Factorial Invariance and The Specification of Second-Order Latent Growth Models

Latent growth modeling has been a topic of intense interest during the past two decades. Most theoretical and applied work has employed first-order growth models, in which a single manifest variable serves as indicator of trait level at each time of measurement. In the current paper, we concentrate on issues regarding second-order growth models, which have multiple indicators at each time of measurement. With multiple indicators, tests of factorial invariance of parameters across times of measurement can be tested. We conduct such tests using two sets of data, which differ in the extent to which factorial invariance holds, and evaluate longitudinal confirmatory factor, latent growth curve, and latent difference score models. We demonstrate that, if factorial invariance fails to hold, choice of indicator used to identify the latent variable can have substantial influences on the characterization of patterns of growth, strong enough to alter conclusions about growth. We also discuss matters related to the scaling of growth factors and conclude with recommendations for practice and for future research.