Specification and Inference in Nonparametric Additive Regression

This article revisits the Bayesian inferential problem for the class of nonparametric additive models. A new identification scheme for the unknown covariate functions is proposed and contrasted with existing approaches, and is used to develop an efficient Markov chain Monte Carlo estimation algorithm. Building upon the identification scheme, the resulting estimation procedure, and a class of proper smoothness priors for the unknown functions, the paper considers the problem of model comparison using marginal likelihoods and Bayes factors. A simulation study illustrates the performance of the proposed techniques. The methods are illustrated in two applications in economics – one dealing with student achievement, and the other with urban growth. Extensions of the methodology to other settings, such as discrete and clustered data, are also discussed.