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Two-scale spatial models for binary data

Journal Article


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.

Publication Date


  • 2018

Citation


  • Hardouin, C. & Cressie, N. (2018). Two-scale spatial models for binary data. Statistical Methods and Applications, 27 (1), 1-24.

Scopus Eid


  • 2-s2.0-85027701766

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/587

Number Of Pages


  • 23

Start Page


  • 1

End Page


  • 24

Volume


  • 27

Issue


  • 1

Place Of Publication


  • Germany

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.

Publication Date


  • 2018

Citation


  • Hardouin, C. & Cressie, N. (2018). Two-scale spatial models for binary data. Statistical Methods and Applications, 27 (1), 1-24.

Scopus Eid


  • 2-s2.0-85027701766

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/587

Number Of Pages


  • 23

Start Page


  • 1

End Page


  • 24

Volume


  • 27

Issue


  • 1

Place Of Publication


  • Germany