Projection predictive variable selection for discrete response families with finite support

The approximate latent-space approach to the projective part of the projection predictive variable selection implemented in the projpred R package recently added support for more response families, including ordinal ones relying on a single latent predictor per observation. Here, we present an exact projection approach for all discrete finite-support response families, called the augmented-data projection. A simulation study shows that the two projection approaches usually behave similarly, but the augmented-data projection tends to perform better. The cost of the slightly better performance of the augmented-data projection is a substantial increase in runtime. Thus, we recommend to use the latent projection in the early phase of a model-building workflow and to use the augmented-data projection for final results. Not illustrated here is that the augmented-data projection adds support for nominal response families which are not supported by the latent projection.