A Comparison of Longitudinal Data Models When Covariance Structure is the Feature of Interest

Keywords:Longitudinal Data, Variance Components, Structured Covariance, Curve Estimation

Abstract: We discuss several approaches to modeling the covariance in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the cross-sectional mean and the influence of covariates on the mean. We describe a flexible, parsimonious class of models for covariance structure appropriate to such analyses, which we call proto-splines. This class extends the set of available random coefficient models by allowing a degree of uncertainty in the design matrix associated with the random coefficients. One important feature of this class is that it provides a decomposition of the variance into interpretable components. We compare several implementations of this class to a more commonly employed mixed effects model to describe the strengths and limitations of each approach. The findings will assist researchers and practitioners in uncovering important aspects of the covariance. We compare these models in the context of long-term trends in wage inequality for young workers.