Dear all,
I'm conducting SEM in R with lavaan, and I'm not certain what is the correct estimator for my model. I have 10 variables in total. 7 of the variables are each composed of 3 items rated on a 7-point Likert scale. The remaining 3 variables are age, sex, and the experimental manipulation (2 conditions). Sample size equals 370, and the variables are non-normal.
Should I use a robust estimator in such a case? Which estimator would be better: MLR, WLSM, WLSMV or maybe DWLS or ML? Or is there a different, more suitable estimator for this kind of model?
Thank you!
Radosław
Disclaimer: I have no great expertise in SEM.
Having said that, you might find this article helpful:
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.
http://psychmodels.ucdavis.edu/uploads/8/6/3/9/86398102/rhemtullabrosseauliardsavalei_pm.pdf
Dear Radosław Trepanowski
Generally speaking, the covariance-based structural modelling (CB-SEM) requires the data to fit a normal distribution and the lack of this property often leads to poor loadings, lack of average extracted variance and thus inability to successfully go through the reliability and validity tests for the measurement model. This leads me to wonder if any of the previously mentioned estimator techniques would work probably with lack of normally distributed data.
Therefore, when the data does not follow the normal distribution, then it is suggested to use the partial least square structural equation modelling (PLS-SEM), which does not apply any restrictions on the data distribution.
The (PLS-SEM) can be applied within the R environment via the following packages:
1. semPLS
2. plspm
Here is a book that was written by the designer of the package to illustrate how to use it
https://www.gastonsanchez.com/PLS_Path_Modeling_with_R.pdf
Also, you can use the SmartPLS software, which is a very powerful software that is mainly dedicated to run the partial least square analysis.
When variables/items are declared ordered, lavaan will automatically switch to the WLSMV estimator: it will use diagonally weighted least squares (DWLS) to estimate the model parameters, but it will use the full weight matrix to compute robust standard errors, and a mean- and variance-adjusted test stastistic (source: https://lavaan.ugent.be/tutorial/cat.html).
You can also use Satorra-Bentler adjustment according to the estimator used.
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