累積羅吉斯迴歸模型常用來推論順序型反應變數與風險因子之間的關係。針對研究中的反應變數為有順序性的情況下，本文分別彙整前瞻式累積羅吉斯迴歸模型的參數估計和適合度檢定，以及回溯式研究中累積羅吉斯迴歸模型的參數估計，並建構回溯式研究中模型的適合度檢定。為了檢測回溯式累積羅吉斯迴歸模型的合適性，本文將順序型反應變數視為兩類，然後應用Cheng and Chen (2004)的方法提出分數形式適合度檢定。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。

In case-control studies, the cumulative logistic regression model is used popularly for inferring the relationship of ordinal response and risk factors. For the ordinal response, this paper summarizes the parameter estimation and goodness-of-fit of the cumulative logistic regression model in the prospective and retrospective studies, respectively. In order to test the goodness-of-fit of the retrospective cumulative logistic regression model, this paper divides the categories of response into two categories and then applies the method of Cheng and Chen (2004) to propose a score type goodness-of-fit test statistic. Simulation studies demonstrate that the
proposed test performs well even in finite samples.

目錄
第一章 緒論	                                    1
第二章 前瞻式研究下累積羅吉斯迴歸分析的整理	            4
  第一節 參數估計	                                    4
  第二節 模型適合度檢定	                            7
  第三節 實例分析	                                    9 
第三章 回溯式研究下累積羅吉斯迴歸模型參數估計的整理	    11
  第一節 參數估計                          	    11
  第二節 虛擬資料分析	                            12
第四章 回溯式研究下累積羅吉斯迴歸模型的分數形式適合度檢定 14	
  第一節 建構分數形式統計量	                    14
  第二節 模擬研究	                                    16
  第三節 虛擬資料分析	                            24
第五章 結論	                                    26
參考文獻	                                            27
附錄1  40位佛羅里達州阿拉楚阿縣居民的精神狀態	    28
附錄2  虛擬的150筆資料	                            29


表目錄

表1：觀測次數的列聯表	                              9
表2：配適前瞻式累積羅吉斯迴歸模型的結果	             10
表3：配適回溯式累積羅吉斯迴歸模型的結果	             13
表4：三類反應變數和一個解釋變數的分數形式適合度檢定模擬結果 20
表5：三類反應變數和兩個解釋變數的分數形式適合度檢定模擬結果 22
表6：四類反應變數和一個解釋變數的分數形式適合度檢定模擬結果 23
表7：四類反應變數和兩個解釋變數的分數形式適合度檢定模擬結果 24

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