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In SEM, we many times face non-normal data. Some software like Lisrel can normalize the data with just a click (and the formula of normalizing could be available in some articles of Joreskog).

You have the other option too: use WLS (or DWLS too)?

I tried both options in some path model with non-normal data, but in each, the results are different. In both ways, the models have good P-value (large one) and Good RMSE (small one).

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DWLS (Diagonally Weighted Least Squares), in some articles also called (WLSMV; Muthen, du Toit & Spisic, 1997), is the recommended choice of the estimator for non-normally distributed data in SEM (Finney & DiStefano, 2006; Flora & Curan, 2004; Wirth & Edwards, 2007; Yang-Wallentin, Jöreskog & Luo, 2010). If you want to try an alternative, go with the Robust Maximum Likelihood (MLR), which is also not sensitive to moderate deviations from multivariate normality in your data. As for the WLS, I would avoid it because it's computationally heavy (requires large samples), produces more biased results compared to DWLS, and the chance of non-convergence with WLS is much higher (Flora & Curran, 2004).

Key paper here is:

Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466–491.

In addition:

  1. Do not just look at the "p-value" of your model. You need to evaluate fit by using a range of fit statistics. Typically, the recommended ones are the RMSEA, SRMR, CFI, and TLI. Also, look at the factor loadings, they should be > |.30|. If you want to quickly look at the thresholds for evaluating each fit statistic, check my earlier post - it's a convenient summary for you that will save you a lot of time and stress (Is there a standard measure of fit to validate Exploratory factor analysis?).

  2. I would not transform data unless you have a strong reason to do so. Instead, use an appropriate estimator, such as the DWLS (WLSMV). Remember that transformation and normalising are not always possible (so I would argue it's far more complex than a one-click "data normalisation" solution).

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  • $\begingroup$ Thanks mr. PsychomeStats. Your answer was great and detailed (well-supported with articles as well). The last model I was working with was just Path-Model, that's why I went for Lisrel. Otherwise, with latent variables, I don't bother; just use Smart-PLS. $\endgroup$
    – Hussain
    Jan 23, 2022 at 3:06
  • $\begingroup$ @Hussain you're welcome! If you believe the answer was useful to you, please consider upvoting it and accepting it by putting a green mark next to it. Thank you $\endgroup$ Jan 24, 2022 at 0:22

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