A Structural Equation Model for Measuring Residualized Change and Discerning Patterns of Growth or Decline

Abstract

This paper is concerned with two theoretically and empirically important issues in longitudinal research: (1) identifying correlates and predictors of change and (2) discerning patterns of change. Two traditional methods of change measurement—the residualized observed difference and the residualized gain score—are discussed. A general structural equation model for measuring residualized true change and studying patterns of true growth or decline is described. This approach allows consistent and efficient estimation of the degree of interrelation ship between residualized change in a repeatedly assessed psychological construct and other variables, such as studied/presumed correlates and predictors of growth or decline on the latent dimension. Sub stantively interesting patterns of change on the trait level, such as regression to the mean, over- crossing, and fan-spreading, can be discerned. The model is useful in research situations in which it is of theoretical and empirical concern to identify those variables that correlate with, or can be used to predict, such patterns of true growth or decline that deviate from a group-specific trend in longitudinally-measured psychological constructs. The approach is illustrated using data from a cog nitive intervention study of plasticity in fluid intel ligence of aged adults (Baltes, Dittmann-Kohli, & Kliegl, 1986).