Sampling from the posterior distribution in generalized linear mixed models

被引:205
作者
Gamerman, D [1 ]
机构
[1] FED UNIV RIO DE JANEIRO,INST MATEMAT,BR-21945970 RIO JANEIRO,BRAZIL
关键词
Bayesian; blocking; longitudinal studies; Markov chain Monte Carlo; random effects; weighted least squares;
D O I
10.1023/A:1018509429360
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Generalized linear mixed models provide a unified framework for treatment of exponential family regression models, overdispersed data and longitudinal studies. These problems typically involve the presence of random effects and this paper presents a new methodology for making Bayesian inference about them. The approach is simulation-based and involves the use of Markov chain Monte Carlo techniques. The usual iterative weighted least squares algorithm is extended to include a sampling step based on the Metropolis-Hastings algorithm thus providing a unified iterative scheme. Non-normal prior distributions for the regression coefficients and for the random effects distribution are considered. Random effect structures with nesting required by longitudinal studies are also considered. Particular interests concern the significance of regression coefficients and assessment of the form of the random effects. Extensions to unknown scale parameters, unknown link functions, survival and frailty models are outlined.
引用
收藏
页码:57 / 68
页数:12
相关论文
共 35 条
[1]  
Aitkin M., 1980, Applied Statistics, V29, P156, DOI 10.2307/2986301
[2]  
[Anonymous], APPL STAT, DOI DOI 10.2307/2347565
[3]  
[Anonymous], 1991, 9109 PURD U DEP STAT
[4]  
[Anonymous], BAYESIAN STATISTICS
[5]   APPROXIMATE INFERENCE IN GENERALIZED LINEAR MIXED MODELS [J].
BRESLOW, NE ;
CLAYTON, DG .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1993, 88 (421) :9-25
[6]   MULTIVARIATE GENERALIZATIONS OF THE PROPORTIONAL HAZARDS MODEL [J].
CLAYTON, D ;
CUZICK, J .
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY, 1985, 148 :82-117
[7]  
COX DR, 1972, J R STAT SOC B, V34, P187
[8]  
Crowder M.J., 1978, APPLIED STATISTICS, V27, P34, DOI DOI 10.2307/2346223
[9]   BAYESIAN-INFERENCE FOR GENERALIZED LINEAR AND PROPORTIONAL HAZARDS MODELS VIA GIBBS SAMPLING [J].
DELLAPORTAS, P ;
SMITH, AFM .
APPLIED STATISTICS-JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C, 1993, 42 (03) :443-459
[10]  
FIRTH D, 1991, BIOMETRIKA, V78, P545