Non‐Parametric Logistic and Proportional Odds Regression

SUMMARY We describe the additive non‐parametric logistic regression model of the form logit[ p (x)] = α+ ∑ f j ( x j ), where p (x) = p ( y = 1|x) for a 0–1 variable y , x is a vector of p covariates, and the f j are general real‐valued functions. Each of the f j 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[ γ k (x)] = α k –∑ f j ( x j ) for ordinal response data. Here γ k is the probability of the response being at most k: γ k (x) = p ( Y ≤ k | x). Both these models are motivated and described in detail, and several examples are given.