How to do robustness analysis for Structural Equation Modeling (SEM) in R

Hi everyone.

I have conducted SEM analysis in R and used Robust Maximum Likelihood (MLR) estimator since my data is categorical and deviate from multivariate normality. when I submitted my manuscript, one reviewer asked for robustness analysis. I have been searching for such analyses in R but I cannot find anything. I only see resources about robustness check for endogeneity, unobserved heterogeneity, and non-linear effects in PLS-SEM mostly in SmartPLS software. I'm confused whether I need to do robustness analysis and if yes, how it can be done in R.

Some details on the model: there are 4 latent variables in the original model, one is endogenous (intentions) predicted by the other 3 exogenous latent variables (attitudes, subjective norms, perceived behavioral control, The theory is Planned Behavior). Also, in an extended version, I add another variable (Knowledge, not latent) which I hypothesize its effect on intentions is mediated via Attitude latent variable. For the extended model with mediation effect I used bootstrapping.

I really appreciate any input in this regard.

The {lavaan} package provides SEM with robust MLE for categorical variables with the option to output regular standard errors as an alternative option. There's a good UCLA tutorial.

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