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

ABSTRACT

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.

KEYWORDS:

• Latent interaction
• categorical data
• latent moderated structural equations

Acknowledgments

We thank Tihomir Asparouhov and Bengt Muthén for their information about how LMS handles categorical items, and David Budescu and the anonymous reviewers for their comments throughout the paper.

Notes

¹ Equation 7 implies that the outcome $\eta$ is essentially nonnormal even when the items of $\xi$ are multivariate normal.

² This conclusion is based on the number of parameters in LMS which Lodder et al. (2019) reported.

Additional information

Funding

This research was supported by the National Center for Education Research Institute of Education Sciences [R305A120180].