DWLS estimator in lavaan & interpreting indirect effects

Question

I performed SEM using lavaan with RStudio on a model that includes 1 categorical independent variable, 2 parallel mediators (ordinal), which are latent, and 2outcome variables, one of which is ordinal and one has been defined as ordered categorical - the latter one leading to my question.

When calculating the mediation model with an ordered categorical outcome variable, lavaan automatically uses the DWLS estimator (with DWLS = Diagonally Weighted Least Squares). I was wondering whether the indirect effects can actually be interpreted with this estimator. Without the ordered categorical outcome variable, I would usually implement bootstrapping, but with the DWLS estimator, lavaan would not let me perform bootstrapping.

Is the DWLS estimator okay for interpreting the indirect effects or should I implement additional tests / procedures?

Looking forward to some input / advice! :-)

Cordially, Tobias

Answer 1

It does look like you are able to implement estimator = "DWLS" and bootstrapping simultaneously: see here, though it does require you to implement the bootstrapping in one of the less-conventional lavaan-friendly ways. In particular, if you are looking for the speediest multi-core implementation, it looks like using boostrapLavaan() is your best bet.

Also just to note that I see no reason why you wouldn't be able to interpret your defined indirect effect just because it was estimated with DWLS. The estimator is how you get the particular values in your model, but that doesn't change the way that indirect effects are defined (i.e., $ab$, or $c-c'$ if you prefer). The choice of estimator might have some bearing on accuracy/bias of estimation and/or power/precision of testing/estimation (and that might be the sort of question for which there is a reference), and you might have to pay attention to if it changes the units of interpretation on you (my recollection is that lavaan uses probit for categorical outcomes), but otherwise I think the question of whether you can test indirect effects is more or less up to whether you've specified your model properly.