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題名：階層式試題反應理論模式及其等化估計方法
作者：謝典佑
作者(外文)：Hsieh, Tien-Yu
校院名稱：國立臺中教育大學
系所名稱：教育測驗統計研究所
指導教授：郭伯臣
學位類別：博士
出版日期：2011
主題關鍵詞：階層式試題反應理論模式；無參數估計法；等化同時估計法；hierarchical item response theory model；nonparametric estimation；equating concurrent estimation
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本研究以階層式試題反應理論模式為基礎，提出階層式試題反應理論模式的無參數和等化同時估計法，並藉由模擬不同情境(人數、題數、能力分布與試題架構)與臺灣學生學習成就評量資料庫的實徵分析，探討所提出的參數估計方法於量尺分數、迴歸參數與試題參數的估計精準度。
　　模擬研究顯示：
1. 針對具備階層式結構的測驗資料，對於量尺分數、迴歸參數與試題參數的估計，階層式試題反應理論模式的參數、無參數型與等化同時估計法有較高的參數估計精準度。
2. 當量尺分數違反常態分布假設時，階層式試題反應理論模式的無參數估計方法比參數估計方法對於量尺分數、迴歸參數與試題參數有較高的估計精準度。
3. 當受試樣本數、試題數與領域量尺間的相關程度提高時，階層式試題反應理論模式的參數、無參數估計方法，對於量尺分數、迴歸參數與試題參數的估計，有較高估計精準度。
4. 當定錨試題比率增加時，階層式試題反應理論模式的等化同時估計法，對於量尺分數、迴歸參數與試題參數的估計，有較高的參數估計精準度。
　　在實證資料分析方面，透過模式適合度與估計標準誤之檢驗，顯示臺灣學生學習成就評量資料庫的實徵資料較宜使用階層式試題反應理論模式進行量尺分數、迴歸參數與試題參數的估計。
　This paper is to propose non-parametric and equating concurrent estimations. Some simulation experiments were conducted to evaluate the feasibility of the proposed estimations and how the abilities, regressions and item parameters are affected by different factors such as sample sizes, item lengths, ability distributions, and model specifications in comparison to those of one-dimensional and multi-dimensional item response theory models. An analysis of Taiwan Assessment of Student Achievement data is provided as an example.
The simulation results show that:
1. Modeling the data with hierarchical structure for estimating the ability, regression, and item parameters, the accuracy of the parametric, nonparametric, and equating concurrent estimations based on hierarchical item response theory models outperformed that of estimations based on uni- and multi-dimensional item response theory models.
2. When the structure of the prior distribution does not match the assumption of the normal distribution, the accuracy of non-parametric estimation outperformed that of parametric estimation base on hierarchical item response theory models for estimating the ability, regression, and item parameters.
3. The accuracies for estimating ability, regression, and item parameters based on the hierarchical item response theory models increase as the sample sizes, item lengths, and the correlations between the overall and the domain abilities increase.
4. The accuracies of the equating concurrent estimation for estimating ability, regression, and item parameters based on the hierarchical item response theory models increase as the sample sizes, item lengths, the correlations between the overall and the domain abilities and the percentages of anchor items increase.
　　Based on the results of model selection index and standard errors, a hierarchical item response theory model is suitable for analysising Taiwan Assessment of Student Achievement data for estimating ability, regression, and item parameters.
中文文獻
吳慧珉 (2001) 。選項特徵曲線之研究－以核函數之平滑化為估計取向。國立臺中師範學院教育測驗統計研究所碩士論文，臺中市。
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臺灣學生學習成就評量資料庫 (2009) 。檢索日期：2009年11月20日。檢自：http://tasa.naer.edu.tw/Release/index.aspx
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劉湘川 (2001b) 。核平滑化試題選項特徵曲線與選項關聯結構整合擴充模式。測驗統計年刊，9 (1) ，1-18。new window
謝典佑、林佳樺、郭伯臣、施淑娟 (2009，9月)。高層次IRT 模式式適合度檢定之研究─以TASA 數學科為例。「大型教育資料庫建置及相關議題」學術研討會。台中：國立台中教育大學。
謝典佑、曾彥鈞、廖晨惠、郭伯臣 (2009，10月)。同時估計法於高層次試題反應理論之研究。中國測驗學會年會暨心理與教育測驗學術研討會。台北：國立台灣師範大學。
謝典佑、楊智為、許天維、郭伯臣 (2009，10月)。整合無參數與MH-within-Gibbs 技術提升高層次試題反應理論參數估計精準度之研究。中國測驗學會年會暨心理與教育測驗學術研討會。台北：國立台灣師範大學。

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