Analogous AIC/BIC for WLSMV estimator

[Guilherme Parreira]

Hi There.

Is there an Analogous AIC/BIC for WLSMV estimator?

I know that AIC and BIC are only available for ML estimation, because it depends on the value of the log-likelihood.

Is there a "pseudo" AIC when using WLS estimation methods? (More specifically WLSMV?).

I am looking for a parsimonious index

Thanks

[Mauricio Garnier-Villarreal]

A clarification first, AIC and BIC are not measures of parsimony. They are approximation of out-of-sample predictive accuracy, correcting for the overfitting of in-sample predictive accuracy measures (log-likelihood).

As the chi-square is calculted from LL you could theoretically do the same adjustement: chi-square + 2*K, where k is the number of parameters. But I am pretty sure this doesnt work the same way, because these were design for measures of predictive accuracy for continuous variables, so shouldnt be used with other types of estimators

As for measures of parsimony, this is a complex topic on definying parismony. I would even consider gamma-hat as better index of it. You can estimate it from the moreFitIndices function from semTools.

See these references for more details

Preacher, K. J., & Merkle, E. C. (2012). The problem of model selection uncertainty in structural equation modeling. Psychological Methods, 17, 1–14. https://doi.org/10.1037/a0026804

Preacher, Kristopher J. (2006). Quantifying parsimony in structural equation modeling. Multivariate Behavioral Research, 41(3), 227–259. https://doi.org/10.1207/s15327906mbr4103_1