具有随机效应和AR(1)误差的非线性纵向数据模型中组间方差和自相关系数的齐性检验

组间方差和自相关系数的齐性是纵向数据分析的基本假设之一,然而这种假设需要进行统计检验. Zhang \&; Weiss$^{15]}$ 讨论了线性随机效应模型的组间和组内方差齐性的检验问题；林金官 \&; 韦博成$^{10]}$ 研究了具有AR(1)误差但没有随机效应的非线性模型的自相关系数的齐性检验.该文研究具有随机效应和AR(1)误差的非线性模型的组间方差和自相关系数的齐性检验问题,构造了几个score检验统计量, 并通过Monte Carlo模拟方法研究了检验统计量的性质.最后利用该文的方法分析一组实际数据和一组模拟数据.

Testing for Homogeneity of Between-individual Variances and Autocorrelation Coefficients in Longitudinal Nonlinear Models with Random Effects and AR(1) Errors

Homogeneity of between-individual variances and/or autocorrelation coefficients is one of standard assumptions in longitudinal analysis. However, this assumption needs to be tested statistically. Zhang \& Weiss$^{15]}$ discussed the tests for heterogeneity of between - and/or within-individual variances in linear models with random effects. Lin \& Wei$^{10]}$ considered the tests for homogeneity of between-individual autocorrelationcoefficients in nonlinear models with AR(1) errors but without random effects. However, for such models, the tests for homogeneity of autocorrelation coefficients between individuals as autocorrelation on all individuals exists, have not been considered. This paper is devoted to the tests for homogeneity of between-individual variances and/or autocorrelation coefficientsin the framework of nonlinear regression models with random effects and AR(1) errors. Several diagnostic tests using score statistic are constructed. The properties of test statistics are nvestigated through Monte Carlo simulations. An real-data and simulated-dat examples are analyzed in Section 5 to illustrate the proposed methodology.