Semiparametric Bayesian Analysis of Mixed Models for Clustered data
Date Issued
2004
Date
2004
Author(s)
Tung, Yi-Liang
DOI
zh-TW
Abstract
In this thesis I consider Bayesian semi-parametric analysis of mixed-effects models for clustered data. Particularly, I consider the additive mixed model and varying-coefficient mixed model, and use nonparametric arbitrary smooth functions to represent the covariate effects. I model the nonparametric functions using the qth-degree polynomial penalized splines with fixed knots, and specify the prior for the corresponding smoothing parameter of each function. A computationally efficient Markov chain Monte Carlo (MCMC) algorithm is proposed to simulate posterior samples for inference. In addition to the continuous response setting, the binary and count data are also considered and discussed in detail. Special attention is necessary due to the non-conjugacy for binary data with logit link and count data with log link. I also develop a modified Metropolis-Hastings algorithms to mix the Markov chain and increase the speed. The simulation studies show that the posterior mean via nonparametric approach captures well the true functional forms. In addition to the estimation, I also address the problem of model choice between the competing parametric and semi-parametric specifications using marginal likelihoods and Bayes factors. Finally, the data of multicenter AIDS cohort study (Kaslow et al. 1987) are considered for illustration.
Subjects
邊際機率
計數資料
二元資料
馬可夫鏈蒙地卡羅法
長期追蹤資料
無參數化迴歸
懲罰性節點
變化係數混合效應模式
貝氏因子
貝氏模式比較
相加性混合效應模式
Longitudinal data
Count data
Binary data
Markov Chain Monte Carlo
Marginal likelihood
Nonparametric regression
Varying-coefficient mixed models
Penalized splines
Bayesian model comparison
Bayes factor
Additive mixed models
SDGs
Type
thesis