Longitudinal Multitrait-Multimethod Models for Developmental Research

Abstract

Multitrait-multimethod (MTMM) confirmatory factor models were combined with longitudinal structural equation models to examine trait and method stability over time. A longitudinal correlated-trait correlated-method (CT-CM) model allowed for the study of trait and method variance in observed scores over time. Longitudinal measurement invariance was examined in the longitudinal CT-CM model to determine the invariance of the trait and method factors. The longitudinal MTMM model was then combined with second-order latent curve models to evaluate within-person change and between-person differences change in the trait factors while accounting for method-related variance. These models were developed and applied to longitudinal behavior-rating data from the National Institute of Child Health and Human Development (NICHD) Study of Early Child Care and Youth Development with externalizing, internalizing, and social skills serving as the traits and mother, father, and teacher serving as methods or informants. Methodological extensions of longitudinal MTMM models and benefits of an MTMM approach to developmental research are discussed.

ACKNOWLEDGMENTS

This research was supported, in part, by the Institute of Education Sciences U.S. Department of Education Award R305B040049 to the University of Virginia. We thank Jack McArdle; John Nesselroade; Keith Widaman; and our colleagues at the Center for the Advanced Study of Teaching and Learning, the Jefferson Psychometric Laboratory, and the Center for Development and Health Research Methodology at the University of Virginia for their helpful comments on this work. The opinions and views expressed in this article are ours and do not necessarily represent the views and opinions of the U.S. Department of Education.

Notes

¹ The equality constraint on the variances of the mother, father, and teacher method factors across grade was imposed because of expectations regarding interindividual differences in rater severity. However, relaxing this constraint led to a small nonsignificant change in the chi-square compared with the change in degrees of freedom (δχ² = 17, δdf = 9, p = ns).

² The initial series of longitudinal MTMM models is a very loose set of models as there are many parameters to estimate (i.e., 321); however, the benefit of this initial model is its generality. One of the encountered convergence problems could be alleviated by estimating the unique variances for first-grade externalizing completed by the child's mother and fifth-grade externalizing completed by the child's father but fixing their unique covariances to zero. These restrictions were not imposed because admissible parameter estimates were obtained and full convergence was achieved when the longitudinal MTMM model was combined with the second-order growth models.