Modelling count data based on weakly dependent spatial covariates using a copula approach: application to rat sightings
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Not all environmental processes are observed in a way that allows a straight forward easy modelling. Nevertheless, insights can also be gained by exploring weakly dependent covariates paying attention to details of the distribution. Using the concept of copulas, it is possible to explore the dependence of a multivariate distribution without the distortion of the marginal distribution functions acting on typical correlation measures. Furthermore, copulas turn the attention to the dependence across the entire range of the multivariate distribution and do not only summarise it in a single correlation measure. In our application, we study counts of rat sightings in the city of Madrid. The brown rat lives with mankind and adversely affects public health by transmission of diseases, bites and allergies. Better understanding behavioural and spatial correlation aspects of this species can contribute to its effective management and control. We explore weakly to moderately correlated covariates based on distances to broken sewers, feeding grounds and markets as well as population density. The use of copulas is motivated by the different dependence structures of the four covariates and the asymmetries therein. In order to deal with the discrete zero-inflated counts, we present a new approach that assigns conditional random ranks to discrete data. This way, we mimic an underlying continuous variable easing the vine copula estimation, but do not destroy the dependence as in a uniform randomisation. We show that a 5-dimensional vine copula model is able to capture the dependence in our application.
KeywordsCounts Point pattern Rats Vine copulas
We thank Ibon Tamayo-Uria, Manuel Garcia and Jose Maria Camara for their invaluable help and in all cases the Technical Unit Vectors Madrid for their cooperation. Two reviewers and the associated editor raised important points that re-shaped the study and considerably improved the manuscript. Carlos Ayyad and Jorge Mateu have been partially funded by Grants P1-1B2012-52 and MTM2013-43917-P. The research of Benedikt Gräler has partially been funded by the German Research Foundation (DFG PE 1632/4-1).
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