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

Youngjo Lee,Maengseok Noh,Lars Rönnegård,Anna Skarin,Md. Moudud Alam

doi: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 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.

Highlights

Fecal pellet-group counts have long been used in wildlife management to map population densities of large herbivores and their habitat selection
We introduce a quasi-Poisson hierarchical generalized linear model (HGLM) with a spatial correlation to fit reindeer pellet-group counts, and we show that a Poisson GLM, by ignoring spatial correlation, can lead to a poor model fit
The regression kriging prediction based upon those residuals, which is often suggested in the literature, may result in poor spatial prediction

Summary

Introduction

Fecal pellet-group counts have long been used in wildlife management to map population densities of large herbivores and their habitat selection (see, e.g., Fattorini, Ferretti, Pisani, & Sforzi, 2011; Neff, 1968; Skarin, 2008). From the initial survey data, collected over the 2 years 2009–2010, appearance of large numbers of 0 counts was identified as a challenge for the data analysis. This situation is not unusual in that data pertaining to spatial species counts

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