Non-Normal Data in CFA and SEM

QuantFish instructor Dr. Christian Geiser discusses the use of non-normal data in structural equation modeling (SEM) and confirmatory factor analysis (CFA). Also check out his video on how to address non-normal data in Mplus: • Mplus Estimators for N...
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[@louiebrown1]

Thank you for your generous and succinct sharing of all things CFA! I'm finding your videos very helpful in navigating my analysis on a current project.

[@fmunozt]

Very clarifying. Thank you very much.

[@abt9123]

My non-normal data and SEM become a nightmare fore me, thank you for your help for a Phd fellow here will defend her prospectus in 2 weeks.

[@RYBeth]

You have saved me from hours of research, reading and study. I cannot tell enough how grateful I am.
Previously, I have also found papers saying MLE is not a good option for ordinal data. I would like to learn about handling ordinal data and pay for it.
Finally, I am wondering if you can provide references for the video, for example you said SE and test statistics are problem when working with non-normal data but not model fit indices. Additionally, you mentioned DWLS is not advisable to use with small sample sizes, but I have seen studies using it - somehow- therefore, having a good source would help.
Thanks so much! (do you have Patreon account? I would definitely buy you a coffee :) )

[@QuantFish]

I'm glad you found this video helpful. Below are some references where you can find more info:
Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course. Greenwich, CT: Information Age Publishing.
Jöreskog, K. and Moustaki, I. (2001). Factor analysis for ordinal variables: A comparison of three approaches. Multivariate Behavioral Research, 36, 347-387.
Li, C. H. (2016). The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21(3), 369-387.
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373.
Best, Christian Geiser

[@daj1058]

Great video! Thanks so much!

[@will74lsn]

Thanks.
How do you determine in the first place to what extent the assumption of normality is satisfied? I suppose you want to determine this before applying some other approach other than ML.

[@QuantFish]

There are tests such as Mardia's test of multivariate normality (see my video here: ruclips.net/video/RsA4WFmGkoU/видео.html) but they are of limited utility. Most social science applications probably deal with at least slightly non-normal data. Therefore, it is perhaps best to routinely apply robust ML estimation methods such as the Satorra-Bentler correction (MLM) or MLR in Mplus.
Best, Christian Geiser

[@will74lsn]

Many thanks! I did find your video on the Mardia's test. I have already run it with many data sets (in STATA)-> all tests are highly significant. I will possible use it as a complementary piece of information.@@QuantFish

[@_chisquare_]

Many thanks for this input. Where would you see the limits of robust estimation of SEs with regard to skewness and kurtosis? And how about estimating models with count data variables (poisson or nb distribution) using MLR?
Thanks, Urs

[@will74lsn]

What about DWLS (in lavaan)? Do you also need thousands of cases? I recently read a paper (Reimann et al. 2024) who used DWLS in a CFA with a sample of 130 participants.

[@QuantFish]

Unlike WLS for continuous indicators, DWLS (referred to as WLSMV in Mplus) for ordinal data does not require thousands of cases. This has been shown in several simulation studies, for example:
Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least
squares estimation in CFA. Structural Equation Modeling, 13, 186-
203. doi:10.1207/s15328007sem1302_2
Li, C. H. (2016). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48, 936-949.
Nussbeck, F. W., Eid, M., & Lischetzke, T. (2006). Analysing multitrait-multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: What sample size is needed for valid results?. British Journal of Mathematical and Statistical Psychology, 59(1), 195-213.
Best, Christian Geiser

[@will74lsn]

Awesome!@@QuantFish