The functional form of a model can be a constraint in the correct prediction of discrete choices. The flexibility of a nonparametric model can increase the likelihood of correct prediction. The likelihood of correct prediction of choices can further be increased if more predictors are included, but as the number of predictors approaches or exceeds the sample size, more serious complications can be generated than the improvement in prediction. With high dimensional predictors in discrete choice modeling, we propose a generalized additive model (GAM) where the predictors undergo dimension reduction prior to modeling. A nonparametric link function is proposed to mitigate the deterioration of model fit as a consequence of dimension reduction. Using simulated data with the dependent variable having two or three categories, the method is comparable to the ordinary discrete choice model when the sample size is sufficiently large relative to the number of predictors. However, when the number of predictors exceeds substantially the sample size, the method is capable of correctly predicting the choices even if the components included in the model account for only 20% of the total variation in all predictors. The method is also used in predicting income deciles from demographic and geographic indicators, proportion of income coming from different sources, and proportion of expenditures on different items using household level data in the Philippines.