Simplex Mixed-Effects Models for Longitudinal Proportional Data

被引:52
作者
Qiu, Zhenguo
Song, Peter X. -K. [1 ]
Tan, Ming [2 ]
机构
[1] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada
[2] Univ Maryland, Div Biostat, Greenebaum Canc Ctr, College Pk, MD 20742 USA
基金
加拿大自然科学与工程研究理事会;
关键词
bias correction; dispersion model; Laplace approximation; overdispersion; penalized quasi-likelihood; restricted maximum likelihood; robustness; simplex distribution;
D O I
10.1111/j.1467-9469.2008.00603.x
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Continuous proportional outcomes are collected from many practical studies, where responses are confined within the unit interval (0,1). Utilizing Barndorff-Nielsen and Jorgensen's simplex distribution, we propose a new type of generalized linear mixed-effects model for longitudinal proportional data, where the expected value of proportion is directly modelled through a logit function of fixed and random effects. We establish statistical inference along the lines of Breslow and Clayton's penalized quasi-likelihood (PQL) and restricted maximum likelihood (REML) in the proposed model. We derive the PQL/REML using the high-order multivariate Laplace approximation, which gives satisfactory estimation of the model parameters. The proposed model and inference are illustrated by simulation studies and a data example. The simulation studies conclude that the fourth order approximate PQL/REML performs satisfactorily. The data example shows that Aitchison's technique of the normal linear mixed model for logit-transformed proportional outcomes is not robust against outliers.
引用
收藏
页码:577 / 596
页数:20
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