Generalized nonlinear modeling with multivariate free-knot regression splines

Journal article

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 We illustrate the method on a number of examples, including two previously unpublished datasets relating to the spatial smoothing of multivariate accident data in Texas and the modeling of credit card use across multiple retail sectors.

Authors: Holmes, C; Mallick, B

• Publication status: Published
• Journal: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• Volume: 98
• Issue: 462
• Pages: 352-368
• Publication date: 2003-06-01
• DOI: 10.1198/016214503000143
• EISSN: 1537-274X
• ISSN: 0162-1459
• Keywords: generalized nonlinear regression; piecewise linear; multivariate spline; Bayesian nonlinear regression; local linear regression; seemingly unrelated regression; multivariate nonlinear regression