Testing Measurement Invariance over Time with Intensive Longitudinal Data and Identifying a Source of Non-invariance

Longitudinal measurement invariance (LMI) is a critical prerequisite to assessing change over time with intensive longitudinal data (ILD). For LMI testing with ILD, we propose cross-classified factor analysis (CCFA) to detect non-invariant item parameters and alignment optimization (AO) to detect non-invariant time points as a supplement to CCFA. In addition, we use a covariate in CCFA to identify a source of non-invariance. To evaluate the proposed models under unique features of ILD, such as autoregression (AR), we conducted a Monte Carlo simulation study. The results showed CCFA can be an excellent tool for ILD LMI testing regardless of simulation factors even when AR was misspecified and can identify a source of non-invariance using a covariate. AO can supplement CCFA to find non-invariant time points although AO requires a large number of persons. We provide detailed discussions and practical suggestions.