Generalized nonlinear modeling with multivariate free-knot regression splines

• 成果类型: Article
• 署名作者: Holmes, CC; Mallick, BK
• 署名单位: Imperial College London; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503000143
• 发表日期: 2003
• 页码: 352-368
• 关键词: bayesian regression; inference; binary

摘要

A Bayesian method is presented for the nonparametric modeling of univariate and multivariate non-Gaussian response data. Data-adaptive multivariate regression splines are used where the number and location of the knot points are treated as random. The posterior model space is explored using a reversible-jump Markov chain Monte Carlo sampler. Computational difficulties are partly alleviated by introducing a random residual effect in the model that leaves many of the posterior conditional distributions of the model parameters in standard form. The use of the latent residual effect provides a convenient vehicle for modeling correlation in multivariate response data, and as such our method can be seen to generalize the seemingly unrelated regression model to non-Gaussian data. We illustrate the method on a number of examples, including two previously unpublished datasets relating to the spatial smoothing of multivariate accident data in Texas and the modeling of credit card use across multiple retail sectors.