[R-sig-ME] glmer: Downdated X'X is not positive definite

[Ross Boylan]

 > r2 <- glmer(sa~(1|id), data=sexpartner, family=poisson(), nAGQ=6)
Error in mer_finalize(ans) : Downdated X'X is not positive definite, 1.
Running a closely related (specifically, the outcome variables match on 
missings)
 > r <- glmer(pAnyUAVI~pIsMale+pEthnic+(1|studyidx), data=sexpartner,
   family=binomial, nAGQ=6)
produces no error.

I trimmed the covariates until only the intercept was left.  I used id 
<- factor(studyidx) in case the fact that studyidx was a character was a 
problem (the archive had a statement that it needed to be a factor).  
The original count data had a minimum of 1; sa was the count -1 so that 
it would look more as expected.  At every step along the way I got the 
same error.

My searches suggested the message usually indicates a colinearity 
problem, but I can't see how it could be, or why it wouldn't have shown 
up for the binomial as well as the poisson.

My data are unusual; cluster size varies widely and there are lots of 
singleton clusters.  I tried simulating data with lots of singletons; 
the poisson fit them fine.  As mentioned the counts have no zeros 
(though the sa outcome above does).

Can anyone suggest steps to diagnose or fix the problem?

R 2.15.2; lme4 Version: 0.999999-0, Date: 2012-06-22 from CRAN.

Ross Boylan

P.S.   Would extending the model to a poisson distribution conditional 
on the value being greater than 0 be hard?