This article is published in Environmetrics as a special issue on TIES 2008: Quantitative Methods for Environmental Sustainability, edited by Sylvia R. Esterby, University of British Columbia Okanagan, Canada.
Special Issue Papers
Mapping spatial aggregation from counts data: a penalized likelihood approach†
Article first published online: 15 NOV 2010
Copyright ©2010 John Wiley & Sons, Ltd.
Special Issue: TIES 2008: Quantitative methods for environmental sustainability
Volume 21, Issue 7-8, pages 834–848, November - December 2010
How to Cite
Grevstad, N. (2010), Mapping spatial aggregation from counts data: a penalized likelihood approach. Environmetrics, 21: 834–848. doi: 10.1002/env.1077
- Issue published online: 23 DEC 2010
- Article first published online: 15 NOV 2010
- Manuscript Accepted: 24 AUG 2010
- Manuscript Received: 1 NOV 2008
- negative binomial;
- penalized likelihood;
- smoothing spline;
A model for counts data on a spatial domain is presented. The counts are assumed to follow the negative binomial distribution, with both the mean and dispersion parameter allowed to vary spatially. The ratio of the mean to the dispersion parameter is estimated via non-parametric penalized likelihood regression, and is equivalent to David and Moore's ecological index of aggregation. The dispersion parameter is assumed to follow a parametric model whose parameters are estimated via minimization of a variant of the well-known generalized approximate cross-validation (GACV) score, which is simultaneously used to estimate the smoothing parameter associated with estimation of the mean to dispersion parameter ratio. The increased flexibility of the model permitted by allowing the dispersion parameter to vary spatially is illustrated through spatial maps of David and Moore's and other indices of aggregation, such as Lloyd's indices of crowding and patchiness, using real and simulated data. Copyright © 2010 John Wiley & Sons, Ltd.