Spatial modeling of data with excessive zeros applied to reindeer pellet‐group counts |
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| Authors: | Youngjo Lee Md Moudud Alam Maengseok Noh Lars Rönnegård Anna Skarin |
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| Affiliation: | 1. Department of Statistics, Seoul National University, Seoul, Korea;2. School of Technology and Business Studies, Dalarna University, Falun, Sweden;3. Department of Statistics, Pukyong National University, Busan, Korea;4. Department of Animal Nutrition and Management, Swedish University of Agricultural Sciences, Uppsala, Sweden |
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| Abstract: | We analyze a real data set pertaining to reindeer fecal pellet‐group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi‐Poisson hierarchical generalized linear model (HGLM), zero‐inflated Poisson (ZIP), and hurdle models. The quasi‐Poisson HGLM allows for both under‐ and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi‐Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi‐Poisson HGLM with spatial random effects. |
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| Keywords: | excessive zeros habitat preference hierarchical generalized linear model pellet‐group count Poisson model spatial correlation |
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