We propose a functional random effect time‐varying coefficient model to establish the dynamic relationship between the response and predictor variables in longitudinal data. This model allows us not only to interpret time‐varying covariate effects, but also to depict random effects via time‐varying profiles that are characterized by functional principal components. We develop the functional profiling‐backfitting method to estimate model components, which includes the profiling and backfitting procedures via a set of least squares type estimating equations. Asymptotic properties of the resulting estimator are obtained. Furthermore, we investigate the finite sample performance of the proposed method through simulation studies and present an application to primary biliary cirrhosis data. Copyright © 2012 John Wiley & Sons, Ltd.

中文翻译：

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纵向数据的函数随机效应时变系数模型。


我们提出了一个函数随机效应时变系数模型来建立纵向数据中响应变量和预测变量之间的动态关系。该模型不仅使我们能够解释时变协变量效应，还能够通过以功能主成分为特征的时变曲线来描述随机效应。我们开发了功能分析反拟合方法来估计模型组件，其中包括通过一组最小二乘型估计方程进行分析和反拟合程序。获得了所得估计量的渐近性质。此外，我们通过模拟研究研究了所提出方法的有限样本性能，并提出了对原发性胆汁性肝硬化数据的应用。版权所有 © 2012 约翰威利父子有限公司