Testing measurement invariance in longitudinal data with ordered-categorical measures.

TLDR

Measurement invariance is essential for longitudinal developmental research, yet ordered‑categorical indicators such as Likert scales often violate the assumption of continuous normality, complicating factor‑model analyses. This didactic article extends prior measurement‑invariance work to longitudinal studies with ordered‑categorical indicators. The authors address common challenges in longitudinal invariance testing—model identification, sparse and missing data, and estimation—by developing a practical procedure and R program, illustrating it with a Mexican American Cultural Values subscale, and comparing the capabilities of lavaan, Mplus, and OpenMx. They demonstrate that lavaan, Mplus, and OpenMx differ in their handling of longitudinal measurement invariance and provide scripts to facilitate these analyses. PsycINFO database record.

Abstract

A goal of developmental research is to examine individual changes in constructs over time. The accuracy of the models answering such research questions hinges on the assumption of longitudinal measurement invariance: The repeatedly measured variables need to represent the same construct in the same metric over time. Measurement invariance can be studied through factor models examining the relations between the observed indicators and the latent constructs. In longitudinal research, ordered-categorical indicators such as self- or observer-report Likert scales are commonly used, and these measures often do not approximate continuous normal distributions. The present didactic article extends previous work on measurement invariance to the longitudinal case for ordered-categorical indicators. We address a number of problems that commonly arise in testing measurement invariance with longitudinal data, including model identification and interpretation, sparse data, missing data, and estimation issues. We also develop a procedure and associated R program for gauging the practical significance of the violations of invariance. We illustrate these issues with an empirical example using a subscale from the Mexican American Cultural Values scale. Finally, we provide comparisons of the current capabilities of 3 major latent variable programs (lavaan, Mplus, OpenMx) and computer scripts for addressing longitudinal measurement invariance. (PsycINFO Database Record