[R-sig-ME] Modelling with uncertain (but not missing) categorical random effect values

[Michael Lawson]

I have a dataset where I have offspring paternity of females with
males of different species. However, many of the offspring have
ambiguous paternity - where I know the offspring must be from
particular fathers, but not from others. The data currently looks a
bit like this (but with many more rows per mum_id):

mum_id  mum_sp  dad_sp dad_id                    con

Af1          A              A           Am1 / Am2             1
Af1          A              A           Am2                       1
Bf1          B             A           Am1 / Am2 / Am4   0
Bf2          B              B          Bm1 / Bm3              1

Which I have so far run as a binomial GLMM with con (conspecific mating) as
a binary response, mum_sp and dad_sp (species) as fixed factors and
mum_id as a random factor - and have just not included dad_id as
a random factor. The ambiguously assigned fathers in dad_id is also
non-random, i.e.
certain individuals are more likely to be ambiguously assigned than
others, so just leaving these cases as NA is problematic.

For some of the ambiguous assignments, I can also extract
probabilities that a possible male is the father of the offspring,
e.g. for the first row, father Am1 is 60% likely to be the father and
Am2 40% likely.

Are there any approaches where I can include the ambiguous dad_id in
a GLMM framework? - where the uncertainty of the assignment contributes to the
overall uncertainty in the tested relationship.

Thank you for any suggestions,
Mike