Gibbs point process models with mixed effects
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 disc...
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ftuglasgow:oai:eprints.gla.ac.uk:199450 2023-05-15T16:29:29+02:00 Gibbs point process models with mixed effects Illian, Janine B. Hendrichsen, Ditte K. 2010-04-26 http://eprints.gla.ac.uk/199450/ unknown Wiley Illian, J. B. <http://eprints.gla.ac.uk/view/author/51577.html> and Hendrichsen, D. K. (2010) Gibbs point process models with mixed effects. Environmetrics <http://eprints.gla.ac.uk/view/journal_volume/Environmetrics.html>, 21(3-4), pp. 341-353. (doi:10.1002/env.1008 <http://dx.doi.org/10.1002/env.1008>) Articles PeerReviewed 2010 ftuglasgow https://doi.org/10.1002/env.1008 2020-01-10T02:01:02Z 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). Article in Journal/Newspaper Greenland University of Glasgow: Enlighten - Publications Clayton ENVELOPE(-64.183,-64.183,-65.167,-65.167) Greenland Strauss ENVELOPE(-73.182,-73.182,-71.649,-71.649) Environmetrics 21 3-4 341 353 |
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Open Polar |
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University of Glasgow: Enlighten - Publications |
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ftuglasgow |
language |
unknown |
description |
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). |
format |
Article in Journal/Newspaper |
author |
Illian, Janine B. Hendrichsen, Ditte K. |
spellingShingle |
Illian, Janine B. Hendrichsen, Ditte K. Gibbs point process models with mixed effects |
author_facet |
Illian, Janine B. Hendrichsen, Ditte K. |
author_sort |
Illian, Janine B. |
title |
Gibbs point process models with mixed effects |
title_short |
Gibbs point process models with mixed effects |
title_full |
Gibbs point process models with mixed effects |
title_fullStr |
Gibbs point process models with mixed effects |
title_full_unstemmed |
Gibbs point process models with mixed effects |
title_sort |
gibbs point process models with mixed effects |
publisher |
Wiley |
publishDate |
2010 |
url |
http://eprints.gla.ac.uk/199450/ |
long_lat |
ENVELOPE(-64.183,-64.183,-65.167,-65.167) ENVELOPE(-73.182,-73.182,-71.649,-71.649) |
geographic |
Clayton Greenland Strauss |
geographic_facet |
Clayton Greenland Strauss |
genre |
Greenland |
genre_facet |
Greenland |
op_relation |
Illian, J. B. <http://eprints.gla.ac.uk/view/author/51577.html> and Hendrichsen, D. K. (2010) Gibbs point process models with mixed effects. Environmetrics <http://eprints.gla.ac.uk/view/journal_volume/Environmetrics.html>, 21(3-4), pp. 341-353. (doi:10.1002/env.1008 <http://dx.doi.org/10.1002/env.1008>) |
op_doi |
https://doi.org/10.1002/env.1008 |
container_title |
Environmetrics |
container_volume |
21 |
container_issue |
3-4 |
container_start_page |
341 |
op_container_end_page |
353 |
_version_ |
1766019182298660864 |