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Biostatistics 2004 5(4):633-648; doi:10.1093/biostatistics/kxh014
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Biostatistics Vol. 5 No. 4 © Oxford University Press 2004; all rights reserved.

Mixed models for the analysis of replicated spatial point patterns

Melanie L. Bell*

Department of Preventive and Social Medicine, University of Otago, PO Box 913, Dunedin, New Zealand
melanie.bell{at}stonebow.otago.ac.nz

Gary K. Grunwald

Department of Preventive Medicine and Biometrics, University of Colorado Health Sciences Center, 4200 E. 9th Avenue, Denver, Colorado 80262, USA

* To whom correspondence should be addressed.

The statistical methodology for the analysis of replicated spatial point patterns in complex designs such as those including replications is fairly undeveloped. A mixed model is developed in conjunction with maximum pseudolikelihood and generalized linear mixed modeling by extending Baddeley and Turner's (2000, Australian and New Zealand Journal of Statistics 42, 283–322) work on pseudolikelihood for single patterns. A simulation experiment is performed on parameter estimation. Fixed- and mixed-effect models are compared, and in some respects the mixed model is found to be superior. An example using the Strauss process for modeling neuron locations in post-mortem brain slices is shown.

Keywords: Berman–Turner device; Generalized linear mixed models; Maximum pseudolikelihood; Pairwise interaction; Strauss process


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