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Czado, Claudia; Song, Peter X.-K. (2006): State space mixed models for longitudinal obsservations with binary and binomial responses. Sonderforschungsbereich 386, Discussion Paper 503

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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 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.

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