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題名 多維列聯表離群細格的偵測研究
Identification of Outlying Cells in Cross-Classified Tables
作者 陳佩妘
Chen, Pei-Yun
貢獻者 江振東
Chiang, Jeng-Tung
陳佩妘
Chen, Pei-Yun
關鍵詞 列聯表
適合度檢定
離群細格
近似獨立性
Contingency tables
Goodness-of-fit
Outliers
Quasi-Independence
日期 1996
上傳時間 28-Apr-2016 11:48:52 (UTC+8)
摘要 在處理列聯表時，適合度檢定的結果如果是顯著的話，則意味著配適的模式並不恰當，這其中一個可能的原因是資料中存在離群細格．因此我們希望能夠針對問題癥結所在，找出離群細格，使得我們的資料可以利用一個比較簡單且容易解釋的模式來做分析．在這篇論文中，我們主要依據施苑玉[1995]所提出的方法作些許的改變，使得改進後的方法可以適用於三維列聯表的所有情形．此外我們也將 Simonoff 在1988年所提出的方法，以及 BMDP 統計軟體的程序 4F ，與我們所提出的方法相比較．由模擬實驗的結果可發現我們的方法比前述兩種方法更具可行性．
When fitting a loglinear model to a contingency table, a significant goodness-of-fit can be resulted because of the existence of a few outlyingcells. Since a simpler model is easier to interpret and conveys more easilyunderstood information about a table than a complicated one, we would liketo identify those outliers so that a simpler model would fit a given data set. In this research, a modification of Shih`s [1995] procedure is provided, and the revised method is now applicable to any type of models related tothree-way tables. Some data sets are simulated to compare outliers detectedusing procedures proposed by Simonoff [1988], and BMDP program 4F with our proposed method. Based on the results through simulation, our revised procedure outperforms the other two procedures most
參考文獻 1. Agresti, A. (1990), Categohcal Data Analysis, New York: Wiley.
2. Barnett, V. and Lewis, T. (1984), Outliers in Statistical Data (2nd ed.), Chichester,
U.K. : John Wiley.
3. Bishop, YM.M. and Fienberg, S.E. (1969), "Incomplete Two-Dimensional Contingency Tables", Biometrics, 25, 118-128.
4. Bishop, YM.M., Fienberg, S.E., and Holland, P.W. (1975), Discrete Multivanate
Analysis, Cambridge, MA: MIT Press.
5. BMDP Statistical Software, Inc. (1992), BMDP Statistical Software Manual, Version 7.0, Los Angeles, CA: BMDP Statistical Software, Inc.
6. Bradu, D., and Hawkins, D.M. (1982), "Location of Multiple Outliers in Two-Way
Tables, Using Tetrad", Technomethcs, 24, 103-108.
7. Brown, M.B. (1974), "Identification of the Sources of Significance In Two-Way
Contingency Tables", Applied Stat istics, 23, 405-413.
8. Daniel, C. (1959), "Use of Half-Normal Plots in Interpreting Factorial Two Level
Experiments", Technometrics, 1, 311-341.
9. Fienberg, S.E. (1969), "Preliminary Graphical Analysis and Quasi-Independence for Two-Way Contingency Tables", Applied Statistics, 18, 153-168.
10. Fienberg, S.E. (1970), "Quasi-Independence and Maximum Likelihood Estimation in Incomplete Contingency Tables", Journal of the American Statistical Association, 65,1610-1616.
11. Fienberg, S.E. (1972), "The Analysis of Incomplete Multi-Way Contingency Tables",Biometrics, 28, 177-202.
12. Freeman, D.H. (1987), Applied Categorical Data Analysis. Marcel Dekker, New York.
13. Fuchs, C, and Kenett, R. (1980), "A Test for Detecting Outlying Cells in the
Multinomial Distribution and Two-Way Contingency Tables", Journal a/(he American Statistical Association, 75, 395-398.
14. Goodman, L.A (1968), "The Analysis of Cross-Classi fied Data: Independence, QuasiIndependence,and Interactions in Contingency Tables With or Without Missing
Entries", Journal of the American Statistical Association, 63, 1091-1131.
15. Habennan, D.M. (1973), "The Analysis of Residuals in Cross-Classified Tables",
Biometrics, 29, 205-220.
16. Habennan, D.M. (1978), Analysis of Qualitative Data, Vols. 1 and 2. New York:
Academic Press.
17. Kotze, T.J van W., and Hawkins, D.M. (1984), "The Identification of Outliers in TwoWay Contingency Tables Using 2 x 2 Subtables", Applied Statistics, 33, 215-223.
18. Mantel, N. (1970), "Incomplete Contingency Tables", Biometrics, 26, 291-304.
19. Nelder, J.A. (1971), "A Statistician`s Point of View", in Mathematical Models in
Ecology. The j),11 Symposium of (he British Ecological Society, Grange-over-Sands,
Lancashire, 367-373, Oxford: Blackwell Scientific Publications.
20. Shih, Y. (1995), "Detecting Outlying Cells in Cross-Classified Tables", Unpublished Master Thesis, Graduate Institute of Statistics, National Chengchi University, Taipei,Taiwan.
21. Simonoff, 1.S. (1988), "Detecting Outlying Cells in Two-Way Contingency Tables Via Backwards-Stepping", Teci1nometrics, 30, 339-345.
22. Watson, G.S. (1956), "Missing and `Mixed-Up` Frequencies in Contingency Tables",Biometrics, 12,47-50.
描述 碩士
國立政治大學
統計學系
83354014
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002002798
資料類型 thesis
dc.contributor.advisor 江振東zh_TW
dc.contributor.advisor Chiang, Jeng-Tungen_US
dc.contributor.author (Authors) 陳佩妘zh_TW
dc.contributor.author (Authors) Chen, Pei-Yunen_US
dc.creator (作者) 陳佩妘zh_TW
dc.creator (作者) Chen, Pei-Yunen_US
dc.date (日期) 1996en_US
dc.date.accessioned 28-Apr-2016 11:48:52 (UTC+8)-
dc.date.available 28-Apr-2016 11:48:52 (UTC+8)-
dc.date.issued (上傳時間) 28-Apr-2016 11:48:52 (UTC+8)-
dc.identifier (Other Identifiers) B2002002798en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/87311-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 83354014zh_TW
dc.description.abstract (摘要) 在處理列聯表時，適合度檢定的結果如果是顯著的話，則意味著配適的模式並不恰當，這其中一個可能的原因是資料中存在離群細格．因此我們希望能夠針對問題癥結所在，找出離群細格，使得我們的資料可以利用一個比較簡單且容易解釋的模式來做分析．在這篇論文中，我們主要依據施苑玉[1995]所提出的方法作些許的改變，使得改進後的方法可以適用於三維列聯表的所有情形．此外我們也將 Simonoff 在1988年所提出的方法，以及 BMDP 統計軟體的程序 4F ，與我們所提出的方法相比較．由模擬實驗的結果可發現我們的方法比前述兩種方法更具可行性．zh_TW
dc.description.abstract (摘要) When fitting a loglinear model to a contingency table, a significant goodness-of-fit can be resulted because of the existence of a few outlyingcells. Since a simpler model is easier to interpret and conveys more easilyunderstood information about a table than a complicated one, we would liketo identify those outliers so that a simpler model would fit a given data set. In this research, a modification of Shih`s [1995] procedure is provided, and the revised method is now applicable to any type of models related tothree-way tables. Some data sets are simulated to compare outliers detectedusing procedures proposed by Simonoff [1988], and BMDP program 4F with our proposed method. Based on the results through simulation, our revised procedure outperforms the other two procedures mosten_US
dc.description.tableofcontents Chapter
1. Introduction..........1
1.1 Motivation..........1
1.2 Outline..........3
2. Literature Review..........4
2.1 Basic Definitions for Two-Way Contingency Tables..........4
2.2 Basic Definitions for Three-Way Contingency Tables..........7
2.3 Brown’s Method..........10
2.4 Simonoff’s Method..........13
2.5 Shih’s Method..........15
2.6 Other Methods..........16
3.Detecting Outliers in Some Three-Way Contingency Tables..........18
3.1 Complete Independence Models..........18
3.2 No Three-Factor Interaction Model..........27
4.Extensions to Three-Way Contingency Tables Using Simonoff’s Backwards-Stepping Procedure..........35
4.1 Complete Independence Models..........35
4.2 Complete Independence Models..........35
4.2 One Partial Association Models..........36
4.3 Two Partial Association Models..........37
4.4 No Three Factor Interaction Models..........38
5.Examples of Outliers Detection in Two-Way and Three-Way Contingency Tables..........40
5.1 Two-Way Independence Models..........41
5.2 Three-Way Complete Independence Models..........45
5.3 Three-Way One Partial Association Models..........49
5.4 Three-Way Two partial Association Models..........54
5.5 Three-Way No Three Factor Interaction Models..........57
5.6 Summary of the results..........64
6. Concluding Remarks..........65
References..........66
Appendices
A..........69
B..........74
C..........76
D..........77
E..........81
F..........89
G..........92
H..........95
I..........99		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002002798en_US
dc.subject (關鍵詞) 列聯表zh_TW
dc.subject (關鍵詞) 適合度檢定zh_TW
dc.subject (關鍵詞) 離群細格zh_TW
dc.subject (關鍵詞) 近似獨立性zh_TW
dc.subject (關鍵詞) Contingency tablesen_US
dc.subject (關鍵詞) Goodness-of-fiten_US
dc.subject (關鍵詞) Outliersen_US
dc.subject (關鍵詞) Quasi-Independenceen_US
dc.title (題名) 多維列聯表離群細格的偵測研究zh_TW
dc.title (題名) Identification of Outlying Cells in Cross-Classified Tablesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 1. Agresti, A. (1990), Categohcal Data Analysis, New York: Wiley.
2. Barnett, V. and Lewis, T. (1984), Outliers in Statistical Data (2nd ed.), Chichester,
U.K. : John Wiley.
3. Bishop, YM.M. and Fienberg, S.E. (1969), "Incomplete Two-Dimensional Contingency Tables", Biometrics, 25, 118-128.
4. Bishop, YM.M., Fienberg, S.E., and Holland, P.W. (1975), Discrete Multivanate
Analysis, Cambridge, MA: MIT Press.
5. BMDP Statistical Software, Inc. (1992), BMDP Statistical Software Manual, Version 7.0, Los Angeles, CA: BMDP Statistical Software, Inc.
6. Bradu, D., and Hawkins, D.M. (1982), "Location of Multiple Outliers in Two-Way
Tables, Using Tetrad", Technomethcs, 24, 103-108.
7. Brown, M.B. (1974), "Identification of the Sources of Significance In Two-Way
Contingency Tables", Applied Stat istics, 23, 405-413.
8. Daniel, C. (1959), "Use of Half-Normal Plots in Interpreting Factorial Two Level
Experiments", Technometrics, 1, 311-341.
9. Fienberg, S.E. (1969), "Preliminary Graphical Analysis and Quasi-Independence for Two-Way Contingency Tables", Applied Statistics, 18, 153-168.
10. Fienberg, S.E. (1970), "Quasi-Independence and Maximum Likelihood Estimation in Incomplete Contingency Tables", Journal of the American Statistical Association, 65,1610-1616.
11. Fienberg, S.E. (1972), "The Analysis of Incomplete Multi-Way Contingency Tables",Biometrics, 28, 177-202.
12. Freeman, D.H. (1987), Applied Categorical Data Analysis. Marcel Dekker, New York.
13. Fuchs, C, and Kenett, R. (1980), "A Test for Detecting Outlying Cells in the
Multinomial Distribution and Two-Way Contingency Tables", Journal a/(he American Statistical Association, 75, 395-398.
14. Goodman, L.A (1968), "The Analysis of Cross-Classi fied Data: Independence, QuasiIndependence,and Interactions in Contingency Tables With or Without Missing
Entries", Journal of the American Statistical Association, 63, 1091-1131.
15. Habennan, D.M. (1973), "The Analysis of Residuals in Cross-Classified Tables",
Biometrics, 29, 205-220.
16. Habennan, D.M. (1978), Analysis of Qualitative Data, Vols. 1 and 2. New York:
Academic Press.
17. Kotze, T.J van W., and Hawkins, D.M. (1984), "The Identification of Outliers in TwoWay Contingency Tables Using 2 x 2 Subtables", Applied Statistics, 33, 215-223.
18. Mantel, N. (1970), "Incomplete Contingency Tables", Biometrics, 26, 291-304.
19. Nelder, J.A. (1971), "A Statistician`s Point of View", in Mathematical Models in
Ecology. The j),11 Symposium of (he British Ecological Society, Grange-over-Sands,
Lancashire, 367-373, Oxford: Blackwell Scientific Publications.
20. Shih, Y. (1995), "Detecting Outlying Cells in Cross-Classified Tables", Unpublished Master Thesis, Graduate Institute of Statistics, National Chengchi University, Taipei,Taiwan.
21. Simonoff, 1.S. (1988), "Detecting Outlying Cells in Two-Way Contingency Tables Via Backwards-Stepping", Teci1nometrics, 30, 339-345.
22. Watson, G.S. (1956), "Missing and `Mixed-Up` Frequencies in Contingency Tables",Biometrics, 12,47-50.		zh_TW