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2010 Spatial logistic regression and change-of-support in Poisson point processes
A. Baddeley, M. Berman, N.I. Fisher, A. Hardegen, R.K. Milne, D. Schuhmacher, R. Shah, R. Turner
Electron. J. Statist. 4: 1151-1201 (2010). DOI: 10.1214/10-EJS581

Abstract

In Geographical Information Systems, spatial point pattern data are often analysed by dividing space into pixels, recording the presence or absence of points in each pixel, and fitting a logistic regression. We study weaknesses of this approach, propose improvements, and demonstrate an application to prospective geology in Western Australia. Models based on different pixel grids are incompatible (a ‘change-of-support’ problem) unless the pixels are very small. On a fine pixel grid, a spatial logistic regression is approximately a Poisson point process with loglinear intensity; we give explicit distributional bounds. For a loglinear Poisson process, the optimal parameter estimator from pixel data is not spatial logistic regression, but complementary log-log regression with an offset depending on pixel area. If the pixel raster is randomly subsampled, logistic regression is conditionally optimal. Bias and efficiency depend strongly on the spatial regularity of the covariates. For discontinuous covariates, we propose a new algorithmic strategy in which pixels are subdivided, and demonstrate its efficiency.

Citation

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A. Baddeley. M. Berman. N.I. Fisher. A. Hardegen. R.K. Milne. D. Schuhmacher. R. Shah. R. Turner. "Spatial logistic regression and change-of-support in Poisson point processes." Electron. J. Statist. 4 1151 - 1201, 2010. https://doi.org/10.1214/10-EJS581

Information

Published: 2010
First available in Project Euclid: 8 November 2010

zbMATH: 1329.62253
MathSciNet: MR2735883
Digital Object Identifier: 10.1214/10-EJS581

Subjects:
Primary: 62H11 , 62J12
Secondary: 60E99 , 60G55 , 62M30

Keywords: Change of support , complementary log-log regression , ecological fallacy , exponential family , generalized linear models , geographical information systems , likelihood , logistic regression , missing information principle , mixed pixels , mixels , modifiable area unit problem , modulated Poisson process , Poisson point process , prospective geology , prospectivity , spatial point process , spatial statistics , split pixels , Western Australia

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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