國家教育研究院

　　本研究主要探討階層式試題反應理論（hierarchical item response theory, HIRT）模式之建立、參數估計、等化方法及大型測驗之應用。當測驗架構是階層式的，包括次級量尺分數以及高層次量尺分數時，應使用階層式試題反應理論，透過同時估計的方式對所有量尺分數進行參數估計，否則會因忽略各階層間彼此相依之情形，導致估計精準度降低。目前HIRT之研究著重於模式建立及參數估計，但仍有許多限制有待改善，如僅探討次級量尺與試題間關係為「題間多向度」之架構、僅考慮單一高層次能力情形、假設各量尺皆為常態分佈、參數估計方法缺乏效率等問題。再者，HIRT的相關應用領域，如等化、大型測驗中可能值方法等皆尚待進一步探索。本研究擬應用MH-within-Gibbs sampling和kernel smoothing，改善上述之限制，並加入題內多向度之模式，同時針對符合HIRT架構之大型測驗提出HIRT之等化方式及可能值方法，以臺灣學生學習成就評量資料庫（TASA）為例，建立大型測驗標準化分析流程。

　　A Hierarchical Item Response Theory Model and Its Applications in Large-scale Assessment This paper is to explore the model building, estimates of parameters, equation methods and applications in large-scale assessment based on a hierarchical item response theory (HIRT). A hierarchical structure of ability organization, the general ability on the top and multiple more specialized (domain) abilities at the lower levels, has been well adopted in large-scale assessment settings. Under this framework, if the correlations between the general ability and domain abilities are ignored, the ability estimates will be unreliable. Some studies have been conducted using simultaneous estimation of HIRT regarding the general and domain abilities to increase precision of estimates. However, these studies have some limitations: (i) focusing on between-item multidimensional model, (ii) using only single higher-order ability, (iii) normal distribution assumptions in abilities, (iv) time-consuming process of parameters estimates. Moreover, the practical applications of the HIRT model have not yet been explored, such as equation, and plausible values methodology in large-scale assessment. This study will apply MH-within-Gibbs sampling and kernel smoothing to improve the problems in estimation of parameters, and to explore within-item multidimensional model. Using Taiwan assessment of student achievement (TASA ) as a empirical example to provide insight into the equation methods and plausible values methodology based on HIRT and to establish a large-scale standardized assessment analysis procedure.