Simplex Mixed-Effects Models for Longitudinal Proportional Data
Simplex Mixed-Effects Models for Longitudinal Proportional Data
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DOI：
10.1111/j.1467-9469.2008.00603.x
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发表时间：
2008-12-01
影响因子：
1
通讯作者：
Tan, Ming
中科院分区：
文献类型：
--
作者：
Qiu, Zhenguo;Song, Peter X. -K.;Tan, Ming
连续比例结果是从许多实际研究中收集的，其中响应被限制在单位区间 (0,1) 内。利用 Barndorff-Nielsen 和 Jorgensen 的单纯形分布，我们提出了一种新型的纵向比例数据广义线性混合效应模型，其中比例的期望值通过固定效应和随机效应的 logit 函数直接建模。我们在所提出的模型中沿着 Breslow 和 Clayton 的惩罚准似然 (PQL) 和限制最大似然 (REML) 建立统计推断。我们使用高阶多元拉普拉斯近似推导出 PQL/REML，这给出了模型参数的令人满意的估计。通过模拟研究和数据示例说明了所提出的模型和推论。仿真研究得出结论，四阶近似 PQL/REML 表现令人满意。数据示例表明，Aitchison 用于 Logit 转换比例结果的正态线性混合模型技术对于异常值并不稳健。
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.