Should I use ML with bootstrapping or MLR with nonnormal data?

[Joy]

I am using R to run a latent variable SEM model and my indicators are all on a 7-point scale. From what I gather, in the instance of categorical variables with 5+ categories it is fine to use ML estimation with a large enough sample. My variables are non-normal and I'm wondering if using MLR estimation or ML with bootstrapping would be better? An advantage of MLR would be that it provides robust fit indices as well as standard errors, while ML with bootstrapping will only correct standard errors. I've also read something about the CIs obtained with the bootstrapping method being more accurate, but I'm really not sure and at least from what I can find not much compares the methods.

[Terrence Jorgensen]

With 7+ categories, MLR provides sufficiently unbiased results, and is much less computationally intensive than bootstrapping.  Off hand, I can't think of an advantage to using bootstrapping in the situation you describe.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Joy]

Thank you for the reply Dr. Jorgensen. May I ask, what might be a situation when bootstrapping would have an advantage?

[Terrence Jorgensen]

what might be a situation when bootstrapping would have an advantage?

When you need to estimate an empirical distribution of a statistic for which we have no sufficiently good (unbiased, or at least consistent) analytical methods to estimate it.  For example, to calculate the difference between 2 group's R-squared values for the same outcome (very difficult to specify constraints for a Wald test, but fairly simple to calculate from output in each bootstrap sample).

[Soumya Ray]

Joy, I think the debate is still wide open.  Falk (2017) uses simulations to once again make the case for percentile bootstrap over robust estimators.

Falk, C. (2017). Are Robust Standard Errors the Best Approach for Interval Estimation With Nonnormal Data in Structural Equation Modeling? Structural Equation Modeling: A Multidisciplinary Journal 25(2), 1-23. https://dx.doi.org/10.1080/10705511.2017.1367254