Fitting complex random effect models with standard software using data augmentation: application to a study of male and female fecundability

We discuss fitting of a complex random effect model using a standard statistical package (Stata) to carry out block-wise Gibbs sampling within a multiprocessor computing environment. The application involves a dataset concerning artificial insemination by donor (AID). Success or failure at each of 12 100 menstrual cycles is modelled with a mixed model with random effects due to woman, conception attempt within woman, semen donor, donation within donor, and physician who carries out the treatment. Given the availability of software within Stata to fit a model with single random effect, the full model can be fitted by an alternating imputation algorithm (Clayton and Rasbash, 1999) implemented with five copies of Stata running on separate processors and communicating via disk files.