We are running a mediational model (SEM) with categorical variables as the mediator and outcome. We used the "WLSMV" estimator and defined the categorical variables as ordered.
Is it possible to convert the output (i.e., effects) to logits and odds ratios? If not, how should the (un)standardized effects be interpreted?
Thanks in advance!
No, the (D)WLS estimation routine for caategorical outcomes is equivalent to a probit model. That is just a different link function and error distribution in the GLM, which typically make very similar predictions. But you cannot convert coefficients between the two (i.e., logit and probit models are not statistically equivalent).
On the latent-response metric. The categorical-(D)WLS estimation routine begins by estimating thresholds and polychoric correlations, on the assumption that each ordinal outcome is really a crude discretization of an underlying continuum.
https://doi.org/10.1080/10705510701758406
https://psycnet.apa.org/doi/10.1037/1082-989X.12.1.58 (search PubMed for a free copy)
So you can interpret the fully standardized solution, where the latent-response scale of your ordinal mediator is in units of SD (i.e., they are z scores).