Testing for Heteroscedasticity and/or Autocorrelation in Longitudinal Mixed Effect Nonlinear Models with AR(1) Errors

Abstract

For longitudinal data on several individuals collected over time, nonlinear models (including linear models) that contain both random effects across individuals and first-order autocorrelation in the within-individual errors need to be considered for fitting the data (Diggle et al., 2002). This article is devoted to studying the tests for variance heterogeneity and/or autocorrelation in the framework of nonlinear regression models with random effects and AR(1) errors. Several diagnostic tests using score statistic are constructed, and illustrated with plasma concentrations data (Davidian and Giltinan, 1995). The properties of test statistics are investigated through Monte Carlo simulations.