病例對照研究中多元羅吉斯迴歸模型的適合度檢定

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题名:	病例對照研究中多元羅吉斯迴歸模型的適合度檢定
其它题名:	A goodness-of-fit test of multinomial logistic regression model in case-control studies
作者:	許育愷;Shiu, Yu-kai
贡献者:	淡江大學統計學系碩士班陳麗菁
关键词:	拔靴法;病例對照研究;適合度檢定;多元羅吉斯迴歸;半參數最大概似估計量;Bootstrap method;case-control studies;Goodness-of-fit test;multinomial logistic regression;semiparametric maximum likelihood estimator
日期:	2014
上传时间:	2015-05-04 09:53:12 (UTC+8)
摘要:	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.
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