Non‐Parametric Logistic and Proportional Odds Regression

We describe the additive non‐parametric logistic regression model of the form logit[p(x)] = α+ ∑fj(xj), where p(x) =p(y = 1|x) for a 0–1 variable y, x is a vector of p covariates, and the fj are general real‐valued functions. Each of the fj can be chosen to be either linear, general non‐linear (estimated by a scatterplot smoother) or step functions for discrete covariates. The functions are estimated simultaneously using the “ local scoring algorithm”. The model can be used as an exploratory tool for uncovering the form of covariate effects or it can be used in a more formal manner in model building. We also describe the additive proportional odds model logit[γk(x)] = αk–∑fj(xj) for ordinal response data. Here γk is the probability of the response being at most k: γk(x) = p(Y ≤ k | x). Both these models are motivated and described in detail, and several examples are given.