不完全二維列聯表之準獨立估計

A Quasi-Independent Estimate of Incomplete Two Way Contingency Table

劉文宏(Wen-Hung Liu)

指導教授 ： 李孟峰

國立臺北大學/商學院/統計學系/碩士(2011年)

摘要

在二維列聯表的調查之中，格機率很小的細格不容易有樣本出現，因此實務上會產生所謂的抽樣零格。本次研究中，列聯表主對角線上的細格均為結構零格，而二維列聯表中若有抽樣零格與結構零格產生，稱之為(Incomplete Two-Way Contingency Table)。
抽樣零格的估計，若採用最大概似估計(Maximum Likelihood Estimation)，其估計值必然為零。過去的學者提供了許多不同的方法來解決這樣的問題，但是都各有其優缺點與限制性。有許多的研究者，採用插補的方法來估計抽樣零格。進行插補時，通常會假設母體滿足隨機缺失(MAR)等條件，若不滿足此條件，就無法利用相關的統計方法進行分析。本篇研究將資料中次數較高的資料先予以移除，使移除後的資料滿足準獨立(Quasi-Indenpedent)的假設。利用(Iterative Proportional Fitting Algorithm)來估計抽樣零格，便能有效縮小估計值與觀察值之間的離差，使資料能更具有完整性與正確性。

關鍵字

抽樣零格 ； 不完全二維列聯表 ； 遞迴比例配適法

並列摘要

In the two-way contingency table investigation, the sparse cells do not appear likely to have samples, so the practice will produce the sampling zero cells. In this study, contingency table on the main diagonal of cells are structural zeros, and two-way contingency table in the format and structure of zero if the zero sampling grid generation, called the incomplete two-way contingency table.
Sampling zero estimates, the use of maximum likelihood estimation (MLE), the estimated value must be zero. The scholars of the past in many different ways to solve this problem, but all have their advantages and disadvantages and restrictive. Many researchers, using the interpolation method to estimate sampling zero cells. Interpolation, it is usually assumed to missing at random (MAR) and other conditions, if this condition is met, you can not make use of relevant statistical methods for analysis. The data in this study a higher number of data to be removed first, after the removal of information to satisfy the quasi-independent assumptions. Then use of rIterative Proportional Fitting Algorithm to estimate the sampling zero cells, can effectively reduce the estimated value and the deviation between the observed values, so that data can be more completeness and accuracy.

並列關鍵字

Sampling Zero ； Incomplete Two-Way Contingency Table ； Iterative Proportional Fitting Algorithm

參考文獻

Chen, T., and S. E. Fienberg (1974). Two-dimensional contingency tables with both completely and partially cross-classified data. Biometrics, 30, 629-642.

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Choi, S.C., and D.M. Stablein (1988). Comparing incomplete paired binomial data under non-random mechanisms. Statistics in Medicine, 7, 929-939.

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Gelfand, A. E. and Bradley, P. C. (1993), “Maximum Likelihood Estimation for Constrained or Missing Data Method”, The Canadian Journal of Statistics 21(3), 303-311