Cross-Level Group Measurement Invariance When Groups Are at Different Levels of Multilevel Data

Studies comparing groups that are at different levels of multilevel data (namely, cross-level groups) using the same measure are not unusual such as student and teacher agreement in education or congruence between patient and physician perceptions in health research. Although establishing measurement invariance (MI) between these groups is important, testing MI is methodologically challenging because the groups compared for MI are at different levels with one group nested within the other group. We propose a multilevel confirmatory factor analysis (CFA) model that allows MI testing between cross-level groups at the between level and demonstrated testing MI between students and teachers using the promoting social interaction scale. Along with the demonstration, some methodological issues in implementing the proposed model (e.g., cluster invariance and reliability) and evaluating the model fit of multilevel CFA (e.g., Delta CFI and level-specific fit indices) and alternative approaches to the proposed model are discussed.