MIRT模型中多维能力及其相关矩阵估计的影响因素

多维项目反应理论因其模型本身的天然优势及其兼具因素分析与项目反应理论于一身的优点,而被广大研究者及应用者所重视.本研究在前人研究基础上,重点讨论MIRT多维能力及能力间相关矩阵的参数估计问题.研究采用Monte Carlo模拟方法进行,在三因素完全随机设计（4 ×3×3）下,使用MCMC算法,探讨测验维度数、维度间的相关大小和测验项目数三个因素对MIRT能力及其相关矩阵估计的影响.

The Parameter Estimation of Ability and Its Correlation Matrix of MIRT Model

Multidimensional item response theory（MIRT） is a well known theory which combines the advantages of the factor analysis theory and the item response theory. The current study discussed the parameter estimation of ability and its correlation matrix of 3PL - MIRT model with MCMC algorithm. Monte Carlo method was used to explore how to the three factors - the number of dimensions and test items and the size of correlations between dimensions, effect the estimated precision of ability and its correlation matrix. The findings suggested：（ 1 ）Under the thirty six experiment conditions, the estimation precision on ability and correlation matrix parameters were great relatively,and the robustness of this model was relatively strong; （2）All the three factors detected in this paper were important factors that effect the estimation precision on ability parameters. In detailed, the more the dimension, the more the number of items, and the greater the correlation between ability dimensions, the greater the estimation precision on ability parameters will be; （ 3 ） While the three factors showed no raw of the effects on the correlation matrix parameters, which asked more discussions; （4） The three factors could represent about 92.6 percentage variations on ability estimation, which indicated that they were the most major factors affect the ability estimation;（ 5 ）The three factors could only represent about 15 percentage variations on correlation matrix estimation, which reflected that the factors affect the correlation matrix estimation were more complicated, there were more important factors required to detect.