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Spatial Model Selection Using Bayes Factor and Ratio of Variabilities for Asthma Mortality Data

使用貝氏因子與變異項比值進行氣喘死亡率地理空間資料模型之選擇

摘要


以階層式模型分析空間地理資料,除了可考慮有規則性的變異量之外,亦可針對隨機變異量加以處理。在認為各地死亡率係受另一隨機分佈(即事前分佈)支配的前提下,階層式模型透過所假設的隨機分配以解釋隨機變異,其中最常用的兩種模式即為conditional autoregressive(CAR)模式與exchangeable(EX)模式。然而,欲在這兩種代表不同意義的模式間進行選擇,卻往往欠缺判斷的準則。本研究以台北地區氣喘死亡率資料為例,在面對兩種不同死亡原因的假說的情況下,我們兼採CAR模式與EX模式來探討氣喘死亡率的地理趨勢,並利用Fully Bayesian方法與Monte Carlo Markov Chain原理(如Gibbs sampling)來估計參數。除了須選出一適當的模式來描述其地理分佈狀況外,更希望透過所選用模式的意義來了解氣喘死亡的可能成因。我們選採兩個指標-貝氏因子與局部作用之變異量與整體作用之變異量比值-作為模式選擇的依據。研究結果發現:(1)由貝氏因子可直接看出資料較支持何種模式;而變異量比值則顯示資料本身的性質與是否應將局部作用放入模式中加以考慮,在模式的選擇上,二者應相互配合使用。(2)由指標來判斷,對氣喘死亡率資料而言,以EX模式較為適恰。由此亦推論內湖區、南港區有較高死亡率;而仍存在於地區間的變異則較可能由地區間彼此獨立的因素所引起。

並列摘要


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.

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