Testing Time-Invariance of Variable Specificity in Repeated Measure Designs Using Structural Equation Modeling

Abstract

A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term associated with repeated administration of each measure. The procedure can be used in the search for parsimonious versions of multiwave multiple-indicator models, to test for variable specificity in them, and to examine assumptions underlying particular parameter estimation procedures in repeated measure designs. The outlined method is illustrated with empirical data.

ACKNOWLEDGMENTS

We are grateful to P. B. Baltes, F. Dittmann-Kohli, and R. Kliegl for permission to use data from their project “Aging and Plasticity in Fluid Intelligence” for method illustration purposes, as well as to J. Tisak for valuable discussions on reliability estimation in multiwave, multiple-indicator models. We are indebted to the editor and two anonymous referees for critical comments on an earlier draft of this article, which contributed considerably to its improvement.

Notes

¹Demonstration of identifiability of the model can be obtained from the first author on request.

^aFixed parameter; all remaining parameters are free, except loadings constrained for temporal stability.