AUTHOR=Im Myung H. , Kim Eun S. , Kwok Oi-Man , Yoon Myeongsun , Willson Victor L. TITLE=Impact of Not Addressing Partially Cross-Classified Multilevel Structure in Testing Measurement Invariance: A Monte Carlo Study JOURNAL=Frontiers in Psychology VOLUME=7 YEAR=2016 URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2016.00328 DOI=10.3389/fpsyg.2016.00328 ISSN=1664-1078 ABSTRACT=
In educational settings, researchers are likely to encounter multilevel data with cross-classified structure. However, due to the lack of familiarity and limitations of statistical software for cross-classified modeling, most researchers adopt less optimal approaches to analyze cross-classified multilevel data in testing measurement invariance. We conducted two Monte Carlo studies to investigate the performances of testing measurement invariance with cross-classified multilevel data when the noninvarinace is at the between-level: (a) the impact of ignoring crossed factor using conventional multilevel confirmatory factor analysis (MCFA) which assumes hierarchical multilevel data in testing measurement invariance and (b) the adequacy of the cross-classified multiple indicators multiple causes (MIMIC) models with cross-classified data. We considered two design factors, intraclass correlation (ICC) and magnitude of non-invariance. Generally, MCFA demonstrated very low statistical power to detect non-invariance. The low power was plausibly related to the