Bayesian Estimation for the Polytomous Rasch Model

• Main Authors: Po-Chun Huang, 黃柏鈞
• Other Authors: Zu-Wei Zheng
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/855m3w

碩士 === 中原大學 === 應用數學研究所 === 106 === 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.