I have about 20 000 cases with discrete variables (some are counts,
some are factors).  I'm interested in fitting a series of models
outcome ~ 1
outcome ~ sex
outcome ~ sex + age
outcome ~ age * sex
outcome ~ age * sex + location
...

I do NOT expect to get any statistical significance out of this at all;
it's purely exploratory (this is a small sample of the full data set).

I'm trying multinom (present continuous because it is not a fast method);
what are recommended ways of doing it?

As part of this question, what would fitting a "Naive Bayes" model look
like in R?

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