wanted a linear model, than you should have
estimated one to begin with and openly suffer all the consequences.

> 2. Stata omits ethnic origin 1 and 2 from the results, but I want to
> omit only 2.

That has to do with the weird way you specified the base-value: -i(1
3/8)bn.ethnic_origin-. With that you said -bn-, meaning there is no
base value. You manually override it by specifying all values you want
to include, but the -bn- part is dominant so Stata thinks it has to
exclude another value. You can (and should) prevent this problem by
just specifying -ib2.ethnic_origin-.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


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