st: margins after xtlogit

[Traci Schlesinger <traci.schlesinger@gmail.com>]

hi all:

i am analyzing racial disparities in pretrial diversions (a yes no,
i.e. 0/1, criminal justice outcome) using individual level data from
the SCPS, which is clustered by county--an observation for every
individual charged with a felony in sampled counties is included.  to
account for the county level sampling, i'm using xtlogit with county
level random effects.

however, i'm having difficulty interpreting the results from margins
after xtlogit.

if i estimate a model with logistic and then ask for margins on race i get:

. margins race1, post

Predictive margins                                Number of obs   =      46019
Model VCE    : OIM

Expression   : Pr(diversion), predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       race1 |
          1  |   .1025184   .0023145    44.29   0.000      .097982    .1070548
          2  |   .0848741   .0020596    41.21   0.000     .0808374    .0889109
          3  |   .0858849   .0023203    37.01   0.000     .0813372    .0904327

------------------------------------------------------------------------------

which i interpret as meaning that if everyone in my sample were white
(race1 = 1), 10% of defendants would be offered pretrial diversions.
if everyone were black (race1=2), only 8% of defendants would be
offered pretrial diversions.  (race1=3 are Latinos, with 8.5% of
people getting diversions).

however, if i estimate xtlogit --either getting my results as
coefficients or odds-ratios-- and then margins, i get the following
table.

. margins race1, post

Predictive margins                                Number of obs   =      46019
Model VCE    : OIM

Expression   : Linear prediction, predict()

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       race1 |
          1  |  -3.580741   .2277247   -15.72   0.000    -4.027073   -3.134409
          2  |  -3.919428   .2274633   -17.23   0.000    -4.365248   -3.473608
          3  |   -3.67982   .2301685   -15.99   0.000    -4.130942   -3.228698
------------------------------------------------------------------------------

i am at a loss as to how to interpret this.  for starters, it seems
strange that all three racial groups have negative margins.  also, i'm
clearly not looking at the percent of defendants who get a pretiral
diversion any more.  i've looked through the manual, but have not been
able to figure this out.  i would appreciate any help.

cheers,
traci
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