Estimation of parameters in the extended growth curve model via outer product least squares for covariance

Abstract

In this paper, estimation of parameters in the extended growth curve model without assumption of normality is presented via outer product least squares for covariance (COPLS). The COPLS estimator for covariance can be explicitly expressed and proved to follow a linear transformation of k+1 independent Wishart distributions for a normal error matrix, where k is the number of profiles of the growth curve. Then two-stage generalized least squares (GLS) estimators for regression coefficients are elaborately derived. Finally, the COPLS estimator and the two-stage GLS estimators are shown to have desired properties both in finite and large samples. Simulation studies for finite sample sizes are provided to confirm that the COPLS estimator and the two-stage GLS estimators are alternative competitors with some evident merits to the existing maximum likelihood estimators in small samples. A real data set is analyzed to demonstrate the proposed methodology.