My subjects are clustered within households and “Clusters”. The specification above gives me only the variances of the House and Cluster random effects but I also want the correlation between the house and Cluster. Is it possible to specify a model which gives that?

Hi,
if I understand you correctly, the correlation between House and Cluster is not a meaningful quantity. Correlation is usually defined by taking a set of pairs of values, i.e. there is the same number of realizations/draws from both variables being correlated. But from your definition it appears that you have multiple households in each cluster. Maybe if you elaborate a bit on what your scientific/real world question is, we might find how it maps to the model better? Or am I missing something about the model structure?

Sorry for a very late response to your email below.

The question that I want to address is for example, whether the risk of an event (first sexual encounter) at a given time is reduced when a Christian family resides in a largely Christian community. See page 441 of this article https://ideas.repec.org/a/bla/jorssa/v168y2005i2p439-455.html

I don’t think this question is well understood as a correlation. Couldn’t you model this directly? I.e. encode the religion of the family and the religion of the cluster (and potentially their interaction) as a predictor?