Assessing Measurement Invariance for Longitudinal Data through Latent Markov Models

ABSTRACT

We propose a general approach to detect measurement non-invariance in latent Markov models for longitudinal data. We define different notions of differential item functioning in the context of panel data. We then present a model selection approach based on the Bayesian information criterion (BIC) to choose both the number of latent states and the measurement structure. We show the practical relevance by means of an extensive simulation study, and illustrate its use on two real–data examples from the social sciences. Our results indicate that BIC is able to select the correct measurement equivalence structure more than 95% of times.

KEYWORDS:

• Latent Markov model with covariates
• measurement invariance
• differential item functioning
• direct effects
• model comparison

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ http://psidonline.isr.umich.edu

² Log-likelihood, BIC and Number of free parameters (# par) for $K=2,\dots ,6$ are available in the online appendix.

³ https://gss.norc.org/