Spatial logistic regression and change-of-support in Poisson point processes

Baddeley, Adrian; Berman, Mark; Fisher, N. I.; Hardegen, Andrew; Milne, Robin K.; Schuhmacher, Dominic; Shah, Rohan; Turner, Rolf

doi:10.1214/10-ejs581

Cited by 73 publications

(111 citation statements)

References 66 publications

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“…The cloglog link has its own appeal because of its connection with Poisson point processes (Baddeley et al, 2010); the asymmetric aspect of the cloglog also often performs better when the probability of an event is much less or much more than 0.5, which is the case with Indiana bat hibernacula affected by WNS. We hypothesized that size of, proximity to, and direction to infected sources would be important predictors of risk.…”

Section: Methodsmentioning

confidence: 99%

Space-Time Models for a Panzootic in Bats, With a Focus on the Endangered Indiana Bat

Thogmartin

King

Szymanski

et al. 2012

Journal of Wildlife Diseases

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ABSTRACT:Knowledge of current trends of quickly spreading infectious wildlife diseases is vital to efficient and effective management. We developed space-time mixed-effects logistic regressions to characterize a disease, white-nose syndrome (WNS), quickly spreading among endangered Indiana bats (Myotis sodalis) in eastern North America. Our goal was to calculate and map the risk probability faced by uninfected colonies of hibernating Indiana bats. Model covariates included annual distance from and direction to nearest sources of infection, geolocational information, size of the Indiana bat populations within each wintering population, and total annual size of populations known or suspected to be affected by WNS. We considered temporal, spatial, and spatiotemporal formulae through the use of random effects for year, complex (a collection of interacting hibernacula), and year3complex. Since first documented in 2006, WNS has spread across much of the range of the Indiana bat. No sizeable wintering population now occurs outside of the migrational distance of an infected source. Annual rates of newly affected wintering Indiana bat populations between winter 2007 to 2008 and 2010 to 2011 were 4, 6, 8, and 12%; this rate increased each year at a rate of 3%. If this increasing rate of newly affected populations continues, all wintering populations may be affected by 2016. Our models indicated the probability of a wintering population exhibiting infection was a linear function of proximity to affected Indiana bat populations and size of the at-risk population. Geographic location was also important, suggesting broad-scale influences. For every 50-km increase in distance from a WNS-affected population, risk of disease declined by 6% (95% CI55.2-5.7%); for every increase of 1,000 Indiana bats, there was an 8% (95% CI51-21%) increase in disease risk. The increasing rate of infection seems to be associated with the movement of this disease into the core of the Indiana bat range. Our spatially explicit estimates of disease risk may aid managers in prioritizing surveillance and management for wintering populations of Indiana bats and help understand the risk faced by other hibernating bat species.

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Section: Methodsmentioning

confidence: 99%

Space-Time Models for a Panzootic in Bats, With a Focus on the Endangered Indiana Bat

Thogmartin

King

Szymanski

et al. 2012

Journal of Wildlife Diseases

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“…Most often, a logit link is used to model the presence probability as a function of predictors. Alternatively, a complementary log-log link provides a more natural parameterization for continuous point process models observed in discrete space (Prentice & Gloeckler 1978) and can facilitate comparisons and predictions across grids that differ in their grid cell size (Baddeley et al 2010). All of these response variables attempt to link the distribution of an organism to the environmental conditions at which it is observed.…”

Section: H a B I T A T U S E A N D P R E F E R E N C E I N D I S C R mentioning

confidence: 99%

“…In particular, we focus on point and count data. Owing to work performed by others (Diggle 1990;Cressie 1993;Diggle & Rowlingson 1994;Baddeley & Turner 2000;Lele & Keim 2006;Lele 2009;Baddeley et al 2010;Diggle, Kaimi, & Abellana 2010a;Warton & Shepherd 2010), it is possible to show that the Poisson likelihood function used for count data, and likelihood functions used for point methods [e.g. Weighted Distribution Theory (WDT) and point Logistic regression] can be motivated by the same underlying inhomogeneous Poisson point process (IPP) model.…”

Section: Introductionmentioning

confidence: 99%

Comparative interpretation of count, presence–absence and point methods for species distribution models

2011

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Summary1. The need to understand the processes shaping population distributions has resulted in a vast increase in the diversity of spatial wildlife data, leading to the development of many novel analytical techniques that are fit‐for‐purpose. One may aggregate location data into spatial units (e.g. grid cells) and model the resulting counts or presence–absences as a function of environmental covariates. Alternatively, the point data may be modelled directly, by combining the individual observations with a set of random or regular points reflecting habitat availability, a method known as a use‐availability design (or, alternatively a presence – pseudo‐absence or case–control design).2. Although these spatial point, count and presence–absence methods are widely used, the ecological literature is not explicit about their connections and how their parameter estimates and predictions should be interpreted. The objective of this study is to recapitulate some recent statistical results and illustrate that under certain assumptions, each method can be motivated by the same underlying spatial inhomogeneous Poisson point process (IPP) model in which the intensity function is modelled as a log‐linear function of covariates.3. The Poisson likelihood used for count data is a discrete approximation of the IPP likelihood. Similarly, the presence–absence design will approximate the IPP likelihood, but only when spatial units (i.e. pixels) are extremely small (Electric Journal of Statistics, 2010, 4, 1151–1201). For larger pixel sizes, presence–absence designs do not differentiate between one or multiple observations within each pixel, hence leading to information loss.4. Logistic regression is often used to estimate the parameters of the IPP model using point data. Although the response variable is defined as 0 for the availability points, these zeros do not serve as true absences as is often assumed; rather, their role is to approximate the integral of the denominator in the IPP likelihood (The Annals of Applied Statistics, 2010, 4, 1383–1402). Because of this common misconception, the estimated exponential function of the linear predictor (i.e. the resource selection function) is often assumed to be proportional to occupancy. Like IPP and count models, this function is proportional to the expected density of observations.5. Understanding these (dis‐)similarities between different species distribution modelling techniques should improve biological interpretation of spatial models and therefore advance ecological and methodological cross‐fertilization.

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“…[47, p. 24]), pixel-based logistic regression is essentially equivalent to fitting a Poisson point process with intensity of loglinear form (2). See [9,67]. True nonparametric estimation of ρ in the general form (1) is studied in this paper.…”

Section: (U) = ρ(X(u))mentioning

confidence: 99%

“…This is equivalent to pixel-based logistic regression of the probability of the presence of a gold deposit against distance to nearest fault [1,9,67]. We estimated the parameters α, β by maximum likelihood [9].…”

Section: Murchison Datamentioning

confidence: 99%

Nonparametric estimation of the dependence of a spatial point process on spatial covariates

Baddeley

Chang

Song

et al. 2012

Statistics and Its Interface

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In the statistical analysis of spatial point patterns, it is often important to investigate whether the point pattern depends on spatial covariates. This paper describes nonparametric (kernel and local likelihood) methods for estimating the effect of spatial covariates on the point process intensity. Variance estimates and confidence intervals are provided in the case of a Poisson point process. Techniques are demonstrated with simulated examples and with applications to exploration geology and forest ecology.

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Spatial logistic regression and change-of-support in Poisson point processes

Cited by 73 publications

References 66 publications

Space-Time Models for a Panzootic in Bats, With a Focus on the Endangered Indiana Bat

Space-Time Models for a Panzootic in Bats, With a Focus on the Endangered Indiana Bat

Comparative interpretation of count, presence–absence and point methods for species distribution models

Nonparametric estimation of the dependence of a spatial point process on spatial covariates

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