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研究生:徐亭媺
論文名稱:排序實驗不完全資料分析
論文名稱(外文):Missing data analysis of ranking experiments
指導教授:林建甫林建甫引用關係黃怡婷黃怡婷引用關係
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:60
中文關鍵詞:排序資料不完全資料多重填補Bradley-Terry modelproportional hazard modeldiscrete choice model
外文關鍵詞:rank dataincomplete datamultiple imputationBradley-Terry modelproportional hazard modeldiscrete choice model
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  • 被引用被引用:0
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評估多種類似項目的排序資料,在日常生活中相當常見。完全的排序資料來自於隨機完全區集設計 (randomized complete block design) ,其中集區即決策者 (受訪者、投票者),可為個人、家族、公司、法官、或任何決策單位,而每一位決策者 (受訪者、投票者) 被要求針對某些項目 (候選人) 作排序。但是,並非保證能取得所有排序資料,於是排序資料可能是不完全的、有遺失值的。而此不完全排序資料通常來自於隨機平衡 (balanced) 或非平衡 (unbalanced) 的不完全區集設計,故不完全排序資料包含遺失值,且在醫學和社會學的研究上是不可避免的。
這篇論文中,我們提出一種多重填補 (multiple imputation) 方法來分析不完全排序資料,此方法結合了離散機率模型及多重填補。遺失資料的填補是根據三種離散機率模型:Bradley-Terry model、proportional hazard model和discrete choice model,對於填補後的資料進行分析,也是根據三種離散機率模型。參數估計及假說檢定則依據多重填補的變異性而調整。藉由模擬,比較這三個離散機率模型在填補前 (不完全排序資料) 和填補後對資料分析的影響。
由模擬結果可發現,我們所提出的方法可取得好的參數估計,且可改善參數估計的平均平方誤差 (Mean Square Errors, MSEs),尤其在小樣本的情況下更加明顯。由最大概似比檢定中,每一個項目排名皆相同的虛無假設下,可獲得較小的型I誤差和較高的檢定力。但以上所有好的結果大部份只有在Bradley-Terry model和proportional hazard model中成立。
此外,我們將藉由實際的不完全排序資料來驗證本文的方法。此資料取自於某家咖啡製造公司,
採行非平衡區集設計,欲得知消費者對於各種不同即溶咖啡的喜好程度。由實證中,發現參數估計
在填補後比填補前有較小的平均平方誤差且較有效;再者,填補資料與不完全資料的排名差別並不
大。因此,在模擬或實證的結果中,皆證明出吾所提的方法對於不完全資料分析的確有助益,尤其
在參數估計和參數估計的平均平方誤差中表現較為明顯。
Ranking several items is very common in daily life and produces rank data. Complete rank data arise from a (randomized) complete block design. The block is decision-maker (respondents, voters). The decision-makers can be people, households, firms, judges, or any other decision making unit. Each decision-makers (respondents, voters) is asked to rank a set of items (candidates). However, a rank data set may be incomplete with missing responses. Incomplete rank data usually arise from (randomized) balanced, partial balanced or unbalanced incomplete block design. Incomplete rank data contain missing responses and missingness is a ubiquitous problem in the medical or social researches.
In this paper, we develop a multiple imputation method to analyze incomplete rank data with missing responses. The proposed method combines discrete probability models and multiple imputation. Imputing the missing values is based on 3 discrete probability models, Bradley-Terry model, proportional hazard model and discrete choice model. And analyzing the multiple imputed data sets is also based on these 3 discrete probability models. Point estimation and testing hypothesis are adjusted considering the variabilities from multiple imputations.
In simulation studies, we compared the results of these 3 discrete probability models in the analysis of incomplete rank data before (with missing data) and after multiple imputations (with imputed data). The results show the proposed method produces reasonably good parameter estimates, and improves mean square errors (MSEs) of parameter estimates, especially, for small sample size. The results also show that likelihood ratio test has lower type I error under null hypothesis of equal ranking and achieve good power. Most of these good results are only confined to Bradley-Terry model and proportional hazard model.
We provide an analysis of a real rank data with missing responses. The data arised from that a coffee company conducted an unbalanced block design to determine consumers'' preference of various flavors added to their coffee. We show that the imputed data has smaller MSEs of parameter estimates than those of the missing data. Furthermore, the rank ordering of the imputed data is almost the same with that of the missing data. Analysis for incomplete rank data which contains missing responses with multiple imputations should be an important factor in decreasing MSEs and in deciding the rank ordering.
1 Introduction
1.1 Rank Data
1.2 Background
1.3 Looking Ahead
2 Literature Review
2.1 Discrete Probability Models
2.1.1 Bradley-Terry Model
2.1.2 Proportional Hazard Model
2.1.3 Discrete Choice Model
2.2 Assumption and Limitations
2.3 Missing Data Analysis with Multiple Imputation
2.3.1 Assumptions of Missingness
2.3.2 Multiple Imputation
2.3.3 Estimation of Multiple Imputations
2.3.4 Inference of Multiple Imputations
3 Method
4 Simulation
5 Example: Coffee Flavors Preferences
6 Discussion
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