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| Title: | 摩根量表分析：多元計分試題下受試者潛在特質排序之相關探討
Mokken scale analysis: A study of ordering respondents on the latent trait for polytomous items |
| Authors: | 江怡萱
Chiang, Yi Hsuan |
| Contributors: | 江振東
江怡萱
Chiang, Yi Hsuan |
| Keywords: | 試題反應理論
摩根量表
單調同質性模型
單調概似比性質
部分計分模型
item response theory
Mokken scale
monotone homogeneity model
monotone likelihood ratio
partial credit model |
| Date: | 2013 |
| Issue Date: | 2014-07-14 11:29:27 (UTC+8) |
| Abstract: | 架構於摩根量表(Mokken scale)的單調同質性模型(The Monotone Homogeneity Model, MHM)為試題反應理論(Item Response Theory, IRT)中假設條件較寬鬆的模型。Grayson (1988) 與Huynh (1994) 證明在單調同質性模型成立下，受試者對二元計分試題的回答總分與潛在特質間具有單調概似比(Monotone Likelihood Ratio, MLR)性質，並可推得總分對於潛在特質具有隨機排序(Stochastic Ordering of the Latent Trait by the Total Test Score, SOL)性質。然而在多元計分試題，Hemker等人(1996、1997)指出僅屬於有母數試題反應理論的部分計分模型(Partial Credit Model, PCM)與其特例評定量表模型(Rating Scale Model, RSM)具MLR與SOL性質。由於有母數試題反應理論模型均為單調同質性模型之特例，因此可透過有母數試題反應理論模型，生成符合摩根量表單調同質性模型的試題反應。假設受試者對於多元計分試題的反應可藉由部分計分模型加以描述，則無論維持原始的多元計分資料形式，獲得每位受試者的多元計分總分，抑或是將每題多元計分試題化為二元計分的方式，得到受試者的二元計分總分，這兩種總分對於潛在特質都應具有隨機排序性質，而可用來衡量受試者潛在特質的大小順序。經模擬結果發現，使用多元計分總分排序受試者潛在特質的整體正確率，與使用二元計分總分排序受試者潛在特質的整體正確率，都有七成五以上，然而二元計分總分排序受試者潛在特質的整體正確率變動較大，較不穩定，而且與如何從多元計分轉化為二元計分的方式有關。再者，由於使用多元計分總分與二元計分總分分別能排序的受試者不完全一致，使用整體正確率作為比較多元計分總分與二元計分總分何者在排序受試者潛在特質上正確程度較高並不完全合適。因此我們也定義條件正確率作為另一種評比的指標，其主要目的是想要比較兩種計分總分均可排序的受試者中，分別排序正確的比例。模擬結果也顯示，整體而言，多元計分總分在排序受試者潛在特質上較二元計分總分準確。
The monotone homogeneity model (MHM) of Mokken scale is the most general item response theory (IRT) model and all parametric IRT models are its special cases. For dichotomous items, the total test score has monotone likelihood ratio (MLR) in the latent trait, and which in turn implies stochastic ordering of the latent trait by the total test score (SOL) under the MHM. However, for polytomous items, MLR only holds for the partial credit model (PCM) and its special case, the rating scale model (RSM).
When analyzing polytomous items, some researchers use the total test score calculated by the polytomous item scores to order respondents on the latent trait. The others combine some of the polytomous item scores in each item, treat these items as new dichotomous items, and calculate the total test score by the new dichotomous items to order the latent traits of the respondents.
Results of the simulation study show that, when item responses satisfy the partial credit model, both the total test scores calculated by the polytomous item scores and by the new dichotomous items have more than 75% accuracy rate of ordering respondents on the latent trait. Nevertheless, the accuracy rates of ordering respondents on the latent trait by the dichotomous total test score are more variable. In order to compare which of the total test score is better for ordering the latent traits of the respondents on the same basis, we define another accuracy rate, conditional accuracy rate. It shows that the conditional accuracy rate of the polytomous total test score tends to be higher than that of the dichotomous total test score as well. |
| Reference: | 1. Han, K. T. (2007). WinGen: Windows software that generates IRT parameters and item responses. Applied Psychological Measurement, 31(5), 457-459.
2. Hemker, B. T., Sijtsma, K., Molenaar, I. W., & Junker, B. W. (1996). Polytomous IRT models and monotone likelihood ratio of the total score. Psychometrika, 61(4), 679–693.
3. Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59(1), 77-79.
4. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.
5. Sijtsma, K., & Molenaar, I. W. (Eds.). (2002). Introduction to nonparametric item response theory (Vol. 5). Sage.
6. Sijtsma, K., & Verweij, A. C. (1992). Mokken scale analysis: Theoretical considerations and an application to transitivity tasks. Applied Measurement in Education, 5(4), 355-373.
7. Stochl, J., Jones, P. B., & Croudace, T. J. (2012). Mokken scale analysis of mental health and well-being questionnaire item responses: a non-parametric IRT method in empirical research for applied health researchers. BMC Medical Research Methodology, 12(1), 74.
8. Van der Ark, L. A. (2005). Stochastic ordering of the latent trait by the sum score under various polytomous IRT models. Psychometrika, 70(2), 283–304.
9. Van der Ark, L.A. (2007). Mokken scale analysis in R. Journal of Statistical Software, 20(11), 1–19.
10. Van der Ark, L. A. (2012). New developments in Mokken scale analysis in R. Journal of Statistical Software, 48(5), 1–27.
11. Van der Ark, L. A., & Bergsma, W. P. (2010). A note on stochastic ordering of the latent trait using the sum of polytomous item scores. Psychometrika, 75(2), 272–279.
12. Van Schuur, W. (2011). Ordinal item response theory: Mokken scale analysis (Vol. 169). SAGE Publications.
13. Watson, R., van der Ark, L. A., Lin, L. C., Fieo, R., Deary, I. J., & Meijer, R. R. (2012). Item response theory: How Mokken scaling can be used in clinical practice. Journal of Clinical Nursing, 21(19pt20), 2736-2746. |
| Description: | 碩士
國立政治大學
統計研究所
101354008
102 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0101354008 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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