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Czado, Claudia; Song, Peter X.-K. (2001): State Space Mixed Models for Longitudinal Observations with Binary and Binomial Responses. Sonderforschungsbereich 386, Discussion Paper 232
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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).

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