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Re: st: MIXLOGIT: marginal effects


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: MIXLOGIT: marginal effects
Date   Thu, 9 Feb 2012 10:47:19 +0100

On Thu, Feb 9, 2012 at 10:11 AM, Brendan Halpin wrote:
> To play devil's advocate, let me mention Mood (2010), who argues that
> where unobserved heterogeneity makes it invalid to compare log-odds
> estimates sizes across samples, the LPM estimate can be more consistent.
>
> Mood (2010), 'Logistic Regression: Why We Cannot Do What We Think We Can
> Do, and What We Can Do About It', European Sociological Review, Volume
> 26, Issue 1 Pp. 67-82.

To be exact it is not unobserved heterogeneity per se that is causing
the problem but the difference in the amount of heterogeneity across
groups (heteroskedasticity). As long as you can reasonably believe
that the amount heterogeneity is similar, e.g. because you performed a
randomized experiment, the odds ratios are perfectly accurate.

Anyhow, the characteristic that the estimates are less sensitive to
heteroskedasticity is "bought" with the assumptions of linearity in
the parameters that people don't like about the linear probability
model.

So how to choose between the "wrong" LPM and the "wrong" logistic
regression? Most importantly, do _not_ go looking for a true model,
that is just an oxymoron: a model is and should be a simplification of
reality, and a simplification is just another word for being wrong in
some useful way. Think of the modeling exercise as taking the
information from the observations and using that to build an argument.
That argument is just a set of logical statements that lead from the
observations to the conclusion. It will involve a couple/many untrue
assumptions/simplifications, but as long as they are clearly stated
your audience can make up their own mind whether they buy your
argument or not and whether they can think of a better argument.
Within this framework I am unwilling to exclude the linear probability
model in all situations, but I do want to see a reason for using it
when it is being used. That reason does not have to be "true", it just
has to state the trade-off that has been made.

-- Maarten

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


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