SEM Episode 6: Advanced Topics

In this final episode of Office Hours focused on the SEM, Patrick concludes with a review of several advanced topics that are commonly encountered in practice...

He begins by reviewing the assumption of normality in maximum likelihood estimation, and describes what happens if dependent variables in a model are non-normally distributed. He then describes alternative methods that do not assume normality. He then explores options for SEMs with discrete dependent variables (binary, ordinal, counts). Next, he discusses fitting SEMs to two or more groups simultaneously, both when the grouping variable is observed (multiple groups models) and when it is unobserved (latent mixture models). He concludes with a brief description of several applications of SEM with longitudinal data. Several suggested citations on each of these topics are below.

Bauer, D. J., & Curran, P. J. (2004). The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities. Psychological Methods, 9(1), 3-29.

Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective (Vol. 467). John Wiley & Sons.

Grimm, K. J., Ram, N., & Estabrook, R. (2017). Growth modeling: Structural equation and multilevel modeling approaches. New York, NY: Guilford

Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525-543.

Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49(1), 115-132.

West, S. G., Finch, J. F., & Curran, P. J. (1995). Structural equation models with nonnormal variables: Problems and remedies. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 56-75). Thousand Oaks, CA: Sage Publications.

Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12(1), 58-79.