Chapter 11: Within-Subject Residual Variance–Covariance Structures in Longitudinal Data Analysis

This chapter demonstrates how to specify the alternative within-subject residual variance-covariance (V–CV) structures in a 2-level growth model. We begin with a brief literature review on how existing studies have specified the within-subject V–CV structures in their analyses using multilevel modeling (MLM). We provide an overview of the consequences of misspecifying the within-subject V–CV structures that have been identified in previous simulation studies. Then we describe the model formulation in terms of the decomposition of the between- and within-subject V–CV components in a simple linear growth model in the MLM framework. Following that, we extend the model formulation to be in matrix algebra form under the generalized linear modeling framework, which elaborates the variance components of the growth models. Then we introduce a set of alternative V–CV structures for modeling the within-subject residual components that are offered in popular statistical software packages. Finally, we demonstrate how to select the within-subject residual V–CV that fits the data better in MLM using an empirical dataset from the National Longitudinal Study of Youth 97 (NLSY97) project.