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Re: st: MIXLOGIT: marginal effects


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: MIXLOGIT: marginal effects
Date   Tue, 7 Feb 2012 09:00:01 +0000

I love logits too and I am not especially an advocate of the linear
probability model, but its defence seems simple. It is a model people
might want to consider if it fits fairly well over the range of the
data, not least because statistical people find probability a useful
scale to think on. This can happen when the response proportion
doesn't vary very much. Naturally I agree that a logit model might
work as well or better in this circumstance.

Turn and turn about, most models have absurd implications if you look
carefully. In the auto data I just regressed gallons per mile [NB] on
weight and I get a positive intercept, which is quite unphysical. If I
had a negative intercept, that would have been unphysical too. But I
see no need to force the regression through the origin; that's a
pragmatic decision. What would you do?

Virtually every application of a model involves some absurdity if only
as an indirect implication. Even fitting a normal (Gaussian) always
means a positive probability of something (physically, biologically,
economically, ...) preposterous, but the probability is usually so
small that we forget about it or realise that it is not a worry.

Mechanics problems old-style sometimes had a facetious edge
underlining the art in approximation: An elephant, whose mass may be
neglected [taken as zero], .... Most social science models seem to
involve approximations even more outrageous (no names, no packdrill).

Nick

On Tue, Feb 7, 2012 at 7:50 AM, Clive Nicholas
<clivelists@googlemail.com> wrote:

> Arne Risa Hole replied to Maarten Buis:
>
>> Thanks Maarten, I take your point, but as Richard says there is
>> nothing stopping you from calculating marginal effects at different
>> values of the explanatory variables (although admittedly it's rarely
>> done in practice). Also the LPM is fine as an alternative to binary
>> logit/probit but what about multinomial models?
>
> I'm coming in on this late, but this is to say two things. I tend to
> agree with you over Maarten (whose posts I always read) about the
> usefulness of marginal effects and how they should be used (although
> Maarten is right that using such statistics as a single summary
> measure undermine the whole point of fitting non-linear models).
>
> However, both of you, IMVHO, are wrong, wrong, wrong about the linear
> probability model. There is no justification for the use of this model
> _at all_ when regressing a binary dependent variable on a set of
> regressors. Pampel's (2000) excellent introduction on logistic
> regression spent the first nine or so pages carefully explaining just
> why it is inappropriate (imposing linearity on a nonlinear
> relationship; predicting values out of range; nonadditivity; etc).
> Since when was it in vogue to advocate its usage? I'm afraid that I
> don't really understand this.
>
> Simply put, it's logistic regression or, otherwise, don't bother yourself.
>
> Pampel FC (2000) Logistic Regression: A Primer (Sage University Papers
> Series on QASS, 07-132), Thousand Oaks, CA: Sage
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