Using covariance structure analysis to detect correlates and predictors of individual change over time.

TLDR

Individual growth modeling and covariance structure analysis can be integrated to investigate systematic interindividual differences in change, requiring longitudinal continuous data across many individuals to detect correlates and predictors of change. The article explains how to reformat individual growth models into LISREL measurement and structural components and illustrates the method with a worked example. The authors reformulate the hierarchical growth models into LISREL measurement and structural components with mean structures, applying the approach to longitudinal panel data. The integrated approach offers flexible covariance analysis to examine systematic interindividual differences in change and to assess relationships between true change and its predictors.

Abstract

Recently, methodologists have shown how two disparate conceptual arenas—individual growth modeling and covariance structure analysis—can be integrated. The integration brings the flexibility of covariance analysis to bear on the investigation of systematic interindividual differences in change and provides another powerful data-analytic tool for answering questions about the relationship between individual true change and potential predictors of that change. The individual growth modeling framework uses a pair of hierarchical statistical models to represent (a) within-person true status as a function of time and (b) between-person differences in true change as a function of predictors. This article explains how these models can be reformatted to correspond, respectively, to the measurement and structural components of the general LISREL model with mean structures and illustrates, by means of worked example, how the new method can be applied to a sample of longitudinal panel data. Questions about correlates and predictors of individual change over time are concerned with the detection of systematic interindividual differences in change, that is, whether individual change in a continuous outcome is related to selected characteristics of a person's background, environment, treatment, or training. Examples include the following: Do the rates at which students learn differ by attributes of the academic programs in which they are enrolled? Are longitudinal changes in children's psychosocial adjustment related to health status, gender, and home background? Questions like these can be answered only when continuous data are available longitudinally on many individuals, that is, when both time points and individuals have been sampled representatively. Traditionally, researchers have sampled individual status at only two points in time, a strategy that has proven largely inadequate because two waves of data contain only min