評定量表的貝氏分析

Bayesian Estimation for the Polytomous Rasch Model

10.6840/cycu201800011

黃柏鈞

項目反應定理 ； 多元計分 ； 評定量表模型 ； 部分計分模型 ； 貝氏分析 ； 蒙地卡羅馬可夫鏈 ； IRT ； PCM ； RSM ； Bayesian analysis ； MCMC

中原大學應用數學系學位論文

2018年

碩士

鄭子韋

繁體中文

古典測驗理論有著樣本依賴性的問題，所以本篇文章採用項目反應理論，而它也是近代較常使用的測驗理論。其模型包括二元計分的一參數模型、二參數模型、三參數模型，還有多元計分的部分計分模型和評定量表模型。 在本篇研究中，利用部分計分模型和評定量表模型分析中原大學105學年度第二學期的微積分第一次大會考，採取貝氏分析利用蒙地卡羅馬可夫鏈(MCMC)模擬出的參數估計分析試題的難度。而此次考試的學生有1523位，試題為多元計分的資料。 部分計分模型和評定量表模型為二元計分一參數模型的延伸，前者估計出的梯級難度參數可以分析出每一個給分梯級之間的難度關係，後者估計出的總體難度參數可以分析出每一題間的難度關係，之後再做難度的探討。

Classical test theory has the problem of sample dependence, so item response theory(IRT) is used to cope with this issue, which is an important ingredient in modern test theory. It includes one-parameter model, two-parameter model, three-parameter model, and partial credit model and rating scale model with polytomous scoring. In this paper, both of the polytomous IRT models, partial credit model and rating scale model, are used to analyze the data from the first Joint Calculus Examination held in the fall semester 2016 in Chung Yuan Christian University. In general, because we are not assuming independence between the each of the individual parameters this integral is difficult to compute, especially if there are many parameters. This is the situation in which Monte Carlo Markov chain(MCMC) simulation is most commonly used. There are 1523 students in this examination, and these items are polytomous scoring data. Partial credit model and rating scale model are the extensions of the binary scoring of the one parameter model. The former estimates the threshold difficulty parameters which represent the difficulty between each category. The latter estimates the item difficulty parameters which represent the difficulty between each item. After that, we will discuss the relationship of difficulty.

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