近年來，隨著基因探索與醫療領域的蓬勃發展，分析大量因子資料成為現代化統計的一項重大挑戰。在分析資料的過程中，我們會想要在多因子的資料下挑選出對於反應變數有顯著影響性的解釋變數，所以善用選擇模型的方法就顯得非常重要。選擇模型的方法發展至今已有許多，而本篇論文研究的是兩個針對反應變數為連續型，解釋變數為類別型的選模方法：MB-MDR與SPV。
在比較這兩個選模方法時，我們利用電腦程式模擬出資料型態為數量性狀基因座(QTL)的基因資料，並分為大量因子與少量因子個數。利用MB-MDR與SPV分析資料後，使用平均準確率與平均錯誤率來評估選模的結果。結果顯示SPV在大樣本之下挑選主效應的平均準確率表現不錯，在小樣本之下較不理想，再者混合(主效應加交互作用)的平均準確率在所有樣本數設定下皆表現不理想，反觀其平均錯誤率皆很低。MB- MDR在所有樣本數設定之下其挑選交互作用的平均準確率都表現不錯，但相對的所有參數設定下其平均錯誤率較高。
根據模擬的結果可知，選用MB-MDR或是SPV可視需求而定，例如想要探討的是模型的主效應或是交互作用，又或者要求是選模方法的高準確率或是低錯誤率，可由使用者自行斟酌後選用。

In recent years, following the gene’s exploration and the development in medical field, analyzing the high dimensional of factors in data is a major challenge to modern statistics. In the process of data analyzing, we would identify the influential multifactor interactions which are significant to the response variable in a multifactor data, so the choice of model selection method is very important. Model selection method has been developed through different approaches so far, and in this paper the authors studied the two model selection methods which are for the response variable to be continuous and the independent variables to be categorical: MB-MDR and SPV.
In comparing the two model selection methods, we use computer programs to simulate two sets of data for the quantitative trait loci (QTL). One set of data contained a large number of factors and the other contained a small number of factors. After analyzed the data with both MB-MDR and SPV methods, we use the average accuracy and average error rate to evaluate the results. The results showed that the SPV performed well in the average accuracy rate when identifying the main effects in the large sample, but did worse when deal with small samples. Furthermore, the results for mixed average accuracy (main effects with interactions) is worse than ideal under all samples settings, however, the average error rates are very low under all situations. The average accuracy rate of interactions based on MB-MDR in all samples setting, are all performed well, but it has higher average error rate under all situations.
According to the simulation results, the selection of MB-MDR or SPV is based on the requirement of the user. For example, the user might be interested in exploring the main effects or interactions effects in a model, or requiring a high accuracy or low error rate, the users can make the choices based on their needs.

目錄
第一章	緒論	1
第一節	研究動機	1
第二節	研究議題	2
第三節	研究方法	4
第二章	文獻探討	6
第一節	SNPs和疾病的相關分析	6
2.1.1 關聯分析(Association Study)	6
2.1.2 連鎖分析(Linkage Analysis)	8
第二節	基因與基因之間的交互作用分析	12
2.2.1 多因子降維法(Multifactor Dimensionality Reduction)	13
2.2.2 羅吉斯迴歸(logistic regression)	15
2.2.3 分類迴歸樹法(Classification And Regression Trees)	17
第三節	數量性狀基因座(Quantitative Trait Loci)	18
第四節	資料型態	21
2.4.1 使用QTL分析近交系老鼠的血漿HDL膽固醇濃度及動脈硬化易感性	22
2.4.2 酒、香菸及大麻在不同人種與性別下的使用比例	23
2.4.3 鳶尾花品種預測	23
2.4.4原發性膽汁肝硬化	24
第三章	研究方法	25
第一節	迴歸方法	25
3.1.1順向選取法(The Forward Selection Procedure)	25
3.1.2反向淘汰法(The Backward Elimination Procedure)	26
第二節	Model-Based Multifactor Dimensionality Reduction	28
第三節	Stepwise Pairing Down Variation	31
第四章	模擬分析	35
第一節	生成資料	35
第二節	模擬結果	41
第五章	分析實際資料	47
第六章	結論與建議	52
附錄	54
參考文獻	59

表目錄
表格 1  case-control數目關係	7
表格 2  SNP40與SNP252交互作用之下其多點位基因型的分類	14
表格 3  資料型態與適用選模方法	21
表格 4  170個因子數的QTL參數設定	36
表格 5  170個解釋變數的10個上位效應參數設定	36
表格 6  170個解釋變數的20個上位效應參數設定	37
表格 7  46個解釋變數的QTL參數設定	38
表格 8  46個解釋變數的10個上位效應參數設定	39
表格 9  46個解釋變數的20個上位效應參數設定	40
表格 10  SPV的平均準確率	41
表格 11  SPV的平均錯誤率	42
表格 12  MB-MDR的平均準確率	44
表格 13  MB-MDR的平均錯誤率	45
表格 14  Framingham心臟研究變數選取	48
表格 15  Framingham心臟研究變數選取(續)	49
表格 16  Framingham心臟研究在SPV與MB-MDR的分析結果	49
表格 17  Framingham心臟研究在SPV與MB-MDR的分析結果(續)	50
表格 18  高中生喝酒、吸菸、吸大麻按照性別與種族之分類	54
表格 19  鳶尾花資料	55
表格 20  PBC資料	56
表格 21  PBC資料	56
表格 22  PBC變數名稱	57
圖目錄
圖 1 基因輿圖	11

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