空間迴歸模型廣泛地應用於地質、大氣、水文、生態等相關領域的資料分析，其中如何配適合理的空間迴歸模型及該如何從候選模型中選出較適合的解釋變數組合都是重要的議題。空間統計中常用的選模準則有AICc，BIC與RIC。過往的研究顯示AICc較傾向選到解釋變數較多的模型，而BIC和RIC則是比較傾向選到解釋變數較少的模型。然而在實際的資料分析中，資料背後真正的解釋變數個數是未知的，同時資料間的相關結構也是未知的。因此若這些選模準則選出不同的模型，我們將無從判斷哪個模型才是最適合實際資料的描述。本研究提出一個均方預測誤差的準則去公平地比較各式準則所選出的模型並決定一個較適合實際資料的最終模型。本研究透過模擬實驗驗證所提方法的有效性。最後，我們使用法國默茲河附近的一筆重金屬汙染的空間資料去說明所提方法的實用性。

Spatial regression models are widely used in geology, atmosphere, hydrology, ecology and other related fields for data analysis, where how to select a suitable subset of covariates among candidate models is an important issue. Commonly used selection criteria such as AICc, BIC, and RIC can be applied for model selection. Past researches had shown that AICc tends to select a model with more covariates while BIC and RIC tend to select a model that has less covariates. Moreover, the covariance structure of the observed data set is generally unknown in practice. Therefore, how to determine an appropriate model for the observed data set is a difficult issue, especially when the covariance structure is misspecified or these criteria select different models. In this thesis, a mean squared prediction error criterion is proposed to fairly compare the selected models and then a final model can be determined. Simulation studies show that our proposed method has an adaptive feature which can’t be achieved by AICc, BIC, and RIC. Finally, a real data example regarding a heavy metal pollution near the Meuse river in France is analyzed for illustration.

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