A Monte Carlo Study of Variable Selection and Inferences in a Two Stage Random Coefficient Linear Regression Model With Unbalanced Data

A growth curve analysis is often applied to estimate patterns of changes in a given characteristic of different individuals. It is also used to find out if the variations in the growth rates among individuals are due to effects of certain covariates. In this paper, a random coefficient linear regression model, as a special case of the growth curve analysis, is generalized to accommodate the situation where the set of influential covariates is not known a priori. Two different approaches for selecting influential covariates (a weighted stepwise selection procedure and a modified version of Rao and Wu’s selection criterion) for the random slope coefficient of a linear regression model with unbalanced data are proposed. Performances of these methods are evaluated by means of Monte-Carlo simulation. In addition, several methods (Maximum Likelihood, Resmcted Maximum Likelihood, Pseudo Maximum Likeliiood and Method of Moments) for estimating the parameters of the selected model are compared. Proposed variable selection schemes and estimators are applied to the actual indusmal problem which motivated this investigation.