臺灣博碩士論文加值系統

中文摘要
因素分析 (Factor Analysis) 在探索資料方面常扮演著極重要的角色，主要目的是對多個且彼此間具有相關性的變數作歸類。透過線性代數的理論方法，轉換資料的共變異矩陣 (Covariance Matrix)，取得解釋變異最大的數個因子 (Common Factors) 達到降低資料維度(Dimension Reduction)的目的。
ㄧ般資料透過適當的分層處理，可減少分層變項 (Stratified Variable) 帶給資料的變異。當分層資料進行統計分析時，技巧上需有適當修正，本研究對統計上的因素分析(Factor Analysis) 提出組平均校正法(Group-mean-corrected method) ，及聯合共變異矩陣法 (Pooled-amount-variation method)二種簡易的修正方法以處理分層資料。
本研究所提出的胎兒資料(Fetal Data)，為數個不同部位之血流脈衝指數(Pulsatility Index)，利用分層技巧控制懷孕週數所造成的偏差(Bias)，再透過因素分析得到解釋變異最大的倆個共同因子。與二元反應變項(出生胎兒正常或不正常)連結時，應用邏輯斯迴歸分析 (Logistic Regression Analysis)及迴歸分類樹(CART) 分析進行二元區分。區分結果顯示，當資料與懷孕週數有高度相關時，修正的資料有較低的錯歸率 (misclassification rate)。
關鍵詞：分層資料(Stratified Data)、因素分析(Factor Analysis)、胎兒資料(Fetal Data)、脈衝指數(Pulsatility Index)。

Abstract
Factor Analysis is one method of exploring the data structure. The main point is to classify correlated variables to reduce the dimension of data. Based on covariance matrix, factor analysis extracts common factors and remains most of variance through matrix algebra.
In practice, stratified data can reduce the additional variance due to the extra variable. In modeling, Conditional logistic regression model, and Stratified PH model are available for stratified data. Factor analysis for stratified data is somehow complicated and not available in software. In this thesis, two methods, pooled-amount-variation and group-mean-corrected methods, are proposed for data correction before factor analysis used.
In this fetal data, Pulsality Index (PI) values are measured from several parts of vessels. The effect caused from gestational age effect is reduced by corrected methods. Two factors remaining most of variation are generated from factor analysis. Combining the binary fetal outcome (normal or abnormal), logistic regression analysis and CART analysis are used for binary discrimination. The discrimination result has lower misclassification rate from corrected data when data highly correlate with gestational age.
Keywords：Stratified Data、Factor Analysis、 Fetal Data、Pulsatility Index﹒

Reference List
Alvin C. Rencher; Methods of Multivariate Analysis 2nd Edition; (2002) John Wiley & Sons, Inc.
Chien, Using Conditional Logistical Regression Model in Classifying Binary Data. (2003) National Yang-Ming University Master Thesis.
C. Subbarao, N.V.Subbarao, S.N. Chandu, Characterization of Groundwater Contamination Using Factor Analysis. Environmental Research 1996; vol28: No.4: 175-180.
David W. Hosmer, Jr., Stanley Lemeshow. Applied Logistic Regression 2nd (2002) John Wiley & Sons. Inc.
Franciois Sainfort, The Use of Factor Analysis Techniques. Medical Decision Making 2002 Sep.-Otc; 451-2.
Gregory P. Beehler, John M. Weiner, Susan E. McCann, John E.Vena, and David E. Sandberg, Identification of Sport Fish Consumption Patterns in Families of Recreational Anglers through Factor Analysis. Environmental Research Section 2002;A 89, 19-28.
H.S.Park, R.Dailey, and D. Lemus, The Use of Exploratory Factor Analysis and Principal Component Analysis in Communicaiton Research. Human Communication Research 2002 Otc.; Vol.28: No. 4: 562-577.
Hair, Anderson, Tatham, Black. Multivariate Data Analysis. 5th Edition;1998 Prentice-Hall, Inc.
Hsu, Using Unsupervised Learning Method to Supplement Supervised Learning Method. (2003) National Yang-Ming University Master Thesis.
Jeng-Hsiu Hung, Chong-Yau Fu, Chiou-Chung Yuan, Cheng-Li Chen, Man-Li Yang, Li-Ping Shu, and Chih-Chieh Wu, Nuchal Translucence Incorporated into A One-Stage Multifactorial Screening Model For Down Syndrome Prediction at Second-Trimester Pregnancy. Ultrasound in Med. & Bio. 2003; Vol. 29, No. 12, pp. 1667-1674.
James A. Hanley, and Barbara J. McNeil, The Meaning and Using of The Area under a Receiver Operating Characteristic (ROC) Curve. Radioilogy April 1982; 143: 29-36,.
James A. Hanley, and Barbara J. McNeil, A Method of Comparing The Areas under Receiver Operating Characteristic Curves Dervied from the Same Cases. Radioilogy Sep. 1983, 148: 839-843.
Leo Breiman, Jerome H. Friedman, Richard A. Olshen, Charles J. Stone. Classification and Regression Trees. 2000.
Paul Kline;An Easy Guside to Factor Analysis; (1994)
Petra M. Kuhnert, Kim-Anh Do, Rod McClure. Combining non-parametric models with logistic regression：an application to motor vehicle injury data. Computational statistics & Data analysis 2000; 34, 371-386.
Richard A. Johnson & Dean W. Wichern; Applied Multivariate Statistical Analysis 5th Edition; (2002) Prentice-Hall, Inc.
Sainfort F., Editorial: The Use of Factor Analysis Techniques. Medical Decision Making. 2002; 22: 451-452.
SAS Institute Inc., SAS/STAT® User’s guide, Version 8, Cary, NC: SAS Institute Inc., 1999.1123-1192 pp.
Spearman, C; ‘General Intelligence’, objectively determined and measured. American Journal of Psychology, 1904; 15: 201-93.
StataCorp. 2003. Stata Statistical Software: Release 8.0. College Station, Tx: Stata Corporation.
Susan ES., Lasarev MR., McCauley K., Factor Analysis of Gulf War Illness: What Does It Add to our Understanding of Possible Health Effects of Deployment? Am. J. Epidemiology. 2002; 156: 578-585.