Semiparametric Nonlinear Mixed-Effects Models and Their Applications
半参数非线性混合效应模型及其应用AI 解读 ↓
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半参数非线性混合效应模型及其应用
- 研究问题
- 如何在重复测量数据中兼顾均值曲线的灵活性、参数的可解释性，以及同一个体内观测的相关性。
- 方法与思路
- 作者结合参数与非参数均值函数、第二阶段固定和随机效应及平滑样条，用拉普拉斯近似实施估计。
- 材料陈述的贡献
- 摘要称提出统一的半参数模型类，比较两种估计程序并构造近似贝叶斯区间，以模拟和加拿大温度数据示例。
- 阅读关注点
- 核对个体内相关结构、样条惩罚与平滑参数的处理，以及两种估计程序和近似区间的适用条件。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未提供模拟数值、近似误差或区间覆盖表现，不能推断刊本变化。
原文摘要
Nonlinear mixed effects models (NLMMs) and self-modeling nonlinear regression (SEMOR) models are often used to fit repeated measures data. They use a common function shared by all subjects to model variation within each subject and some fixed and/or random parameters to model variation between subjects. The parametric NLMM may be too restrictive, and the semiparametric SEMOR model ignores correlations within each subject. In this article we propose a class of semiparametric nonlinear mixed effects models (SNMMs) that extend NLMMs, SEMOR models, and many other existing models in a natural way. A SNMM assumes that the mean function depends on some parameters and nonparametric functions. The parameters provide an interpretable data summary. The nonparametric functions provide flexibility to allow the data to decide some unknown or uncertain components, such as the shape of the mean response over time. A second-stage model with fixed and random effects is used to model the parameters. Smoothing splines are used to model the nonparametric functions. Covariate effects on parameters can be built into the second-stage model, and covariate effects on nonparametric functions can be constructed using smoothing spline ANOVA decompositions. Laplace approximations to the marginal likelihood and penalized marginal likelihood are used to estimate all parameters and nonparametric functions. We propose and compare two estimation procedures, and also show how to construct approximate Bayesian confidence intervals for the nonparametric functions based on a Bayesian formulation of SNMMs. We evaluate the proposed estimation and inference procedures through a simulation study. Applications of SNMMs are illustrated with analyses of Canadian temperature data.