Geostatistical analysis of binomial data: generalised linear or transformed Gaussian modelling?

Authors


Correspondence to: Michelle Stanton, Centre for Neglected Tropical Diseases, Liverpool School of Tropical Medicine, Liverpool L3 5QA, U.K. E-mail: michelle.stanton@liv.ac.uk

Abstract

When fitting a binomial geostatistical model to data obtained by spatially discrete sampling, techniques such as Markov chain Monte Carlo, which are computationally intensive and require careful tuning to each application, need to be employed. As a result, this approach is often infeasible when computational resources are scarce or statistical expertise is unavailable. A practical solution to this problem is to transform the binomial samples such that the conditional distribution of the transformed data can be assumed to be approximately Gaussian. Likelihood-based inference can then be performed analytically, whereas Bayesian inference requires only routine Monte Carlo simulation. In this paper, the predictive performance of the binomial model-fitting method is compared with that of the approximate transformed Gaussian method. A simulation experiment is undertaken in which data are simulated from a binomial geostatistical model, and both methods are then used to make predictive inference. Predictions are assessed using the empirical root mean square prediction error and empirical coverage probabilities of nominal prediction intervals obtained for the approximate method. As expected, the comparative performance of the approximate method deteriorates as the denominator decreases and, to a lesser extent, as the overall proportion of successes in the simulated data deviates from 0.5. Our results provide guidance on when the approximate method can safely be used. We demonstrate the two methods on village-level prevalence data pertaining to the tropical eye disease Loa loa. Copyright © 2013 John Wiley & Sons, Ltd.

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