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.

Automated summary

Longitudinal measurement invariance (LMI) is critical for studying change over time with intensive longitudinal data (ILD). In this study, we propose cross-classified factor analysis (CCFA) and alignment optimization (AO) as methods to detect non-invariant item parameters and non-invariant time points, respectively, in LMI testing with ILD. Our results from a Monte Carlo simulation study show that CCFA is an excellent tool for ILD LMI testing, even when autoregression (AR) is misspecified, and can identify a source of non-invariance using a covariate. AO can supplement CCFA in finding non-invariant time points, but it requires a large number of persons.