Compare the above on MSE of predicted probabilities to latent Y* (which has noise) and NLL on predicted probabilities to observed Y. Also compare on MSE of average marginal effects. Do this for the following settings:
[ ] Well specified logistic DGP (few + many predictors)
[ ] logistic DGP with misspecification in linear component (ommitted variables + interactions + higher order terms)
[ ] well specified probit DGP
[ ] probit DGP with misspecification in linear component
Compare the above on MSE of predicted probabilities to latent Y* (which has noise) and NLL on predicted probabilities to observed Y. Also compare on MSE of average marginal effects. Do this for the following settings: