A structural equation model for measuring residualized change and discerning patterns of growth or decline

This paper is concerned with two theoreticallyand empirically important issues in longitudinalresearch: (1) identifying correlates and predictors ofchange and (2) discerning patterns of change. Twotraditional methods of change measurement-theresidualized observed difference and the residualizedgain score-are discussed. A general structuralequation model for measuring residualized truechange and studying patterns of true growth ordecline is described. This approach allows consistentand efficient estimation of the degree of interrelationshipbetween residualized change in a repeatedlyassessed psychological construct and other variables,such as studied/presumed correlates and predictorsof growth or decline on the latent dimension. Substantivelyinteresting patterns of change on thetrait level, such as regression to the mean, overcrossing,and fan-spreading, can be discerned. Themodel is useful in research situations in which it isof theoretical and empirical concern to identifythose variables that correlate with, or can be usedto predict, such patterns of true growth or declinethat deviate from a group-specific trend inlongitudinally-measured psychological constructs.The approach is illustrated using data from a cognitiveintervention study of plasticity in fluid intelligenceof aged adults (Baltes, Dittmann-Kohli, &Kliegl, 1986). Index terms: correlates of growth/decline, fan-spreading, measurement of change, overcrossing,predictors of growth, regression to themean, structural equations modeling, true change.