Spatial modeling of data with excessive zeros applied to reindeer pellet‐group counts

• Published in: Ecology and Evolution
• Main Authors: Lee, Youngjo, Alam, Md. Moudud, Noh, Maengseok, Rönnegård, Lars, Skarin, Anna
• Other Authors: National Research Foundation of Korea, Ministry of Science, ICT and Future Planning
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 2016
• Subjects: Northern Sweden
• Online Access: http://dx.doi.org/10.1002/ece3.2449; https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fece3.2449; https://onlinelibrary.wiley.com/doi/pdf/10.1002/ece3.2449; https://onlinelibrary.wiley.com/doi/full-xml/10.1002/ece3.2449

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 HGLM s can perform better than the other commonly used models, for example, ordinary Poisson HGLM s, spatial ZIP , and spatial hurdle models, and that the underdispersed Poisson HGLM s with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLM s. 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.