Examining the Impact of and Sensitivity of Fit Indices to Omitting Covariates Interaction Effect in Multilevel Multiple-Indicator Multiple-Cause Models

This study examined the impact of omitting covariates interaction effect on parameter estimates in multilevel multiple-indicator multiple-cause models as well as the sensitivity of fit indices to model misspecification when the between-level, within-level, or cross-level interaction effect was left out in the models. The parameter estimates produced in the correct and the misspecified models were compared under varying conditions of cluster number, cluster size, intraclass correlation, and the magnitude of the interaction effect in the population model. Results showed that the two main effects were overestimated by approximately half of the size of the interaction effect, and the between-level factor mean was underestimated. None of comparative fit index, Tucker–Lewis index, root mean square error of approximation, and standardized root mean square residual was sensitive to the omission of the interaction effect. The sensitivity of information criteria varied depending majorly on the magnitude of the omitted interaction, as well as the location of the interaction (i.e., at the between level, within level, or cross level). Implications and recommendations based on the findings were discussed.