State space mixed models for longitudinal obsservations 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 random linear
predictors. These models allow us to explicitly address the effects
of trend, seaonal or other time-varying covariates while preserving
the power of state space models in modeling serial dependence in
the data. We develop a Markov Chain Monte Carlo algorithm to carry
out statistical inferene for models with binary and binomial
responses, in which we invoke de Jong and Shephard's (1995)
simulaton smoother to establish an efficent sampling procedure for
the state variables. To quantify and control the sensitivity of
posteriors on the priors of variance parameters, we add a
signal-to-noise ratio type parmeter in the specification of these
priors. Finally, we ilustrate the applicability of the proposed
state space mixed models for longitudinal binomial response data in
both simulation studies and data examples.