Multinomial / Categorical Outcomes

[rodonn]

Is this package able to fit Multinomial Logistic Regression models or any other type of model with categorical/multiple discrete outcomes?

These types of models often come up when you need to choose one option out of a finite set of alternatives. They are very similar to binary logistic regression, except that the probabilities are given by the 'softmax' formula: $exp(X_j * Beta) / (1 + \sum_k X_k * Beta)$ rather than the $exp(X_j * Beta) / (1 + exp(X_j Beta))$ in a binary model.

Thanks!

[dmbates]

Not directly. It is possible that it could be modified to do so but I don't really know enough about this model to make such modifications.

[rodonn]

Thanks. I'm looking into how difficult it would be for me to make the modifications. Is the approach in MixedModels similar to what you describe in the lme4 theory documentation?

[Nosferican]

You could use part of the code in Econometrics.jl. That one has multinomial logistic regression. I will work on adding dispatch for ordinal logistic regression too.

[spinkney]

You could use part of the code in Econometrics.jl. That one has multinomial logistic regression. I will work on adding dispatch for ordinal logistic regression too.

Any update on adding ordinal logistic regression?

[Nosferican]

Econometrics.jl has ordinal logistic regression. However, it doesn't support mixed models so it is a simple proportional odds logistic regression. See the example.

[palday]

For multinomial models, you can achieve something similar by moving the response-categories to the predictors side. If you're trying to predict responses, you have to do a post-processing step to see what the probability is for each response, but that's relatively straightforward.

[Nosferican]

For mlogit/ologit in Econometrics.jl,

fitted(model) # Fitted values
predict(model) # Predicted probabilities

[palday]

I've marked this as "big future", but it might make more sense as a spin-off package, much like clmm in R uses lme4 internally but all of the extra multinomial bits are not in lme4. Lean, focused packages are the Julian way.