Exploring the Performance of Latent Moderated Structural Equations Approach for Ordered-Categorical Items

Latent moderated structural equations (LMS) is a popular method in estimating latent interaction effects. Mplus has implemented a variant of LMS (LMS-cat) that uses categorical confirmatory factor analysis to handle ordered-categorical indicators. We conducted a simulation study to examine the performance of the LMS-cat in varying sample size, interaction effect size, missing data rate and scenario, as well as number and symmetry of item response category conditions. Results showed that the LMS-cat is an excellent method in estimating structural parameters (i.e., interaction effect and lower-order effects). However, it could produce highly biased measurement parameters (i.e., factor loadings, and item category thresholds). We illustrated the LMS-cat by testing the interaction effect between participation in teachers` support activities and that of teachers` counterfactual activities (meditation, meditative movement, vigorous physical exercise) on teachers` sense of self-efficacy.