Two-scale spatial models for binary data

Abstract

A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the back-ground. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian-Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence-absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted. Abstract A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the background. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian-Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence-absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted.

Model-based small area estimation at two scales using Moran's spatial filtering

“…Fitting the models to two-scale spatial binary data has become much less complicated, also when the covariates are included. To our best knowledge, this inclusion of covariates in changing support modelling of spatial binary data has not had a solution available in literature until now, although its consideration has been given by Hardouin and Cressie (2018) . The developed models enable the adding of an arbitrary number of external variables that drive the spatial variability of the health outcomes.…”

“…Several new modeling approaches were proposed by Nagle et al (2011Nagle et al ( , 2014, Hardouin and Cressie (2018) and Truong and Stein (2018) . Their work addressed the downscaling of discrete attributes with different foci.…”

“…Truong and Stein (2018) proposed a complex Bayesian hierarchical model to downscale data of disease incidence but with limited identifiability. Hardouin and Cressie (2018) proposed a new modelling scheme to downscale spatial binary data. Their methods allowed for spatial autocorrelation but have not been able to benefit from covariates.…”

“…Their methods allowed for spatial autocorrelation but have not been able to benefit from covariates. Still, making inferences for autologistic models is notoriously difficult, requiring numerical approximaton methods for estimation ( Griffith, 2004;Hughes et al, 2011;Hardouin and Cressie, 2018 ). The main disadvantage is that the extension to multiple scale models increases the dimension of the parameter spaces while the calibration data available do not increase in most cases.…”