Overall Model Fit Does Not Imply Linearity in Longitudinal Structural Equation Models: Examining Linear Change Over Time Using Latent Variable Modeling

Abstract

This article is concerned with the assumption of linear temporal development that is often advanced in structural equation modeling-based longitudinal research. The linearity hypothesis is implemented in particular in the popular intercept-and-slope model as well as in more general models containing it as a component, such as longitudinal structural models with covariates, or models for the study of predictors and correlates of change. In empirical research applications, currently behavioral and social scientists typically evaluate only overall goodness of fit for a considered model. However, this omnibus fit assessment may miss violations of the underlying linearity assumption. To respond to this limitation, the present article discusses a testing procedure for examining the hypothesis of linear growth or decline separately from the widely used overall fit evaluation process. The method is readily utilized with popular latent variable modeling software and is illustrated using a numerical example.

Keywords:

• Change
• intercept-and-slope model
• level-and-shape model
• linearity
• longitudinal data
• structural equation modeling

Acknowledgments

We are grateful to G. A. Marcoulides for valuable discussions on multiple testing procedures and their applications, as well as to S. Gabler and C.-L. Lee for programming support. We are also thankful to the Editor and two anonymous Referees for their critical and helpful comments on an earlier version of the paper, which contributed substantially to its improvement.