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A model for spatio-temporal clustering using multinomial probit regression: application to avalanche counts


A. Lavigne, INRA, UMR 518, 16 rue Claude Bernard, 75005 Paris, France.



Although modeling complex environmental spatio-temporal processes, separability between time and space effects is often assumed as a first approach, even though it may be unrealistic. Hence, the development of adapted non-separable spatio-temporal models is a challenging issue. In this work, we are interested in modeling avalanche counts over the whole French Alps, a large area that exhibits zones characterized by distinct climatic behaviors. We have at our disposal a data set of 405, 63-year series of avalanche counts, one series for one township. We assume the series can be divided into several spatial clusters presenting specific temporal trends. On the latent layer of a hierarchical negative binomial-lognormal structure, the clusters are characterized by independent temporal evolutions, modeled using smoothing splines. The clusters arise as the result of a multinomial probit regression, with spatial coordinates used as covariates. Inference is performed within the Bayesian hierarchical framework. The number of clusters is assessed using cross validation. The best score is obtained for a three-cluster model, but other configurations also share some evidence. The first cluster is located in the east of the French Alps, whereas the others are located together in the west part of the French Alps. The three contrasted temporal trends corresponding to the three clusters result from regional climate change effects, interacting with a strong altitudinal control and data limitation. The proposed model could be used for analyzing various other climatic and environmental data sets. Copyright © 2012 John Wiley & Sons, Ltd.