Efficient estimation of general linear mixed effects models

Abstract

An extension of the linear growth curve model (Biometrics 38 (1982) 963) was proposed by Stukel and Demidenko (Biometrics 53 (1997) 720) to study the effects of population covariates on one or more characteristics of the curve, when the characteristics are expressed as linear combinations of the growth curve parameters. In the present paper, this general growth curve model receives a comprehensive theoretical treatment. A two-stage estimator, consisting of a generalized least squares estimator under constraints for the population parameters and a moment estimator for the variance parameters, is developed for application in the non-Gaussian error situation. Two likelihood based estimators, global maximum likelihood and second-stage maximum likelihood, are also developed. It is shown that all three estimators are consistent, asymptotically normally distributed, and efficient, and are equivalent when the number of individuals tends to infinity. An expression for the bias in the estimator of the population parameters is derived under second stage model misspecification. We show that if parameters that are not of primary interest are incorrectly specified, bias may occur in parameters that are of interest using the standard growth curve model. The general growth curve model does not require specification of such nuisance parameters and is robust in terms of bias. The general linear growth curve model is used to study the effects of host sex on pancreatic tumor growth in rats.