An illustration of Bayesian approximate measurement invariance with longitudinal data and a small sample size

Abstract

This article illustrates the Bayesian approximate measurement invariance (MI) approach in Mplus with longitudinal data and small sample size. Approximate MI incorporates zero-mean small variance prior distributions on the differences between parameter estimates over time. Contrary to traditional invariance testing methods, where exact invariance is tested, this method allows for some “wiggle room” in the parameter estimates over time. The procedure is illustrated using longitudinal data on college students’ academic stress as it changes in the period leading up to and right after an important midterm. Results show that traditional invariance testing methods come to a standstill due to the small sample size. Bayesian approximate MI testing was able to identify non-invariant parameters, after which a partially invariant model could be estimated.