Re: st: re: marginal vs discrete effects in logistic regression

[Maarten Buis <maartenlbuis@gmail.com>]

On Thu, Aug 4, 2011 at 7:25 AM, Kouji Asakura wrote:
> 1) In trying to compute for the marginal effects, i came across two commands in stata that compute for these : prchange and mfx.  From what I have read so far, mfx computes for the change in probability for every increase in your independent variable, while holding the other variables constant at their mean, while for the marginal effects computed by the prchange command, it is described as "MargEfct: the partial derivative of the predicted probability/rate with respect to a given independent variable". My question however is... are these marginal effects applicable if all of your predictor variables are discrete/ at most ordinal scale? I'm hesitant to interpret the marginal effects as "change in probability... while holding other variables constant at their mean" because ordinal variables do not have means.

I am not so worried about that, but it can certainly be useful to use
the -at()- option to evaluate the marginal effect or discrete change
at values of your choice. A third possibility is to use -margins- and
get the average marginal effect (instead of the marginal effect at
average values of the covariates). This latter seems to be more often
prefered, but it is not without problems: In order to live up to its
promise you need to have data that is representative for the
population with respect to all variables in your model, while the
other measures "only" require that the probability of being included
does not depend on the dependent variable.

In practice many -logit- models are approximately linear in the
probability over the observed range, in which case the difference
between these different measures will often be too small to lead to
different conclussion. In those studies where the effects are so
non-linear that these measures have meaningfull differences, you
should worry about whether it is meaningfull to try to summarize such
a non-linear effect with one number anyhow. In your case where you
have only categorical/ordinal variables and the fact that you are only
interested in the additive effect on the probability you can also
consider a linear-probability model (just -regress- with the
-vce(robust)- option). In that case you get the effects directly.

> 2). I am computing the marginal effects also for the purpose of determining the variable's order of influence on the probability of success (which variable has the most influence, has the least, etc) ... but when I compare them with the standardized coefficients, the rankings differ... Which is the more appropriate statistic to use for this purpose?

I don't see much added value for standardized coefficients in your
case: The explanatory variables are dummies, so they have all the same
scale, and the dependent variable also has the same scale. In that
case standardizing coefficients won't give you anything you could not
get when looking at the raw coefficients. This gives you a clue to
what might be going on: The coefficients and especially the odds
ratios (exp(coefficient)) are effects in relative terms, they are
ratios, while marginal effects are effects in absolute terms, they are
differences. Both can be meaningful, and relating the two findings can
be really illuminating. 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.

You said that some of your variables are ordinal. In that case you can
get one coefficients for those ordinal variables using sheaf
coefficients. These are implemented in -sheafcoef-, which you can
download by typing -ssc install sheafcoef-, and which is discussed in
<http://www.maartenbuis.nl/wp/prop.html>.

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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