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題名 Mokken尺度量表下潛在特質排序之正確率探討
A study on the accuracy rate for the ordering of the latent trait in Mokken scale analysis
作者 黃雅雯
Huang, Ya Wen
貢獻者 江振東
黃雅雯
Huang, Ya Wen
關鍵詞 Mokken尺度量表
潛在特質
正確率
日期 2012
上傳時間 11-Jul-2013 16:36:43 (UTC+8)
摘要 Mokken (1971) 提出兩個無母數反應試題理論模型，包含單調同質性模型(MHM)和雙重單調同質性模型(DMM)，Grayson (1988) 和Huynh (1994)說明並證明出在單調同質性模型架構之下，受試者二元反應試題的回答總分與受試者的潛在特質具有MLR(monotone likelihood ratio)的性質，因此也具有SOM(stochastic ordering of the manifest variable)及SOL(stochastic ordering of the latent trait)這兩個隨機排序(stochastic ordering)的特性。另外，Mokken (1971) 也提到在Mokken量表下，受試者的試題回答總分與受試者的潛在特質有高度相關。然而這些好的特性都僅只於理論上的說法，實務的應用上並沒有實際的數字可作為使用者的參考依據。本研究將利用模擬實驗的方式，就上述議題作探討。
模擬結果顯示，未加權的時候，使用答題總分來排序受試者的潛在特質或藉由受試者的潛在特質來預估其答題總分之正確率都會隨著鑑別參數的增加而增加，前者正確率約有七成以上，後者正確率則大約有八成以上；受試者的潛在特質與其答題總分的相關係數也隨著鑑別參數增加而增加，大約介於0.50與0.80之間。
Mokken (1971) proposed two Nonparametric Item Response Theory Models, the Monotone Homogeneity Model (MHM) and the Double Monotonicity Model (DMM). Under MHM, Grayson (1988) and Huynh (1994) showed that the unweighted total score for dichotomous items has monotone likelihood ratio (MLR) in the latent trait θ, which in turn implies two stochastic ordering (SO) properties, namely SOM (stochastic ordering of the manifest variable) and SOL (stochastic ordering of the latent trait). In addition, Mokken (1971) also mentioned that the total score were highly correlated with the latent trait for subjects. However, these properties are only theoretical arguments, and there are no actual figures that can serve as a guideline for practitioners regarding how good the properties are. We hence try to answer some of the questions through simulation experiments in this study.
Simulation results show that the accuracy rate of using unweighted total score to rank the latent trait of subjects and the accuracy rate of using the latent trait to predict the total score for subjects will increase with the discrimination parameters. The former is about more than 70%, while the latter is about more than 80%. The correlation coefficients between the total score and the latent trait of subjects will also increase with the discrimination parameters, ranging between 0.50 and 0.80.
參考文獻 章英華、傅仰止(2006)。台灣社會變遷基本調查五期一次- 綜合問卷組(C00153_1)【原始數據】。取自中央研究院人文社會科學研究中心調查研究專題中心學術調查研究資料庫http://srda.sinica.edu.tw。doi:10.6141/TW-SRDA-C00513_1-1
Grayson, D. A. (1988). Two group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383-392.
Guttman, L. (1950). The utility of scalogram analysis. In S. A. Stouffer, L. Guttman, E. A. Suchman, P. F. Lazarsfeld, S. A. Star, & J. A. Clausen (Eds.), Measurement and prediction. Studies in Social Psychology in World War II (Vol. 4, pp. 122-171). New York, NY: Wiley.
Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables. Psychometrika, 59, 77-79.
Lehmann, E. L. (1986). Testing statistical hypotheses. 2nd Ed., New York: Wiley.
Loevinger, J. (1948). The technique of homogeneous tests compared with some aspects of "scale analysis" and factor analysis. Psychological Bulletin, 45, 507-530.
Mokken, R. J. (1971). A theory and procedure of scale analysis. With applications in political research. Berlin, Germany: De Gruyter (Mouton).
描述 碩士
國立政治大學
統計研究所
100354015
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354015
資料類型 thesis
dc.contributor.advisor 江振東zh_TW
dc.contributor.author (Authors) 黃雅雯zh_TW
dc.contributor.author (Authors) Huang, Ya Wenen_US
dc.creator (作者) 黃雅雯zh_TW
dc.creator (作者) Huang, Ya Wenen_US
dc.date (日期) 2012en_US
dc.date.accessioned 11-Jul-2013 16:36:43 (UTC+8)-
dc.date.available 11-Jul-2013 16:36:43 (UTC+8)-
dc.date.issued (上傳時間) 11-Jul-2013 16:36:43 (UTC+8)-
dc.identifier (Other Identifiers) G0100354015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58784-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 100354015zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) Mokken (1971) 提出兩個無母數反應試題理論模型，包含單調同質性模型(MHM)和雙重單調同質性模型(DMM)，Grayson (1988) 和Huynh (1994)說明並證明出在單調同質性模型架構之下，受試者二元反應試題的回答總分與受試者的潛在特質具有MLR(monotone likelihood ratio)的性質，因此也具有SOM(stochastic ordering of the manifest variable)及SOL(stochastic ordering of the latent trait)這兩個隨機排序(stochastic ordering)的特性。另外，Mokken (1971) 也提到在Mokken量表下，受試者的試題回答總分與受試者的潛在特質有高度相關。然而這些好的特性都僅只於理論上的說法，實務的應用上並沒有實際的數字可作為使用者的參考依據。本研究將利用模擬實驗的方式，就上述議題作探討。
模擬結果顯示，未加權的時候，使用答題總分來排序受試者的潛在特質或藉由受試者的潛在特質來預估其答題總分之正確率都會隨著鑑別參數的增加而增加，前者正確率約有七成以上，後者正確率則大約有八成以上；受試者的潛在特質與其答題總分的相關係數也隨著鑑別參數增加而增加，大約介於0.50與0.80之間。		zh_TW
dc.description.abstract (摘要) Mokken (1971) proposed two Nonparametric Item Response Theory Models, the Monotone Homogeneity Model (MHM) and the Double Monotonicity Model (DMM). Under MHM, Grayson (1988) and Huynh (1994) showed that the unweighted total score for dichotomous items has monotone likelihood ratio (MLR) in the latent trait θ, which in turn implies two stochastic ordering (SO) properties, namely SOM (stochastic ordering of the manifest variable) and SOL (stochastic ordering of the latent trait). In addition, Mokken (1971) also mentioned that the total score were highly correlated with the latent trait for subjects. However, these properties are only theoretical arguments, and there are no actual figures that can serve as a guideline for practitioners regarding how good the properties are. We hence try to answer some of the questions through simulation experiments in this study.
Simulation results show that the accuracy rate of using unweighted total score to rank the latent trait of subjects and the accuracy rate of using the latent trait to predict the total score for subjects will increase with the discrimination parameters. The former is about more than 70%, while the latter is about more than 80%. The correlation coefficients between the total score and the latent trait of subjects will also increase with the discrimination parameters, ranging between 0.50 and 0.80.		en_US
dc.description.tableofcontents 摘要 7
Abstract 8
第一章 緒論 9
1.1 研究背景 9
1.2 研究動機與目的 10
第二章 文獻回顧 11
2.1 Guttman量表 11
2.2 Mokken量表 12
2.3 試題反應函數(Item Response Function, IRF) 13
2.4 試題反應理論模型(Item Response Theory Models) 13
2.4.1 有母數試題反應理論模型 13
2.4.2 無母數試題反應理論模型 15
第三章 研究方法與設計 18
3.1 研究動機 18
3.2 研究方法與設計 19
3.2.1 符合SOM性質之正確率定義及模擬設計 19
3.2.2 符合SOL性質之正確率定義及模擬設計 21
第四章 研究結果 23
4.1 符合SOM性質之正確率探討 23
4.1.1 未加權情況下符合SOM性質之正確率探討 23
4.1.2 加權情況下符合SOM性質之正確率探討 28
4.1.3 未加權與加權情況下符合SOM性質之正確率比較 34
4.2 符合SOL性質之正確率探討 39
4.2.1 未加權情況下符合SOL性質之正確率探討 39
4.2.2 加權情況下符合SOL性質之正確率探討 44
4.2.3 未加權與加權情況下符合SOL性質之正確率比較 49
4.3 附加探討 55
4.3.1 Pearson相關係數與Spearman等級相關係數之比較 55
4.3.2 試題給予不同權重情況下之正確率探討 57
4.3.3 受試者樣本數減少情況下之正確率探討 60
第五章 實證分析 70
第六章 結論與建議 73
6.1 研究結論 73
6.2 研究建議與方向 74
參考文獻 76
附錄 77
一、符合SOM性質之正確率模擬程式 77
二、符合SOL性質之正確率模擬程式 80		zh_TW
dc.format.extent 2771609 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100354015en_US
dc.subject (關鍵詞) Mokken尺度量表zh_TW
dc.subject (關鍵詞) 潛在特質zh_TW
dc.subject (關鍵詞) 正確率zh_TW
dc.title (題名) Mokken尺度量表下潛在特質排序之正確率探討zh_TW
dc.title (題名) A study on the accuracy rate for the ordering of the latent trait in Mokken scale analysisen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 章英華、傅仰止(2006)。台灣社會變遷基本調查五期一次- 綜合問卷組(C00153_1)【原始數據】。取自中央研究院人文社會科學研究中心調查研究專題中心學術調查研究資料庫http://srda.sinica.edu.tw。doi:10.6141/TW-SRDA-C00513_1-1
Grayson, D. A. (1988). Two group classification in latent trait theory: Scores with monotone likelihood ratio. Psychometrika, 53, 383-392.
Guttman, L. (1950). The utility of scalogram analysis. In S. A. Stouffer, L. Guttman, E. A. Suchman, P. F. Lazarsfeld, S. A. Star, & J. A. Clausen (Eds.), Measurement and prediction. Studies in Social Psychology in World War II (Vol. 4, pp. 122-171). New York, NY: Wiley.
Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables. Psychometrika, 59, 77-79.
Lehmann, E. L. (1986). Testing statistical hypotheses. 2nd Ed., New York: Wiley.
Loevinger, J. (1948). The technique of homogeneous tests compared with some aspects of "scale analysis" and factor analysis. Psychological Bulletin, 45, 507-530.
Mokken, R. J. (1971). A theory and procedure of scale analysis. With applications in political research. Berlin, Germany: De Gruyter (Mouton).		zh_TW