Spatial model selection using Bayes factor and ratio of variabilities for asthma mortality data

J. Y. Tzeng, C. K. Hsiao, C. J. Chen

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Hierarchical models are commonly used in analyzing geographical data. They take account of the random variation in addition to the systematic variability among observations. Through specifying a distribution for rates at different areas, various kinds of random mechanism for variability can be considered. The exchangeable (EX) priors and conditional autoregressive (CAR) priors are the two most common approaches. However, it is unclear about how to choose between these two mechanisms. In this study, motivated by looking for the true pattern of the asthma mortality data for Taipei City, we adopt the two competing EX and CAR models to investigate the spatial pattern. With the two hypotheses (the EX or CAR model), we not only need to obtain estimates of quantities of interest but also need to choose an appropriate model since the final decision may result in different etiologic studies. In this paper, we use the fully Bayesian approach with the Monte Carlo Markov Chain to obtain estimates. Then, we focus on two model selection indices - the Bayes factor and the ratio of the variances (the local effect to the global effect) for the asthma study. Based on the study results, we conclude: (1) Both the Bayes factor and the ratio of the local variance to the global variance should be used together for choosing an appropriate model. The Bayes factor offers a direct answer for which model is favored by the data, while the ratio of variances reflects the characteristic of the data and provides a way to evaluate whether it is necessary to consider the area-specific effect. (2) According to the two indices, the EX model is considered more appropriate for the asthma mortality data, and the rates at Neihu and Nankang are higher than other areas. The remaining variation among areas for the EX model may be caused by some spatial-independent variables rather than spatial-correlated variables.

Original languageEnglish
Pages (from-to)158-169
Number of pages12
JournalChinese Journal of Public Health
Issue number2
Publication statusPublished - 1998 Jan 1

All Science Journal Classification (ASJC) codes

  • Public Health, Environmental and Occupational Health

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