st: margins w/mean centered dummies

[William Hauser <whauseriii@gmail.com>]

I'm using xtmelogit with group mean centering to examine several
cross-level interaction terms (as suggested by Enders & Tofighi. 2007.
Centering predictor variables in cross-sectional multilevel models: A
new look at an old issue. Psychological Methods, Vol 12(2):121-138).

I wish to use the margins command to better understand the
interactions but am having trouble understanding the predicted
probabilities for the group mean centered dummy variables. First of
all, under group mean centering the dummy variables are no longer
dichotomous and must be entered in the factor format as continuous
variables (e.g. c.dummy1).  I'm not sure if that violates some
assumption of the margins command.  Second, I can only generate
average marginal effects for these dummy variables ("margins,
dydx(dummy1)") since margins only generates the probability for
non-continuous variables.  I'm not sure what these average marginal
effects even mean under group mean centering.  The centered dummy
variables generally have ranges that  approach 2 (i.e. -1 and 1 are
the logical bounds for the centered dummies) so a 1 unit increase
represents something like almost 50% of the increase possible for the
variable rather than the typical 100% for uncentered dummies.

Is there an easy interpretation here that I'm missing or should I
perhaps not center my dummy variables?

Will Hauser
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