Yeah I'm not buying the last bit about lower MSE with one term in the model vs two (Brier with one outcome category is MSE of the probabilities). That's the sort of thing that would make me go dig to find where I fucked up the calculation.
With one term it gets more robust in the face of excluding endpoints when constructing the jackknife train/test split, I think. But you're right, it does sound fishy.
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