Hi all

We are working on calculating Vuong LRT between mixture models from OpenMx. Specifically, we are adjusting the function vuongtest() from the package nonnest2.

But we are stuck in one step so far, getting the row-wise log-likelihood contributions to the overall model LL. Because of the structure on OpenMx we are able to get the row-wise contributions for each class, but we havent been able to see how these are combined into the overall model fit

Here is an example, were we get to the point of saving the row-wise contibutions, so far my sum of the row contibutions gets us -4680.073 instead of the overal LL -4251.208

Could someone point us in the right way to combine the class contributions to get the total row-wise contributions?

library(tidySEM) ## Import and prepare data dat <- rio::import("https://stats.idre.ucla.edu/wp-content/uploads/2016/02/lca1.dat") dat <- dat[,-1] dat <- as.data.frame(lapply(dat, ordered)) ## use tidySEM to write 2 class LCA model res0 <- mx_lca(dat, classes = 2, run=F) ## add rowDiagnostics to save row-wise results for each class res0$class1$fitfunction$rowDiagnostics <- T res0$class2$fitfunction$rowDiagnostics <- T ## estimate rr <- mxTryHardOrdinal(res0) summary(rr, verbose=T) ## see class proportions wgts <- rr$expectation$output$weights ## see the individual likelihood contributions for each class lc1 <- rr@submodels[["class1"]]$fitfunction$result lc2 <- rr@submodels[["class2"]]$fitfunction$result ## overall model fit rr$fitfunction$result ## -2LL = 8502.416 rr$fitfunction$result*-.5 ## LL = -4251.208 cc <- cbind(l1=log(lc1)*wgts[1], l2=log(lc2)*wgts[2]) sum(rowSums(cc )) ## -4680.073

The row-wise (minus two) log likelihood in a mixture model is the (minus two) log of the weighted sum of the row likelihoods (i.e., densities) from the mixture classes. I think people get confused between the likelihood and the log likelihood. You also have to be careful about the sum of the logs (incorrect) versus the log of the sum (correct) which are not generally equal.

If l1i is the row likelihood for row i in class 1, then -2*log(l1i) is the minus two log likelihood for row i in class 1. See the subject line for the equation. Below is the updated correct code.

Oh,I see i had the order of operations wrong. Thank you so much