Handling Composite Variables in Latent Class Analysis

Question

I am working with secondary survey data that includes 13 dichotomous variables. According to my theoretical model, I need to group these variables into composite variables. However, I understand that after grouping, the resulting composite variables will not be dichotomous.

My main objective is to perform Latent Class Analysis (LCA) with these composite variables. I am aware that LCA typically handles categorical data, but I am unsure how to proceed with non-dichotomous composites.

How should I create composite variables from my dichotomous variables that will be suitable for LCA?

Can I use weights or some form of aggregation that would still allow me to perform LCA effectively?

Any guidance, references, or examples would be greatly appreciated. Thank you!

Answer 1

Provided you are willing to use your composite variables as continuous/interval-scale variables, you could use latent profile analysis (LPA) instead of "classical" latent class analysis (LCA) to find clusters (latent classes) of individuals. LPA identifies profiles of means (rather than conditional response probabilities) and is suitable for continuous/interval-scale variables. See

Ferguson, S. L., G. Moore, E. W., & Hull, D. M. (2020). Finding latent groups in observed data: A primer on latent profile analysis in Mplus for applied researchers. International Journal of Behavioral Development, 44(5), 458-468.

Gibson, W. A. (1959). Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 24(3), 229-252.

Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mifflin.

Pastor, D.A., Baron, K. E., Miller, B. J., & Davis, S. L. (2007). A latent profile analysis of college students’ achievement goal orientation. Contemporary Educational Psychology, 32, 8-47.

Spurk, D., Hirschi, A., Wang, M., Valero, D., & Kauffeld, S. (2020). Latent profile analysis: A review and “how to” guide of its application within vocational behavior research. Journal of Vocational Behavior, 120, 103445.

Vermunt, J. K., Lewis-Beck, M., Bryman, A., & Liao, T. (2004). Latent profile model. The sage encyclopedia of social sciences research methods, 554-555.

Vermunt, J. K., & Magidson, J. (2002). Latent class cluster analysis. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 89–106). Cambridge, UK: Cambridge University Press.

Williams, G. A., & Kibowski, F. (2016). Latent class analysis and latent profile analysis. Handbook of methodological approaches to community-based research: Qualitative, quantitative, and mixed methods, 143-151.