Link LCA with MixtureModels ExpectationMazimization.jl for EM and predict

[dmetivie]

Hello,
I don't know much about (medical?) applications of LCA, however I do know about EM algo.
Looking at your package, I wanted to make you aware (if you are not already) of the MixtureModel from Distributions.jl. Indded the LCA you consider can be seen as a Mixture of Product distribution of Categorical variables.
Moreover, ExpectationMazimization.jl (I am the owner) is made to fit MixtureModels.
It is very generic and support in particular Mixture of Product distribution of Categorical variables.

Suggestion for this Issue: maybe the internal of your EM algo and predict can use ExpectationMazimization.jl?
The interface you design however should be kept as you prefer and as your community wants.
It feels a bit weird to push for "my" package, but here are some potential benefits:

• First, here is a notebook to showcase how to use MixtureModel in your context + that the two packages do the exact same EM.
• Independently of EM.jl, with MixtureModels it is very easy to generate artificial datasets e.g. for testing, unlike the "manual" used in the runtest.jl. See the notebook second example where I create a latent dataset with 4 items of [4, 2, 3, 5] categories with 3 classes.
• EM.jl is faster and use less memory (see notebook benchmarks) -> if you don't agree on the depending on EM.jl you can always improve your EM having in mind my code.
• EM.jl also implement Stochastic EM algo (see notebook at the end), and I aim to implement other methods at some point
• You can focus on other aspect of your package
• Dependencies of EM.jl are quite soft (mainly Distribution.jl)

If you are interested and want to discuss, we could set up a chat. Moreover, I could write a PR to show how small changes in your package's internals could without modifying the user interface support EM.jl (the conversion between LCA.jl and EM.jl is mostly done in the notebook)

I have other suggestions, but I'll open other issues to keep things separate.