Factorial Invariance Within Longitudinal Structural Equation Models: Measuring the Same Construct Across Time

TLDR

Developmental research aims to chart behavioral change over age and examine longitudinal relations among constructs, yet traditionally it assumes a single measure reflects the same construct across occasions. This paper discusses factorial invariance in longitudinal studies, contrasting analytic approaches and highlighting the strengths of a multiple‑indicator approach to modeling developmental processes. Using multiple indicators of a latent construct at each time point allows researchers to evaluate factorial invariance. When factorial invariance constraints are satisfied, latent variable scores across time share a common metric, enabling stronger conclusions.

Abstract

Charting change in behavior as a function of age and investigating longitudinal relations among constructs are primary goals of developmental research. Traditionally, researchers rely on a single measure (e.g., scale score) for a given construct for each person at each occasion of measurement, assuming that measure reflects the same construct at each occasion. With multiple indicators of a latent construct at each time of measurement, the researcher can evaluate whether factorial invariance holds. If factorial invariance constraints are satisfied, latent variable scores at each time of measurement are on the same metric and stronger conclusions are warranted. In this paper we discuss factorial invariance in longitudinal studies, contrasting analytic approaches and highlighting strengths of the multiple-indicator approach to modeling developmental processes.