非线性纵向数据模型中方差和自相关系数的齐性检验

刻画纵向数据的协方差结构有三个可能因素：随机效应、序列相关和随机误差．在纵向数据分析中，模型方差的齐性是一个基本假定．但是，该假设未必正确．Zhang和、Weiss^1]研究了具有随机效应的线性模型的异方差检验．林金官和韦博成^2]将Zhang和、Weiss^1]的结果推广到非线性情形．本文对具有自相关误差的非线性纵向数据模型，研究了方差齐性和相关系数的齐性检验，得到了检验的score统计量并应用于血浆渗透数据(见Davidian和Giltian^3])．最后，本文还给出了模拟结果．

TESTING FOR HOMOGENEITY OF VARIANCE AND AUTOCORRELATION COEFFICIENTS IN NONLINEAR MODELS OF LONGITUDINAL DATA WITH AR(1) ERRORS

There are three possible factors to model covariance structure of longitudinal data: randon. effects, serial correlation and measurement errors. In longitudinal data analysis, homogeneity of variance is a basic assumption. However, this assumption is not necessarily appropriate. Zhang, Weiss, Lin, Wei respectively tested for heteroscedasticity in linear and nonlinear models with random effects based on longitudinal data. This paper discusses the tests for homogeneity of within-individual variances and between-individual autocorrelation coefficients in nonlinear models with AR(1) errors based on longitudinal data and obtains several score test statistics. The plasma concentrations data (Davidian, Giltian) is used to illustrate our results.