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| 研究生： |
陳佩妘 Chen, Pei-Yun |
|---|---|
| 論文名稱： |
多維列聯表離群細格的偵測研究 Identification of Outlying Cells in Cross-Classified Tables |
| 指導教授： |
江振東
Chiang, Jeng-Tung |
| 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： | 1996 |
| 畢業學年度： | 84 |
| 語文別： | 英文 |
| 論文頁數： | 67 |
| 中文關鍵詞： | 列聯表 、適合度檢定 、離群細格 、近似獨立性 |
| 外文關鍵詞： | Contingency tables, Goodness-of-fit, Outliers, Quasi-Independence |
| 相關次數： | 點閱：112 下載：0 |
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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
of the time.
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
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22. Watson, G.S. (1956), "Missing and 'Mixed-Up' Frequencies in Contingency Tables",Biometrics, 12,47-50.
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