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Re: st: -clogit-, -asclogit- and marginal effects


From   rgates@stata.com (Richard Gates)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: -clogit-, -asclogit- and marginal effects
Date   Mon, 29 Oct 2007 10:29:22 -0500

Timothy Dang <tpondang@gmail.com> is interested in comparing the marginal
effects computations of -mfx- after -clogit- with those from -estat mfx- 
after -asclogit-.  In -clogit- postestimation terminology, the marginal effects
of -asclogit- are for the -predict, pc1- estimates of -clogit-.  A formal
definition of this computation is found on page 291 of the reference manual [R]
A-H.  To give a rough idea of the computation I hacked in the formula below:

                                 exp(x_t*b)
     Pr(y_t=1|sum_j(y_j)=1) = -----------------
                              sum_j(exp(x_j*b))

The postestimation program -mfx- will not allow you to obtain marginal effects
using this predictor after -clogit-.  -mfx- uses numerical derivatives to
compute the marginal effects.  If we perturb one of the (alternative-specific)
varibles then all of the probabilities of that group (case) will change.  -mfx-
is not general enough to handle this, so we developed -estat mfx- after
-asclogit-. -estat mfx- uses analytical first order derivatives to obtain the
marginal effects and numerical second order derivatives in the standard error
computation.  The numerical derivatives can fail, and this is the case for two
of the tables observed by Timothy.

-Rich
rgates@stata.com
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