[R-sig-ME] cross-nested random structure in glmmPQL

[Carina Dinkel]

Dear members,
 
I'm trying to fit a GLMM using glmmPQL with a cross-nested random structure. Basically, I have perfectly crossed observations of whether there is a relation between two people (sender and receiver of relation) and I'd like to do a random structure where the relations to an from the same actor are related.
If A and B are the random effects for specific sender and receiver the covariance matrix should look like this:
 
sigma_A^2*I      sigma_AB*I
sigma_AB*I       sigma_B^2*I
 
where I is an n x n identity matrix.
The code I have so far has the random structure of:
 
> const <-  factor(rep(1, length(data$y)))
> mod <- glmmPQL(y ~ as.factor(variableS) + as.factor(variableR), 
>                random = list(const = pdBlocked(list(pdIdent(~1),pdIdent(~sender-1),pdIdent(~receiver-1)))),
>                data=data, family=binomial)
 
I think this code only leads to a diagonal covariance matrix and doesn't consider the covariance sigma_AB I'd like to model. Do you have any suggestions how I have to change the random part of my formula in order to get the right covariance matrix?
 
Any help is highly appreciated!
 
Thank you,
Carrie