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I am conducting a SEM in R using lavaan and I am a bit lost regarding which estimator I should use. I have a model like the following :

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The variables a,b,c,h are binary categorical and the rest are continuous non normal. I have encountered in some sources that categorical variables can cause problems when using the traditional Maximum Likelihood approach, e.g. Washington, S. P., Karlaftis, M. G., & Mannering, F. (2003). Statistical and econometric methods for transportation data analysis. Chapman and Hall/CRC :

Nominal and ordinal scale variables also cause problems in SEMs resulting in biased estimates of X2 test statistics and estimated parameters and their standard errors. One approach, developed by Muthen (1984), consists of a continuous/categorical variable methodology (CVM) weighted least squares estimator and discrepancy function, which results in unbiased, con- sistent, and efficient parameter estimates when variables are measured on nominal and ordinal scales. However, this estimator requires large sample sizes (at least 500 to 1000 cases) and is difficult to estimate for overly complex models (Hoyle, 1995).

What is not clear to me is whether this is the case for any categorical variables within the model or this is just referring to the dependent/endogenous variables. If the case is any categorical variables, then it seems like the option of "WLSMV" available in lavaan should be the way to go.

If the case is that this refers only to dependent variables, lavaan offers the options of "WLS" for weighted least squares (also called ADF), which according to the references I encountered is an appropriate method that does not assume a normal distribution.

I also encountered this answer: Pathmodel - Choosing the "correct" Estimator , suggesting the the Satorra-Bentler (MLM in lavaan) for non missing data when there are categorical exogenous variables. But is this also the case when the variables are latent indicators?

Any recommendations on which approach I should follow? My sample size is quite large (1700 observations). Any references would be greatly appreciated.

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Interesting question. In my opinion, you should use WLSMV in lavaan. It is a robust variant of DWLS that correctly handles non-normal and discrete variables like those in your model. Regardless of this suggestion, I think your main question is whether the nature of the observed variables influence the choice of estimator, and the answer is yes. This is not a matter of the latent variables, but of the observed variables. Personally, I would like to recommend to you "Principles and Practice of Structural Equation Modeling by Rex B. Kline", especially Section "Robust WLS Estimation", Chapter 13.

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    $\begingroup$ Thank you for your answer. I also confirmed from the lavaan google teams that for endogenous categorical data WLSMV is the best approach. $\endgroup$
    – Anna
    Jun 3, 2021 at 16:02

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