A two‐stage model for incidence and prevalence in point‐level spatial count data

Abstract

aWe consider the problem of modeling point-level spatial count data with a large number of zeros. We develop a model that is compatible with scientific assumptions about the underlying data-generating process. We utilize a two-stage spatial generalized linear mixed model framework for the counts, modeling incidence, resulting in 0-1 outcomes, and prevalence, resulting in positive counts, as separate but dependent processes and utilize a Gaussian process model for characterizing the underlying spatial dependence. We describe a Bayesian approach and study several variants of our two-stage model. We fit the models via Markov chain Monte Carlo methods. We study several Markov chain Monte Carlo algorithms, including a version of the Langevin-Hastings algorithm, for exploring the complicated posterior distribution efficiently and recommend an algorithm that is fairly efficient. Finally, we demonstrate the application of our modeling and computational approach on both simulated data and real data from an ecological field survey.

Mapping species abundance by a spatial zero‐inflatedPoisson model: a case study in theWaddenSea, theNetherlands

“…As we mentioned earlier, unlike Recta et al. (); Boyd et al. () who applied zero‐truncated Poisson, we allowed for two sources of zeros: true (Bernoulli) zeros and false (Poisson) zeros.…”

“…Both issues have been tackled separately (Crist ; Fletcher and Sumner ; Potts and Elith ), but very few studies deal with both issues simultaneously (Recta et al. ; Boyd et al. ).…”

“…Recta et al. () mapped the Colorado potato beetle and Boyd et al. () Peruvian anchoveta, a small pelagic fish species.…”

A Spatial Poisson Hurdle Model for Exploring Geographic Variation in Emergency Department Visits

“…However, these models assume independent random effects for the two components, which may lead to biased inferences. To address this potential drawback, Recta et al (2011) recently proposed a correlated spatial hurdle Poisson model for point-referenced (e.g., latitude-longitude) zero-inflated data.…”

Grid-spacing and the quality of abundance maps for species that show spatial autocorrelation and zero-inflation

“…Recta et al, 2012;Boyd et al, 2015) do not treat the question of optimal sampling design. We attempt to 55 fill this gap by following a paper by Lyashevska et al (2016) in simulating fields with zero-inflated, spatially autocorrelated count data, and sampling the fields repeatedly with different sampling designs.…”