在病例對照研究中，羅吉斯迴歸模型常用來推論疾病與風險因子之間的關係。當研究中的反應變數為多個類別時，需考慮使用多元羅吉斯迴歸模型。本文推廣Qin and Zhang (1997)的想法到多元羅吉斯迴歸模型，推導各個病例組與對照組之間的比例關係，並將此模型重參數化得到多組的半參數化模型，以此推論迴歸參數的半參數最大概似估計量。為了檢測模型的合適性，本文推廣Chen and Wang (2013)的方法，針對多元羅吉斯迴歸模型提出動差形式檢定統計量，並使用拔靴法求算檢定統計量的p值。經由模擬研究發現，即使在有限樣本下該檢定統計量亦表現良好。最後以兩組實際資料分析作為範例。

In case-control studies, the logistic regression model is used popularly for inferring the relationship of disease and risk factors. When a response has multiple categories, the multinomial logistic regression should be considered. By generalizing the concept of Qin and Zhang (1997), this study derives a proportional relationship between the control group and each case group. After reparameterisation, the logistic model is equivalent to several semiparametric models and then the semiparametric maximum likelihood estimator is derived based on this finding. This study generalizes the idea of Chen and Wang (2013) to propose a moment-type test statistic for the multinomial logistic regression. A bootstrap method is used to calculate the p-value of the proposed test. Simulation studies demonstrate that the proposed test performs well even in finite samples. An illustration with two real data sets is provided as well.

目錄
第一章 緒論1
第二章 病例對照研究下多元羅吉斯迴歸的統計推論5
第一節 參數估計5
第二節 建構多元羅吉斯迴歸模型的檢定統計量11
第三章 模擬研究14
第四章 實例分析19
第五章 結論21
參考文獻23
附錄一 青少年安置研究資料25
附錄二 城際交通方式選擇資料30

表目錄
1. 動差形式檢定統計量S_0的模擬結果17
2. 動差形式檢定統計量S的模擬結果，J=2 17
3. 動差形式檢定統計量S的模擬結果，J=3 18

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