Geostatistical inference in the presence of geomasking: a composite-likelihood approach

TL;DR

This paper introduces a composite-likelihood method for geostatistical inference that accounts for location errors due to geomasking, improving parameter estimation accuracy over existing methods.

Contribution

It develops a computationally feasible composite-likelihood approach for geostatistics with location errors, outperforming traditional methods in accuracy.

Findings

Composite-likelihood method yields smaller RMSE in parameter estimates.

Method outperforms N-weighted least squares in simulation studies.

Applied to Senegal malnutrition data with geomasked locations.

Abstract

In almost any geostatistical analysis, one of the underlying, often implicit, modelling assump- tions is that the spatial locations, where measurements are taken, are recorded without error. In this study we develop geostatistical inference when this assumption is not valid. This is often the case when, for example, individual address information is randomly altered to provide pri- vacy protection or imprecisions are induced by geocoding processes and measurement devices. Our objective is to develop a method of inference based on the composite likelihood that over- comes the inherent computational limits of the full likelihood method as set out in Fanshawe and Diggle (2011). Through a simulation study, we then compare the performance of our proposed approach with an N-weighted least squares estimation procedure, based on a corrected version of the empirical variogram. Our results indicate that the composite-likelihood approach outper- forms the latter, leading to smaller root-mean-square-errors in the parameter estimates. Finally, we illustrate an application of our method to analyse data on malnutrition from a Demographic and Health Survey conducted in Senegal in 2011, where locations were randomly perturbed to protect the privacy of respondents.