Autoregressive random effects models for circular longitudinal data using the embedding approach

Some conditional models to deal with circular longitudinal responses are proposed, extending random effects models to include serial dependence of Markovian form, and hence allowing for quite general association structures between repeated observations recorded on the same unit. The presence of both these components implies a form of dependence between them, and so a complicated expression for the resulting likelihood. To handle this problem, we introduce an approximate conditional mode and a full conditional model, with no assumption about the distribution of the timevarying random effects. All of the discussed models are estimated by means of an EM algorithm for nonparametric maximum likelihood.