Non‐Parametric Logistic and Proportional Odds Regression

SUMMARY We describe the additive non-parametric logistic regression model of the form logit[P(x)] ==a+ -fj(xj), where P(x) = P(y = 1 1 x) for a 0-1 variable y, x is a vector of p covariates, and the f; are general real-valued functions. Each of the f; 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[yk(x)] = Ik)-fj(X1) for ordinal response data. Here Yk is the probability of the response being at most k: yk(X) = P( Y ? k I x). Both these models are motivated and described in detail, and several examples are given.

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