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研究生:丁雅貞
論文名稱:羅吉斯迴歸模型的變數選取問題
指導教授:黃怡婷試銀慶剛銀慶剛引用關係
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:49
中文關鍵詞:羅吉斯迴歸Newton-Raphson 法最大概似函數強一致性AIC
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進行統計分析時,若想知道一反應變數(response variable)與某些解釋變數(explanatory variable)間是否有關聯,通常會考慮建立迴歸模型。但,如果反應變數為一類別資料時,則一般的線性迴歸模型(linear model)則不適用,而羅吉斯迴歸(logistic regression)為最普遍利用的統計技巧。在迴歸模型選模的過程中解釋變數的選擇是一重要的步驟,因為所選擇的解釋變數會影響到對所分析資料的預測以及描述。近年來複線性迴歸(multiple linear regression)的領域的發展已逐漸完備,但在羅吉斯迴歸上卻非如此。由於羅吉斯迴歸的反應變數並非是連續的,所以對於解釋變數的選擇產生了許多的困難。 Agrestia(1990)建議利用Newton-Raphson 法逼近最大概似估計式(maximum likelihood estimate 簡稱MLE) ,David W,Borko以及Stanley(1989)(簡稱AIC)則提出利Newton-Raphson法求出全模型(full model)之MLE後,在利用此計算結果當作起始值帶入候選模型中做一次遞迴,計算出候選模型之未知參數。以減少對每一候選做Newton-Raphson法的麻煩。本文主要利用的選模準則為Akiake information criterion(1974),Sambamoorthi(1989a)證明並未符合強一致性(strong consistent)並建議將AIC給予適當的修改,使得修飾後的AIC具強一致性。Sambamoorthi(1989b)根據此理論在解釋變數為連續的情況下,予以模擬佐證。發現在大樣本下,修正過後的準則,選到正確模型的機率相當的高。本論文的主要目的是討論在反應變數為二元(binary)的情況下,如何選擇到適當的羅吉斯迴歸模型。在以往的研究中對於羅吉斯迴歸解釋變數的選擇,往往只討論到連續型的解釋變數,並未討論到離散型的解釋變數。但在現實生活中所遇到的問題裡,時常都是解釋變數為離散型或是離散及連續的混合型的資料。所以文獻上的研究並不完全符合現實生活中所遇到的問題。因此本文對於解釋變數為離散型或是離散及連續的混合型時的選模問題加以討論。
A main purpose of this is model section criteria to find suitable in logistic regression models. While the Bayesian information criterion (BIC)(Schwarz, 1928 ) is prove to be strongly consistent in this model. We surprisingly found from the simulation study that BIC may have very poor performances when some of the explanatory variables are of discrete type. Then, a new model selection criterion, which is a hybrid of AIC and BIC is proposed. After suitable weights begin assigned to the penalty terms of AIC and BIC. We show that this new criterion more performs BIC especially when some explanatory variables are discrete and sample size is small. Finally, a example rule of choosing the optimal criterion and AIC, BIC, and new method is proposed.
1.緒論.......................................................1
2.文獻回顧...................................................4
2.1 羅吉斯迴歸之R-Square...................................4
2.2 最小預測類離差準則.....................................5
2.3 維度縮減...............................................7
3.研究方法..................................................11
4.模擬結果..................................................16
5.實證分析..................................................29
6.結論與建議................................................31
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