Thank you for your question. I have searched the web for information about the Diagonally Weighted Least Squares (DWLS) and Unweighted Least Squares (ULS) estimators, and I have found some relevant sources that may help you with your decision.

One of the factors that you should consider when choosing between DWLS and ULS is the sample size. According to Forero et al. (2009)1, DWLS tends to perform better than ULS when the sample size is small (less than 200), but ULS tends to perform better than DWLS when the sample size is large (more than 1000). Since your sample size is 658, it falls in the intermediate range, where both methods may provide similar results.

Another factor that you should consider is the degree of non-normality of your data. According to Finney and DiStefano (2006), DWLS is more robust to non-normality than ULS, especially when the data are highly skewed or kurtotic. However, ULS may be more efficient than DWLS when the data are moderately non-normal or close to normal. Since your data have slight negative skewness and kurtosis, it may not be a serious violation of the ULS assumptions.

A third factor that you should consider is the model fit and parameter estimates. According to Forero et al. (2009)1, both methods provide accurate and similar results overall, but ULS tends to provide more accurate and less variable parameter estimates, as well as more precise standard errors and better coverage rates. However, DWLS has higher convergence rates than ULS, which means that it is less likely to encounter numerical problems or estimation errors.

Based on these factors, it seems that both DWLS and ULS are reasonable choices for your data and model, but ULS may have some advantages over DWLS in terms of efficiency and accuracy. However, you should also check the sensitivity of your results to different estimation methods, and compare them with other criteria such as theoretical plausibility, parsimony, and interpretability.

I hope this answer helps you with your analysis. If you need more information, you can refer to the sources that I have cited below.

1: Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation by Carlos G. Forero, Alberto Maydeu-Olivares & David Gallardo-Pujol in British Journal of Mathematical and Statistical Psychology (2009)

: Non-normal and categorical data in structural equation modeling by Sara J. Finney & Christine DiStefano in Structural equation modeling: A second course (2006)

https://psycnet.apa.org/record/2010-12087-004

https://stats.stackexchange.com/questions/331543/fa-estimation-gls-wls-dwls-uls-and-robustness-of-these-estimators

https://lavaan.ugent.be/tutorial/est.html

Good luck

When deciding between the Diagonally Weighted Least Squares (DWLS) and Unweighted Least Squares (ULS) estimators, you should consider several factors that depend on the nature of your data and the goals of your analysis. These two estimators are commonly used in structural equation modeling (SEM) and related statistical techniques. Here are some key factors to consider:

In summary, the choice between DWLS and ULS depends on the specific characteristics of your data and the goals of your analysis. If your data deviate from multivariate normality or contain outliers, DWLS is often a safer choice. However, it's essential to weigh all the factors mentioned above and select the estimator that aligns best with your research objectives and data properties.

E.A. Gawad from your answer I take you wouldn't oppose the use of ULS in my case, which is helpful to know. Hugo Assunção, your response appears somewhat general. I would appreciate it if you could provide more tailored advice that specifically addresses my case.

Thank you both for valuable insights!

ULS is a method for solving linear equations that contain more variables than equations. ULS finds the solution that minimizes the sum of squares of the differences between the observed values and the expected values. ULS assumes that all observations have the same weight or importance. ULS may be suitable for your case if your data is homogeneous, balanced, and uncorrelated.

Rewrite the answer by another way

Here are some factors to consider when deciding between the Diagonally Weighted Least Squares (DWLS) and Unweighted Least Squares (ULS) estimators for CFA:

• Normality of the data: DWLS is more robust to violations of the normality assumption than ULS. If your data is severely non-normal, DWLS may be a better choice.
• Sample size: DWLS is less efficient than ULS, so it may not be suitable for small samples. If you have a small sample, ULS may be a better choice.
• Outliers: DWLS is less sensitive to outliers than ULS. If your data has outliers, DWLS may be a better choice.
• Fit indices: ULS is generally more likely to produce acceptable fit indices than DWLS. If ULS produces acceptable fit indices for your model, this may be a sign that the assumptions of ULS are not being violated.

In your case, you have a relatively large sample size (658 observations) and your data is only slightly non-normal. Additionally, ULS produced significantly better fit indices for your model than DWLS. This suggests that the assumptions of ULS may not be being violated in your case. However, it is important to note that fit indices are not the only way to assess the validity of a CFA model. It is also important to consider the theoretical plausibility of the model and the results of other statistical tests, such as modification indices and standardized residual covariances.

Here is some relevant literature on the use of DWLS and ULS for CFA:

• Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Diagonally weighted least squares versus unweighted least squares estimation in confirmatory factor analysis: A Monte Carlo study. Structural Equation Modeling: A Multidisciplinary Journal, 16(2), 360-378.
• Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55.
• Kline, R. B. (2015). Principles and practice of structural equation modeling (4th ed.). Guilford Press.

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I hope this information is helpful.

Good luck

Matyáš Strašík