在單一選區兩票制下的準對稱模型之應用

Quasi-Symmetry Model in The Single-Member Districts and Two-Votes System

吳宗憲(TSUNG-HSIEN WU)

指導教授 ： 吳建華

中原大學/理學院/應用數學系/碩士(2008年)

https://doi.org/10.6840/cycu200800241

摘要

若在一樣本中的每一個觀測值和另一樣本中的每一個觀測值具有相關性，則稱為相依樣本。假如兩相依樣本形成配對關係，那麼我們則稱這種成對的類別資料為配對資料(Matched Pairs Data)(Agresti,1996)。例如:在單一選區兩票制中，每位選民的立委選票和政黨選票就是具有相關性的配對樣本。當這配對選票有兩個選項可利用 2×2列聯表來表達這類資料型態，然後以統計方法McNemar檢定(McNemar,1947)和邏輯迴歸模型(Logistic Regression Model)來分析選民立委票和政黨票是否會投給相同的政黨和政黨所提名的立委候選人。假如配對選票有兩個以上的選項，亦為多組配對樣本，既可推廣至 n×n列聯表來達這類資料型態，並且用對數線性模型(Loglinear Model)之延伸模型，如對稱性模型(Symmetry Model)和準對稱性模型(Quasi-Symmetry Model)，來進行統計分析。當訪問民眾有關立委選舉的選票會投給誰，這極為敏感的話題，少數民眾會拒絕回答或隨意回答。為了避免此現象造成統計上的誤差，我們利用Warner(1965)所提出的隨機反應模型(Random Response Model)來分析具敏感性的政治問卷。例如:每位立委候選人和其自身的政黨組成配對樣本，每組配對樣本分成 I 、 II 兩類不同類型的問卷，然而民眾隨機抽取到某一組的第 I類或第 II 類問卷並回答該類裡的題目。我們不知道民眾選中哪一類型的問卷，民眾依照問卷內的每項題目只需回答"是"或"否"兩種答案。因此，藉由這間接性問卷方式我們可以得到出預測參數的估計值。

關鍵字

準對稱模型 ； 隨機反應模型 ； McNemar檢定 ； 配對資料

並列摘要

If each observation in one sample and an observation from another sample have correlation,
then it called the dependent sample. Suppose that two dependent samples come into paired relationship,so the pairs of categorical data are called matched pairs data (Agresti, 1996).For example, both committee member vote and party vote for each electorate which under the single-member districts and two-vote system is an interrelated matched pairs sample.The 2×2 contingency table can express this type of paired sample when vote have two selections,and then use McNemar Test (McNemar,1947) and Logistic Regression Model statistical methods to analysis the votes that whether each electorate throw the same party and committee candidate for party nominated or not. If there are more than two selections for paired samples, it called Multiple Matched pairs sample; we can use n×n contingency table to express this type of paired sample, and use the extensible Loglinear Model,such as Symmetry Model and Quasi-Symmetry Model, to make statistical analysis. It is an extremely sensitive topical subject for the public who be interviewed that voting to whom on this committee election. Sometimes, a few interviewers will reject to answer this question or reply at will. In order to avoid the inaccuracy in statistics by this phenomenon,we make use of Random Response Model which by Stanley L. Warner (1965) to analysis the sensitively political questionnaire. For example, each candidate for committee need to form paired sample with own political party.Everyone paired sample separate into two kinds of questionnaire which is l and II category. Thus, the public will randomly draw out the questionnaire which no matter category l or II and need to answer it. It is impossible for us to know which type of questionnaire the public choose. The public only need to answer "yes" or "no" in accordance with each topic in the questionnaire. For this reason, we can derive the estimated of predictable parameter from the indirect questionnaire way.

並列關鍵字

Matched pairs data ； Quasi-symmetry model ； Random response model ； McNemar test

參考文獻

[4] Agresti, Alan, 1996, "An Introduction to Categorical Data Analysis", New York:Wiley.

[5] Agresti, Alan, 1990, "Categorical Data Analysis", New York:Wiley.

[7] McNemar, Q. 1947. Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika 12:153-157

[8] Mosteller, F. 1952. Some statistical problems in measuring the subjective response to drugs. Biometrics 8:220-226.

[9] Cox, D.R. 1958b. Two further applications of a model for binary regression. Biometrika 45:562-565