[R-sig-ME] Estimate correlated non-nested RE?

[Karl-Oskar Lindgren]

Dear listusers,

I have a newbie question on lmer. Currently I'm working on a  
networklike problem involving dyadic data. I would like to estimate a  
crossed-random effects model in which I take account of  the fact that  
observations are most likely correlated both across rows and columns  
of my dataset (the rows are elite representatives and the columns are  
ordinary citizens, and the dependent variable is elite-mass policy  
congruence). If I specify my model like this:

m2<-lmer(y~1+x1+x2+(1|column_id)+(1|row_id), family=binomial(link="probit"))

(where x1 and x2 are the fixed effects of interest) I get uncorrelated  
crossed-random effects. But I would want to relax the assumption  that  
the unobserved heterogeneity across rows and columns are uncorrelated.  
How do I do that? I guess this is really simple but I have failed to  
accomplish this. All examples that I have come across on the web  
either have correlation between slopes and intercepts or involves  
nested random effects. But I would like to estimate a correlation  
coefficient  between two non-nested random effects. How do I do that?

Thanks in advance (and sorry if the answer is readily available in  
some document that I have missed)

Best
Karl