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doi:10.1016/j.csda.2006.11.008 
Copyright © 2006 Elsevier B.V. All rights reserved.
Computational techniques for spatial logistic regression with large data sets
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Christopher J. Paciorek
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Received 6 October 2005;
Abstract
In epidemiological research, outcomes are frequently non-normal, sample sizes may be large, and effect sizes are often small. To relate health outcomes to geographic risk factors, fast and powerful methods for fitting spatial models, particularly for non-normal data, are required. I focus on binary outcomes, with the risk surface a smooth function of space, but the development herein is relevant for non-normal data in general. I compare penalized likelihood (PL) models, including the penalized quasi-likelihood (PQL) approach, and Bayesian models based on fit, speed, and ease of implementation.
A Bayesian model using a spectral basis (SB) representation of the spatial surface via the Fourier basis provides the best tradeoff of sensitivity and specificity in simulations, detecting real spatial features while limiting overfitting and being reasonably computationally efficient. One of the contributions of this work is further development of this underused representation. The SB model outperforms the PL methods, which are prone to overfitting, but is slower to fit and not as easily implemented. A Bayesian Markov random field model performs less well statistically than the SB model, but is very computationally efficient. We illustrate the methods on a real data set of cancer cases in Taiwan.
The success of the SB with binary data and similar results with count data suggest that it may be generally useful in spatial models and more complicated hierarchical models.
Keywords: Bayesian statistics; Disease mapping; Fourier basis; Generalized linear mixed model; Geostatistics; Risk surface; Spatial statistics; Spectral basis
Article Outline
- 1. Introduction
- 2. Overview of methods
- 2.1. PL-based methods
- 2.1.1. PL and GLMMs
- 2.1.2. PL and generalized cross-validation
- 2.2. Bayesian methods
- 2.2.1. Bayesian GLMMs
- 2.2.2. Bayesian SB representation
- 2.2.3. Bayesian NN
- 2.2.4. Bayesian MRFs
- 2.3. Other methods
- 3. Implementation
- 3.1. Penalized likelihood and GLMMs (PL–PQL)
- 3.2. Penalized likelihood and GCV (PL–GCV)
- 3.3. Bayesian GLMM (Geo)
- 3.4. Bayesian spectral basis (SB)
- 3.5. Bayesian neural network (NN)
- 3.6. Bayesian Markov random field (MRF)
- 4. Simulations
- 4.1. Data sets
- 4.2. Assessment
- 4.3. Results
- 4.3.1. Quality of fit
- 4.3.2. Computational speed and MCMC performance
- 4.3.3. Ease of implementation
- 5. Case study
- 5.1. Background and data
- 5.2. Assessment
- 5.3. Results
- 6. Discussion
- Acknowledgements
- Appendix A. Representing functions in the spectral domain
- Appendix B. Supplementary material
- References
