# Fit indices using MCLUST latent cluster analysis

I conducted latent class/cluster analysis in R using the package MCLUST. I have a revise and resubmit for my paper, and the reviewer suggested making a table of the fit indices for the cluster solutions (as of now I just reported BIC in the text). when I look at a few papers that have used LCA approaches, they report BIC, sample size adjusted BIC, and entropy; the only fit statistic of these that MCLUST gives is BIC. I can find entropy plots but not the entropy statistic. It's a little late for me to re-run my analyses on Mplus (which I figured out was used for the LCA in these papers). frankly, it's a little late to re-run my analyses using another clustering package. from all of my reading it sounds like MCLUST does things a tiny bit differently than some other k-means cluster approaches. ALSO - it seems that sometimes the model with the lowest BIC is selected (in some papers) but in MCLUST the highest one is selected? Why?

so, tldr; what other model selection stats are reported in write-ups when using MCLUST? is it standard/okay to just have bIC? how would I justify that?

• If you're only asking about how mclust works, this question is off topic here. Note that mclust implements finite Gaussian mixture modeling, not k-means. Also, I don't follow the thinking about, eg, controlling for sample size; all the clustering results that would be possible with your data would be based on the same N. Commented Nov 9, 2016 at 2:01

Just a couple thoughts, having used mclust a bit previously.

1) mclust uses the correct BIC selection method; see this post:

Mclust model selection

See the very bottom, but to sum it up, with BIC it depends if you use the negative sign in the formula or not whether you optimize low vs. high:

The general definition of the BIC is BIC=−2×ln(L(θ|x))+k×ln(n)BIC=−2×ln(L(θ|x))+k×ln(n); mclust does not include the negative component.

2) mclust uses mixture models to perform the clustering (i.e., model-based); it's quite different from k-means so I would be careful with the phrasing that it's a "tiny bit different than some of the other k-means cluster approaches" (mainly in what "other" implies here); the process for model selection is briefly described in the mclust manual:

mclust provides a Gaussian mixture fitted to the data by maximum likelihood through the EM algorithm, for the model and number of components selected according to BIC. The corresponding components are hierarchically combined according to an entropy criterion, following the methodology described in the article cited in the references section. The solutions with numbers of classes between the one selected by BIC and one are returned as a clustCombi class object.

It's more useful to see the actual paper for a thorough explanation:

The entropy plot provided by mclust is meant to be interpreted like a scree plot for a factor analysis (i.e., by looking for an elbow to determine the optimal number of classes); I would argue scree plots are useful for justifying the choice of number of clusters, and these plots belong in the appendices.

mclust does also return the ICL statistic in addition to BIC, so you could choose to report that as a compromise to the reviewer:

https://cran.r-project.org/web/packages/mclust/vignettes/mclust.html (see the example on how to get it to output the statistics)

3) if you wanted to create a table of the entPlot values, you can extract them like so (from the ?entPlot example):

## Not run:
data(Baudry_etal_2010_JCGS_examples)
# run Mclust to get the MclustOutput
output <- clustCombi(ex4.2, modelNames = "VII")

entPlot(output$MclustOutput$z, output$combiM, reg = c(2,3)) # legend: in red, the single-change-point piecewise linear regression; # in blue, the two-change-point piecewise linear regression. # added code to extract entropy values from the plot combiM <- output$combiM
Kmax <- ncol(output$MclustOutput$z)
z0 <- output$MclustOutput$z
ent <- numeric()

for (K in Kmax:1) {
z0 <- t(combiM[[K]] %*% t(z0))
ent[K] <- -sum(mclust:::xlog(z0))
}

data.frame(Number of clusters = 1:Kmax, Entropy = round(ent, 3))

Number.of.clusters Entropy
1                  1   0.000
2                  2   0.000
3                  3   0.079
4                  4   0.890
5                  5   6.361
6                  6  20.158
7                  7  35.336
8                  8 158.008


Although the question was asked quite a while ago, there may still be people dealing with this question of how to use the mclust output to find entropy $$R^2$$ values between $$0$$ and $$1$$ (I know I was).

I used the method described by Jeroen Vermunt in this Youtube video.

It requires quite a bit of coding if you want to do it for multiple analyses, but it works.

library(mclust)
library(dplyr)

# first run mclust model
model <- Mclust(data)

# extract necessary information from mclust output
# this code is for a three cluster model, change accordingly if more/less clusters
df_entropy <- model[["z"]]
df_entropy <- as.data.frame(df_entropy)
# depending on the number of clusters, change the next lines accordingly
colnames(df_entropy) <- c("Cluster1", "Cluster2", "Cluster3")
# create first part of entropy formula, also change according to number of cluster
df_entropy <- df_entropy %>%
mutate(ent1 = -Cluster1 * log(Cluster1),
ent2 = -Cluster2 * log(Cluster2),
ent3 = -Cluster3 * log(Cluster3),
ent_sum = ent1 + ent2 + ent3)
a <- mean(df_entropy$ent_sum) # second part of entropy formula using mixing probabilities # again, if more/less clusters change accordingly mixprob <- model$$parameters$$pro b <- (-mixprob[1] * log(mixprob[1]) + -mixprob[2] * log(mixprob[2]) + -mixprob[3] * log(mixprob[3])) # to calculate entropy R2 entropy <- (b - a) / b entropy  To check if it works, you can use the iris dataset and the tidyLPA package which provides a wrapper for mclust. In the code below, I instructed mclust to estimate the same 2 cluster model as tidyLPA estimated. The entropy $$R^2$$ value calculated at the end will be the same as the entropy $$R^2$$ value that tidyLPA provides. library(tidyLPA) library(dplyr) library(mclust) view(iris) # tidyLPA model iris %>% select(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) %>% estimate_profiles(n_profiles = 2) %>% get_fit() %>% as.data.frame() # mclust model iris.mclust <- Mclust(iris[c(1:4)], modelNames = "EEI", G = 2) # LPA summary(iris.mclust, parameters = T) # entropy calculations df_entropy <- iris.mclust[["z"]] df_entropy <- as.data.frame(df_entropy) colnames(df_entropy) <- c("Cluster1", "Cluster2") df_entropy <- df_entropy %>% mutate(ent1 = -Cluster1 * log(Cluster1), ent2 = -Cluster2 * log(Cluster2)) df_entropy <- df_entropy %>% mutate(ent_sum = (ent1 + ent2)) a <- mean(df_entropy$ent_sum)

mixprob <- iris.mclust$$parameters$$pro
b <- -mixprob[1] * log(mixprob[1]) + -mixprob[2] * log(mixprob[2])

entropy <- (b - a) / b
entropy