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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/58784
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/58784

    Title: 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
    Authors: 黃雅雯
    Huang, Ya Wen
    Contributors: 江振東
    Huang, Ya Wen
    Keywords: Mokken尺度量表
    Date: 2012
    Issue Date: 2013-07-11 16:36:43 (UTC+8)
    Abstract: 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。
    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.
    Reference: 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).
    Description: 碩士
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0100354015
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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