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題名：高階層試題反應理論模式延伸與應用
作者：蘇啟明
作者(外文)：Su, Chi-Ming
校院名稱：國立中正大學
系所名稱：心理學研究所
指導教授：王文中
陳淑英
學位類別：博士
出版日期：2011
主題關鍵詞：高層次試題反應理論模式；貝氏估計法；電腦適性測驗；新近選題法；試題曝光率；higher-order multidimensional IRT model；Bayesian estimation；computerized adaptive testing；modern item selection rules；item exposure rate
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本研究旨在擴展高層次潛在能力結構之多向度試題反應模式，並且將其應用在電腦適性測驗中，並檢驗其有效性。本論文共有三個研究：
第一個研究是透過貝氏統計中的馬可夫鍊蒙地卡羅估計法，來進行模式參數的估計回復性的檢驗，結果發現本研究所擴展的高階層試題反應理論模式，其偏誤(bias)及平方根誤差(RMSE)都很小，而且大部分絕對相對誤差(ARB)也都小於.05，指出貝氏估計法所評估的模式具有良好的模式參數回復，WinBUGS是一個合適的估計軟體。
第二個研究則是在階層結構資料下，比較幾種模式的配適度，結果發現PsBF及DIC兩個指標相當敏銳且可以比較出最合適於階層資料的模式，並透過實際資料的分析，說明高層次試題反應理論模式的應用。
第三個研究則是在多向度電腦適性測驗下，分析比較四種估計法，結果證明高層次ＣＡＴ估計法最佳，並修正傳統的最大訊息量選題法，在測驗初期加上隨機成分來控制測驗初期能力估計的誤差，結果發現新近的選題方法能提高題庫使用率，降低試題的曝光率與測驗平均重疊率，支持新的選題法可以提高題庫安全性與保持較佳之測量精確度。最後，作者針對未來研究與實務應用提供若干建議。
The purpose of this study is to extend the higher-order latent trait structure within the multidimensional IRT framework and implement the model in the CAT context, then to assess the effectiveness of various modern item selection rules under the higher-order MCAT procedure. Sheng and Wikle (2008) proposed the MIRT models with a hierarchical structure, Huang (2009) then modified the Sheng and Wikle (2008) MIRT models and applied the proposed hierarchical MIRT models for the CAT procedure. The researcher further extended both these hierarchical MIRT models to the generalized higher-order models. Three studies based on the higher-order MIRT models were explored and discussed.
In the first study, the researcher employed the 2PLM and GPCM models, and considered the hierarchical structure focus on the 2nd-order, 3rd-order hierarchy in the higher-order MIRT models. Through simulation studies, the parameter recovery for the higher-order MIRT models was evaluated. The results showed the magnitudes of bias and RMSE were generally small, indicating the parameters could be recovered fairly well. Most of the ARBs were smaller than .05, which indicated the estimations had a high precision. The WinBUGS software was a suitable analysis program for the hierarchical structure of latent traits.
In the second study, when the model comparison was conducted, the results concurred with the expectation that the DIC would favor the generating model best, independent of the dichotomous or polytomous items, and high or diverse factor loadings. But the PsBF indicator favored the generating model only under the diverse factor loadings. In the real data analysis, three examples illustrated the application of the higher-order model including dichotomous and polytomous items. They showed the 2nd-order latent trait of the higher-order model was more representative for the true ability or performance of subjects.
In the last study, the applications of the higher-order MCAT with four CAT algorithms including direct and indirect approaches were implemented to estimate all latent traits for the duration of CAT. The higher-order CAT approach was the best approach because it had the smallest RMSEs for all kinds of ability estimates and could provide the conditional standard error for the general ability. When the MCAT was compared with the three item selection rules; the point Fisher information (PFI), progressive (PG) and alpha-stratified (AS) methods; the PG method reduced the item exposure rate as well as improved the item pool usage and the effect became larger as the acceleration parameter increased independent of estimation methods. Whereas, the AS method only slightly reduced the item exposure rate as well as improving the item pool usage. Both the PG and AS methods did not guarantee that the item exposure rate would be below a pre-specified level with the maximum item exposure rate set to .2, but it did so when the Sympson and Hetter online freeze (SHOF) was incorporated into the item selection rules. The content balancing and SHOF controls also had significant effect on reducing item exposure rate, especially the SHOF control method. For improving item pool usage, only the PG method accompanied with the SHOF procedure were effective.
In regard to the measurement precision and test mean overlap rate, the overall RMSEs of the higher-order CAT approach were lower than the other two estimate approaches, but the test overlap rates were almost the same as the other two approaches. When compared to the PFI item selection method, the PG method significantly reduced the test mean overlap rate, independent of pool sizes and test lengths, but the AS method only slightly reduced the test mean overlap rate. The PG and the AS methods resulted in a lower the test mean overlap rate when the value of the acceleration parameter and a-stratified number became higher. When incorporating the SHOF into CAT, the test mean overlap rate decreased for almost all conditions, and the effect of SHOF on the overall RMSEs was much smaller. In comparison with the conditions of a high ability correlation, the overall RMSEs increased, but the test mean overlap rate did not shift much with a diverse ability correlation.
In summary, the higher-order CAT approach with both the PG and SHOF procedures improved the item bank security and provided test information for the duration of CAT. Finally, the study limitations and further study suggestions were proposed by the author.
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