Extrapolation for discrete outcomes

Establish whether generalized engression models can extrapolate to covariate values outside the training support when the outcome is discrete, including applications such as predicting species communities under environmental conditions absent from the training data.

Background

Generalized engression models estimate conditional distributions for outcomes that may be continuous, discrete, or mixed. The paper notes that the underlying engression method has been applied to extrapolation beyond the observed covariate support, but the extension to discrete outcomes is unresolved.

This question is practically relevant to ecological prediction, where a fitted model may need to predict species communities under environmental conditions that were not represented in the training sample.