Correlations in “to” and “from” parameters in dyadic models

Justin Gross writes:

Is there a way in lmer to specify a particular nonzero correlation between certain random effects? I’m working with a social relations type model (with logit link)–similar to models by Snijders and Kenny, and Hoff, et al. Among my random effects are sender and receiver effects, s_i and r_j indicating that an observed dyadic relation is from actor i to actor j. But I would like to allow for the possibility that s_i and r_i are correlated, that is actor i’s “gregariousness” is not unrelated to his/her “popularity”. lmer estimates the variance for sender and receiver effects, but If I wish to incorporate covariance between sending and receiving, do I need to just estimate this separately and adjust my estimates manually, or can this be accommodated within lmer.

My quick answer: yes, you can have correlations, no problem. It just gets structured in the same way as correlations in a varying-intercept, varying-slope model. In either case, you have two parameters for each group. Whether this can be done easily in lmer, I’m not sure. But you can do it in Bugs (as long as it runs in reasonable time and doesn’t crash).