st: 3 level xtmelogit woes

[William Hauser <whauseriii@gmail.com>]

Hi all,
I'm working with hierarchical 3 level criminal sentencing data.  The
basic model, without predictors, is of the form "xtmelogit outcome
circuit: || judges: || cases: , or variance".  My primary interest is
in the second level variables and their interaction with the level 1
variables.  I consider the third level a nuisance to be controlled;
there are 20 circuits and no predictors at the circuit level.

The problem is thus:
Some judges operate in multiple circuits so a correctly specified
three level model should be cross-nested but I am certain that such a
model will not converge.  I can impute the judge's modal circuit for
all cases heard by that judge and even then a three level model
specified as above (non crossed) with no predictors will not converge,
probably because there are so few circuits.  So, am I correct in
assuming that the only alternative is to represent circuit with 19
separate dummy variables?  And if so, should I use the variables based
on the judge's modal (or 'typical') circuit or just enter the dummies
as they are (i.e. some judges will have cases in multiple circuits)?

I'd prefer to not impute circuit but am concerned that the unaccounted
cross-nesting of judges in circuits may bias variance estimates in
some unforeseen way.  Remembering that the circuit level is not of
substantive interest, what approach would be advisable in this
situation?

Will Hauser
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