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Generalized Nonlinear Modeling with Multivariate Free-Knot Regression Splines

C. C. Holmes and B. K. Mallick
Journal of the American Statistical Association
Vol. 98, No. 462 (Jun., 2003), pp. 352-368
Stable URL: http://www.jstor.org/stable/30045245
Page Count: 17
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Abstract

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 We illustrate the method on a number of examples, including two previously unpublished datasets relating to the spatial smoothing of multivariate accident data in Texas and the modeling of credit card use across multiple retail sectors.

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