多向度Rasch模型的貝氏分析

測驗理論分為古典測驗理論和項目反應理論，但是古典測驗理論中會有樣本依賴和測驗依賴的問題，所以本次研究則是以項目反應理論來做分析。在項目反應理論中分為二元計分和多元計分，除了計分上面的不同外，進行細分後還可以分為單向度模型和多向度模型，則本篇主要使用的是二元計分中的多向度二參數模型。本篇研究的對象為中原大學102學年度的大一的新生們，對這群學生進行了英文入學測驗，而此次進行考試的學生總共有3138位。使用的統計方法為貝氏分析，利用馬可夫鏈蒙地卡羅法模擬出的估計值來分析各個面向代表的是什麼。多向度二參數模型為單向度二參數模型的延伸，兩者差別在於單向度中的學生能力只有一個面向，多向度則是有多個面向。而此次分析則是對學生的能力拆成兩個面向，可以從不同面相的鑑別度上觀察哪些題目是可以比較有效區分能力的題目，最後使用單向度二參數模型和多向度二參數模型做近一步的探討，檢視其中特別的地方。

關鍵字

項目反應理論；多向度項目反應理論；二參數模型；多向度二參數模型；貝氏分析；馬可夫鏈蒙地卡羅

並列摘要

The test theory can be divided into classical test theory (CTT) and item response theory(IRT). But there are problems with sample dependence and test dependence in CTT. Therefore, this study is based on the IRT. In the IRT, it can be divided into binary scoring and multinomial scoring. In addition to the difference in scoring, it can be divided into unidimensional model and multidimensional model after subdivision. This article mainly uses the multidimensional two-parameter logistic model (M2PLM) in binary scoring. This research is aimed at the freshmen who have just entered the freshman year in Chung Yuan Christian University in 2013 years. An English entrance test was conducted for students. The total number of students taking the exam is 3,138. The statistical method used is Bayesian analysis. The estimated values calculated by the Markov Chain Monte Carlo method to analyze what each representative is. The M2PLM is an extnsion of the two-parameter logistic model (2PLM). The difference between the two is that the student ability in 2PLM has only one aspect, and M2PLM has multiple aspects. And this research is to split the ability into two aspects. It can be observed from the different aspects of discrimination to identify which topics are more effective in distinguishing the ability. Finally, a 2PLM and a M2PLM are used to make a further exploration to examine the special places.

並列關鍵字

IRT ； MIRT ； 2PLM ； M2PLM ； Bayesian analysis ； MCMC

參考文獻

1. Adams, R. J., Wilson, M. R., & Wang, W.C.(1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1-23.

Google Scholar

2. Andreis, F. & Ferrari, P.A. (2014). Multidimensional item response theory models for dichotomous data in customer satisfaction evaluation. Journal of Applied Statistics, 41(9), 2044 – 2055.