Zhang Daowen
Department of Statistics, North Carolina State University, Box 8203, Raleigh, North Carolina 27695-8203, USA.
Biometrics. 2004 Mar;60(1):8-15. doi: 10.1111/j.0006-341X.2004.00165.x.
The routinely assumed parametric functional form in the linear predictor of a generalized linear mixed model for longitudinal data may be too restrictive to represent true underlying covariate effects. We relax this assumption by representing these covariate effects by smooth but otherwise arbitrary functions of time, with random effects used to model the correlation induced by among-subject and within-subject variation. Due to the usually intractable integration involved in evaluating the quasi-likelihood function, the double penalized quasi-likelihood (DPQL) approach of Lin and Zhang (1999, Journal of the Royal Statistical Society, Series B61, 381-400) is used to estimate the varying coefficients and the variance components simultaneously by representing a nonparametric function by a linear combination of fixed effects and random effects. A scaled chi-squared test based on the mixed model representation of the proposed model is developed to test whether an underlying varying coefficient is a polynomial of certain degree. We evaluate the performance of the procedures through simulation studies and illustrate their application with Indonesian children infectious disease data.
对于纵向数据的广义线性混合模型，在线性预测器中常规假设的参数函数形式可能过于受限，无法表示真正的潜在协变量效应。我们通过用时间的平滑但任意函数来表示这些协变量效应来放宽这一假设，同时使用随机效应来模拟个体间和个体内变异所引起的相关性。由于在评估拟似然函数时通常涉及难以处理的积分，因此采用了Lin和Zhang（1999年，《皇家统计学会学报》，B辑61卷，381 - 400页）的双惩罚拟似然（DPQL）方法，通过用固定效应和随机效应的线性组合来表示非参数函数，从而同时估计变化系数和方差分量。基于所提出模型的混合模型表示，开发了一种缩放卡方检验，以检验潜在的变化系数是否为某一特定次数的多项式。我们通过模拟研究评估了这些方法的性能，并用印度尼西亚儿童传染病数据说明了它们的应用。
