State Space Mixed Models for Longitudinal Observations with Binary and Binomial Responses

We propose a new class of state space models for longitudinal
discrete response data where the observation equation is specified
in an additive form involving both deterministic and dynamic
components. These models allow us to explicitly address the effects
of trend, seasonal or other time-varying covariates while
preserving the power of state space models in modeling dynamic
pattern of data. We develop different Markov chain Monte Carlo
algorithms to carry out statistical inference for models with
binary and binomial responses. In a simulation experiment we
investigate the mixing and convergence properties of these
algorithms. In particular, we demonstrate that a joint state
variable update is preferable over individual updates. In addition,
different prior choices are studied. Finally, we illustrate the
applicability of the proposed state space mixed models for
longitudinal binomial response data in the analysis of the Tokyo
rainfall data (Kitagawa 1987).