Semi-Parametric Generalized Linear Models.

This document considers generalized linear models in which the linear predictor is of additive semi-parametric form, linear in most of the explanatory variables but with an arbitrary functional dependence on the remainder. Estimation of the parameters and the non-parametric curve in the model is approached by maximizing a penalized likelihood. Two explicit iterative algorithms are presented. The first, which operates in On time per iteration, applies where there is just one variable entering the model in a non-parametric fashion, and an integrated squared second derivative penalty is used. An example in logistic regression of tumour prevalence is given. The second algorithm is for the much more general case of a regression model specified as an arbitrary composite log-likelihood function, permitting nonlinear dependence and several splined variables. Keywords Maximum penalized likelihood estimation Nonlinear regression Splines. Author