The minimum number of predictors is 0. With that degenerative model, the logistic regression becomes just a test of whether the outcome proportions are equal. If you have one predictor, the logistic also has equivalents from Stat 1. If you have a binary outcome and a classification predictor, it is a type of chi-squared test. If the classification variable is continuous, it is roughly the same as a z-test. The calculations are slightly different, but the results are asymptotically equivalent. Having a lot of predictors may get you a more precise model for that set of data (higher c-index), but it is not necessarily the most accurate or reproducible in general. When you get new or additional data, the model with many variables may break down. Harrell and others have done a lot of simulation work on the impact of over-specifying a model. If you have lots of data (as we often do in data mining), it is less of an issue. Doc Muhlbaier Duke
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