Comparing the performance of two indices for spatial model selection: application to two mortality data

The statistical analysis of spatially correlated data has become an importa nt scientific research topic lately. The analysis of the mortality or morbi dity rates observed at different areas may help to decide if people living in certain locations are considered at higher risk than others. Once the st atistical model for the data of interest has been chosen, further effort ca n be devoted to identifying the areas under higher risks. Many scientists, including statisticians, have tried the conditional autoregressive (CAR) mo del to describe the spatial autocorrelation among the observed data. This m odel has greater smoothing effect than the exchangeable models, such as the Poisson gamma model for spatial data. This paper focuses on comparing the two types of models using the index LG, the ratio of local to global variab ility. Two applications, Taiwan asthma mortality and Scotland lip cancer, a re considered and the use of LG is illustrated. The estimated values for bo th data sets are small, implying a Poisson gamma model may be favoured over the CAR model. We discuss the implications for the two applications respec tively. To evaluate the performance of the index LG, we also compute the Ba yes factor, a Bayesian model selection criterion, to see which model is pre ferred for the two applications and simulation data. To derive the value of LG, we estimate its posterior mode based on samples derived from the BUGS program, while for Bayes factor we use the double Laplace-Metropolis method , Schwarz criterion, and a modified harmonic mean for approximations. The r esults of LG and Bayes factor are consistent. We conclude that LG is fairly accurate as an index for selection between Poisson gamma and CAR model. Wh en easy and fast computation is of concern, we recommend using LG as the fi rst and less costly index. Copyright (C) 2000 John Wiley & Sons, Ltd.