| Summary: | 碩士 === 逢甲大學 === 統計學系統計與精算碩士班 === 101 === Multivariate longitudinal data with irregularly-timed observed repeated measures
and possibly missing outcomes usually occur in clinical trials or biomedical studies. Statistical analysis for such data have recently received increased attention via a vast amount of research. In this thesis, we are devoted to present a
fully Bayesian approach to fitting the multivariate t linear mixed model (MtLMM)
with damped exponential correlated errors under the missing at random (MAR) mechanism. To overcome the slow convergence problem of a conventional Markov chain Monte Carlo (MCMC) method due to a great amount of latent data in the model, the inverse Bayes formulas (IBF) coupled with Metropolis-within-Gibbs sampler is developed for inference on all model parameters as well as latent variables. Meanwhile, the techniques for the imputation of missing values, the estimation of random effects, and the prediction of future responses are also discussed. Simulation studies are carried out for comparing the estimation and fitting performance of computational procedures and various model frameworks. We demonstrate the proposed methodology through analyzing the pregnant women data with genuine missing outcomes.
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