An application of spatial regression with smoothing over the covariates
by
Petra Kuhnert
University of Queensland
Coauthors: Kerrie Mengersen (University of Newcastle)

A strong focus in the spatial statistics literature has been to create smoothed estimates over the response surface by including a form of averaging over geographic neighbourhoods in a regression model. This can be difficult to achieve in a binary setting for complex datasets, where samples have been recorded over an irregular lattice, the observed probability of presence is small, located in sparse areas across the study region, or there are very many covariates.

In this paper, an alternative approach that clusters the covariate surface and averages the responses within these clusters is considered. This approach has the capability to implicitly accommodate complex covariate interactions, which would remain otherwise undetected using geographic smoothing methods or traditional regression models.

The approach described in this paper considers a two stage process for estimation. First, we implement a Bayesian algorithm that uses Reversible Jump Markov Chain Monte Carlo (RJMCMC) methodology to identify clusters in the covariate space. Second, smoothed estimates for the response are formed by averaging over the covariate `neighbourhoods' for a nominal response, by majority rule scheme.

We illustrate this algorithm using three different applications. The first is a simple classification example, well-known in the statistics literature, the Iris data. The second is a small (n=35) but complex application, where interest lies with the prediction of the probability of presence of a rare and threatened species of bird, the Black-breasted Button-quail (Turnix melanogaster). The third application is the motivating problem, a large and complex application (n=24, 380), where interest is in modelling the probability of presence of a species of Eucalypt, Gympie messmate (Eucalypt cloeziana) for a designated sampling region in South-East Queensland, Australia.

Date received: April 29, 2002