Illian, J. B. and Hendrichsen, D. K. (2010) Gibbs point process models with mixed effects. Environmetrics, 21(3-4), pp. 341-353. (doi: 10.1002/env.1008)
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Abstract
We consider spatial point patterns that have been observed repeatedly in the same area at several points in time. We take a maximum pseudolikelihood approach (besag :1976) to parameter estimation in the context of Gibbs processes (Stoyan et al., 1995, Illian et al., 2008). More specifically, we discuss pair‐wise interaction processes where the conditional intensity has a log‐linear form and extend existing models by expressing the intensity and the interaction terms in the pseudolikelihood as a sum of fixed and random effects, where the latter accounts for variation over time. We initially derive a Strauss process model with mixed effects. As this model is too simplistic in the given context, we further consider a more general model that allows for inter‐group differences in intensity and interaction strength and has a more flexible interaction function. We apply the approximate Berman–Turner device (Baddeley and Turner, 2000) to a generalised linear mixed model with log link and Poisson outcome rather than a simple generalised linear model. Estimates are obtained using existing software for generalised linear mixed models based on penalised quasi‐likelihood methods (Bresow and Clayton, 1993). The approach is applied to a data set detailing the spatial locations of different types of muskoxen herds in a fixed area in Greenland at different points in time within several years (Meltofte and Berg, 2004).
Item Type: | Articles |
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Additional Information: | Special Issue: Spatio‐Temporal Stochastic Modelling: Environmental and Health Processes. |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Illian, Professor Janine |
Authors: | Illian, J. B., and Hendrichsen, D. K. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Statistics |
Journal Name: | Environmetrics |
Publisher: | Wiley |
ISSN: | 1180-4009 |
ISSN (Online): | 1099-095X |
Published Online: | 18 August 2009 |
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