The Vuong-Lo-Mendell-Rubin test for latent class and latent profile analysis: A note on the different implementations in Mplus and LatentGOLD

Mplus and LatentGOLD implement the Vuong-Lo-Mendell-Rubin test (comparing models with K and K + 1 latent classes) in slightly differ manners. While LatentGOLD uses the formulae from Vuong (1989; https://doi.org/10.2307/1912557), Mplus replaces the standard parameter variance-covariance matrix by its robust version. Our small simulation study showed why such a seemingly small difference may sometimes yield rather different results. The main finding is that the Mplus approximation of the distribution of the likelihood-ratio statistic is much more data dependent than the LatentGOLD one. This data dependency is stronger when the true model serves as the null hypothesis (H0) with K classes than when it serves as the alternative hypothesis (H1) with K + 1 classes, and it is also stronger for low class separation than for high class separation. Another important finding is that neither of the two implementations yield uniformly distributed p-values under the correct null hypothesis, indicating this test is not the best model selection tool in mixture modeling.