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| 研究生： |
洪淑玲 HONG, SHU-LING |
|---|---|
| 論文名稱： |
因子分析中決定適當因子數 : EM演算法與AIC、CAIC之應用 |
| 指導教授： | 張健邦 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 1992 |
| 畢業學年度： | 80 |
| 語文別： | 中文 |
| 論文頁數： | 53 |
| 相關次數： | 點閱：279 下載：0 |
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1、 緒論.....................1
1. 1 研究動機與目的..................... 1
1. 2 研究方法摘要..................... 2
1. 3 章節架構..................... 3
2、 文獻回顧..................... 4
2.1 因子分析..................... 4
2.2 EM演算法..................... 7
2.3 AIC與CAIC ..................... 10
3、 EM 演算法與AIC、CAIC 於因子分析之應用..................... 14
3.1 因子分析方法..................... 14
3.2 EM演算法之基本理論..................... 22
3.3 EM演算法於因子分析之應用..................... 24
3.4 AIC 與CAIC 之基本理論.....................29
3.5 利用AIC 與CAIC 決定適當因子數..................... 37
4、 實例說明..................... 39
4.1 分析流程..................... 39
4.2 資料來源與描述..................... 41
4.3 計算結果與討論.....................43
5、 結論..................... 52
5.1 研究發現..................... 52
5.2 研究限制..................... 52
5.3 後續研究方向..................... 53
參考文獻
[1] Akaike,H.(1987). "Factor Analysis and AIC". Psychometrika, 52,317-332.
[2] Anderson,T.W.(1984). "An Introduction to Multivariate Statistical Analysis" .New York: Wiley.
[3] Bhansali,R.J. & Downham,D.Y.(1977). "Some properites of the order of an Autoregressive model selected by a Generalization of Akaike's FPE
criterion". Biometrika,64,54 7-551.
[4] Bozdogan,H.(1987). "Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analysical Extensions". Psychometrika,52,345-370.
[5] Bozdogan,H. & Ramirez ,D.E.(1988). "FACAIC : Model Selection Algorithm for the Orthogonal Factor Model Using AIC and CAIC". Psychometrika,53, 407-415.
[6] Davis,M.H. & Vinter,R.B.(1985). Stochastic modelling and control. New York : Chapman and Hall.
[7] Dempster,A.P.,Laird,N.M. & Rubin ,D.B.(1977). "Maximum likelihood from Incomplete data via the EM algorithm". J. R. Statist. Soc. B,39, 1-38.
[8] Dillon,W.R. & Goldstein,M.(1984). Multivariate Analysis,華泰書局，台北.
[9] Gorsuch,R.L.(1983). Factor Analysis,Hillsdale,New Jersey.
[10] Green, J .(1990). "On Use of the EM Algorithm for Penalized Likelihood Estimation". J. R. Statist. Soc . B, 52, 443-452.
[11] Hanna, E.J. & Quinn, B.G.(1979). "The Determination of the Order of an Autoregression". J. R. Statist. Soc. B, 41, 190-210.
[12] Harman,H.(1976). Modern Factor Analysis. Chicago: University of Chicago Press.
[13] Johnson,R.A. & Wichern,D.W.(19SS). Applied Muitivariate Statistical Analysis. Prentice-Hall Inc., New Jersey.
[14] Kendall, M.G. & Stuart, M.A.(1967). The Advanced Theroy of Statistics, New York: Hafner Publishing.
[15] Maxwell, A.E.(1961). "Recent trends in Factor Analysis". J. R. Ststist. Soc. A, 124,49-59.
[16] Meilijson (19S9). "A Fast Improvement to the Em Algorithm on its Own Terms" . J. R. Statist. Soc. B,52,127-138.
[17] Morrison,D.F.(lg90). Multivariate Statistical Methods. New York: McGraw-Hill.
[18] Mulaik,S.A.(1972). The Foundations of Factor Analysis. New Jersey.
[19] Nychka,D.W.(1990). "Some Properties of Adding a Smoothing Step to the EM Algorithm". Statistics & Probability Letters,9 .187-193.
[20] Rubin,D.B. & Thayer,D.T.(1982). "EM Algorithms for ML Factor Analysis" . Psychometrika,34,69-76.
[21] Ruud,P.A.(1991). "Extensions of Estimation Methods using the EM algorithm" . Journal of Econometrics,49,305-341.
[22] SAS/STAT User's Guide,1988.
[23] SAS/IML User's Guide,1988.
[24] SAS Guide to Macro Processing,1990.
[25] Sakamoto,K.,Ishiguro,M. & Kitagawa,G.(1989). "Review of Akaike Information Criterion Ststistics" . Psychometrika,54,539-541.
[26] Silverman,B.W. et.al.(1990). "A Smoothed EM Approach to Indirected Estimation Problems ,with Particular Reference to Stereology and Emission Tomogroaphy". J. R. Statist. Soc. B,52,271-324.
[27] Schwarz,G.(1978). "Estimating the Dimension of a Model". A nnals of Statistics,6,461-464.
[28] Stone,M.(1977). "On Asymptotic Equivalenc of Choice of Model by Cross-Validation and Akaike's Criterion". J. R. Statist. Soc. B,39,44-47.
[29] Woodroofe,M.(1982). "On Model Selection and the Arc Sine Laws" Annals of Statistics,10, 1182-1194.
[30]林清山，多變項分析統計法，東華書局，民國69年初版.
[31]黃俊英著，多變量分析，華泰書局，民國75年二版.
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