A logistic-bivariate normal model for overdispersed two-state Markov processes

We describe a logistic-bivariate normal mixture model for a two-state Markov chain in which each individual makes transitions between states according to a subject-specific transition probability matrix. The use of the bivariate normal mixing distribution facilitates inferences regarding the correlation of the random effects and hence provides insight as to the nature of the subject-to-subject variability in the transition probabilities. Tests regarding the correlation can be based on likelihood ratio, score, or Wald statistics. Estimates of the transition intensities of a latent continuous time conditionally Markov process may also be computed. We illustrate this methodology by application to a parasitic infection field study and contrast our findings with those previously published on this data set.