st: Which probability to use as reference point in a conditional logit?

[paul jacobs <pauldjacobs@gmail.com>]

Thank you in advance for looking at this; I tried very hard to be sure
this question hasn't been answered before but apologies if that is the
case.

I am trying to interpret the marginal effects of several covariates
after running a conditional logit model.  My question concerns how to
choose the correct reference point for comparing the size of these
marginal effects.

I first run a conditional logit model in stata (using the command,
clogit) and then use the following postestimation command to retrieve
marginal effects (which sets the fixed effects, which are person-level
in my case, to zero):

mfx, predict (pu0)

The rationale for choosing that command is explained here:
http://www.stata.com/support/faqs/statistics/predict-option-unsuitable/

My question is: how do I interpret the size of the marginal effects?
On average, let's assume the people in my sample have 33.3 choices
(each person chooses one and only one of the average of 33.3 choices),
implying a mean probability across the sample of choosing any one
outcome of ~3%.  However, when the marginal effects are being
calculated (and the individual fixed effects are suppressed), the mean
predicted probability across the sample is 90%, which appears in the
output for mfx with the pu0 option.  (I've confirmed this
independently as well.)

Let's assume a particular covariate's marginal effect is a 1
percentage point increase in the probability of choosing an outcome.
It matters greatly whether 3% or 90% is my reference point for
comparing the relative size of that marginal effect. 3% seems like the
better comparison because it is the actual probability of choosing an
option across the sample but 90% is the predicted probability after
suppressing fixed effects and the basis of the command which produced
the marginal effects. Which one is the appropriate comparison and why?

I am really stuck on this one; thank you Stata listserve members!
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