Unweighted Versus Weighted Estimation for the Multivariate Growth Curve Model Useful in the Analysis of Longitudinal Data

Abstract

Growth Curve Models (GCMs) are useful in analyzing longitudinal data or studies involving response curves. GCMs, a type of bilinear regression model, include within- and between individual design matrices. Assuming multivariate normality, explicit likelihood solutions exist, often optimal even for small samples. This thesis examines the estimation of mean parameters in GCMs, using simulations to compare unweighted and weighted estimators in various scenarios: large sample (n > p), near singularity (n ≈ p), and high-dimensional (n < p). Longitudinal data with different levels of within-individual correlations were considered, and estimators were compared based on bias and mean squared error (MSE). Matrix bias and matrix MSE aggregation methods were explored for comparative evaluations. Illustrations using three real datasets were provided. Simulation results showed unweighted estimators performed well in most scenarios, except with unstructured variance-covariance matrices. Unweighted estimators were more optimal for structured variance-covariance matrices, regardless of within-individual correlation strength. Further investigation is needed to evaluate weighted estimators in other covariance structures and assess robustness against model misfits and non-normality.