Open AccessSpatial modeling of data with excessive zeros applied to reindeer pellet‐group counts
Author(s) -
Lee Youngjo,
Alam Md. Moudud,
Noh Maengseok,
Rönnegård Lars,
Skarin Anna
Publication year - 2016
Publication title -
ecology and evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.17
H-Index - 63
ISSN - 2045-7758
DOI - 10.1002/ece3.2449
Subject(s) - overdispersion , poisson distribution , count data , generalized linear model , statistics , mathematics , poisson regression , zero inflated model , spatial analysis , quasi likelihood , spatial dependence , random effects model , generalized linear mixed model , medicine , population , meta analysis , demography , sociology
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.