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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   Tue, 7 Feb 2012 11:49:08 +0100

On Mon, Feb 6, 2012 at 7:01 PM, Richard Williams wrote:
> I think knowing the mean of a variable is useful, e.g. is the mean income
> $30K or is it $60K? Likewise I think knowing the AME (Average Marginal
> Effect) is useful, e.g. is the average difference between blacks and whites
> 5% or is it 50%? In neither case do I think the number tells you everything
> you could want to know but it tells you something.

The difference between the mean and AME is that the former a model of
the data while the latter is a model of a model. A model is a
simplification of reality and the aim for that simplification is to
get interpretable results. In that sense I have no problem to use the
mean to summarize the data. On the other hand if one needs an
additional model (marginal effects) to understand an initial model (a
non-linear model like -logit-), than the initial model is not simple
enough. The way to solve such problems is to choose a model that does
what you want instead of adding a post-hoc fix to an inadequate model.

I don't think that there is no use for AMEs whatsoever, the problem I
have is with studies that only report or discuss AMEs. In essence that
is just an unnecessarily complex way of estimating a linear
probability model, and per Occam's razor, the simple linear regression
model should be preferred in such cases. In addition the checking of
the model assumptions is much easier in a simple linear regression
compared to the linear probability model estimated via AMEs.

> Likewise I think an odds ratio can be helpful, but to make it really helpful
> it is useful to see how predictions differ across baseline levels, e.g it
> makes a difference whether the baseline odds are a million to 1 or 1:1, and
> these baseline odds will differ across individuals.

This is also true for AMEs: .5 percentage points increase means
something very different when the baseline is .5% or 50%. For example,
if we look at the percentage of university students than a .5
percentage point increase when one starts for .5% means that the
employees have to teach twice as many students and that twice as many
students have to fit in the lecture halls. From the perspective of the
universities the .5 percentage points increase represents a major
change. If one however started with 50% university students than the
.5 percentage point increase would be much easier to absorb by the
universities, and that .5 percentage point would now represent a small
change.

In essence the problem with AMEs/linear probability models is that the
coefficients aren't relative, while the problem with odds ratios is
that the coefficients aren't absolute. However, in both cases one
needs to know the baseline in order to properly interpret the effect
size.

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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