Functional mixed effects models
Functional mixed effects models
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DOI：
10.1111/j.0006-341x.2002.00121.x
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发表时间：
2002-03-01
期刊：
影响因子：
1.9
通讯作者：
Guo, WS
中科院分区：
文献类型：
--
作者：
Guo, WS
在这篇文章中，一类新的功能模型，其中光滑样条被用来模拟固定效应以及随机效应。通过引入函数随机效应，将线性混合效应模型推广到非参数混合效应模型，并将其建模为零均值随机过程的实现。固定函数效应和随机函数效应在sane函数空间中建模，保证了总体平均曲线和受试者特异性曲线具有相同的光滑性。这些模型继承了线性混合效应模型在处理复杂设计和相关结构方面的灵活性，可以在固定或随机设计矩阵中包含连续协变量以及虚拟因子，并将嵌套曲线模型作为特殊情况。提出了两种估计方法。第一个估计程序利用线性混合效应模型和平滑样条之间的联系，可以使用现有的软件进行拟合。第二个过程是使用卡尔曼滤波的顺序估计过程。该算法避免了对高维矩阵求逆，因此可以应用于大数据集。提出了一种广义最大似然比（GML）检验方法，用于模型的推断和选择。皮质醇配置文件比较的应用程序被用作一个例子。
In this article, a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced. The linear mixed effects models are extended to non-parametric mixed effects models by introducing functional random effects, which are modeled as realizations of zero-mean stochastic processes. The fixed functional effects and the random functional effects are modeled in the sane functional space, which guarantee the population-average and subject-specific curves have the same smoothness property. These models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures, can include continuous covariates as well as dummy factors in both the fixed or random design matrices, and include the nested curves models as special cases. Two estimation procedures are proposed. The first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software. The second procedure is a sequential estimation procedure using Kalman filtering. This algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets. A generalized maximum likelihood (GML) ratio test is proposed for inference and model selection. An application to comparison of cortisol profiles is used as an illustration.