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Heinzl, Felix; Kneib, Thomas; Fahrmeir, Ludwig (8. October 2009): Additive mixed models with Dirichlet process mixture and P-spline priors. Department of Statistics: Technical Reports, No.68
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Longitudinal data often require a combination of flexible trends and individual-specific random effects. In this paper, we propose a fully Bayesian approach based on Markov chain Monte Carlo simulation techniques that allows for the semiparametric specification of both the trend function and the random effects distribution. Bayesian penalized splines are considered for the former, while a Dirichlet process mixture (DPM) specification allows for an adaptive amount of deviations from normality for the latter. We investigate the advantages of DPM prior structures for random effects in terms of a simulation study and present a challenging application that requires semiparametric mixed modeling.