多维项目反应理论:参数估计及其在心理测验中的应用

Parameters Estimation of MIRT Model and Its Application in Psychological Tests

本研究介绍并引进了现代测量理论中的前沿技术——多维项目反应理论,采用MCMC算法实现了其参数估计;并将MIRT应用于瑞文高级推理测验,以探讨MIRT在心理测验中的具体应用。研究结果表明:(1)本研究自主编制的MIRT参数估计程序基本可行,其估计的精度与国外研究结论相当甚至更好。(2)在测验维度和样本容量两因素完全随机实验设计下(2×3),随着被试和题目样本容量的增加,MIRT参数估计的精度越高且估计的稳定性越强;但随着测验维度的增加,MIRT参数估计精度和稳定性均随之降低。(3)MIRT对心理测验的分析比UIRT能提供更为精确和细致的信息。它对心理测验的编制、开发及评价具有重要的指导和参考价值,值得引进及借鉴。

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 developed a parameter estimation method of MIRT model with MCMC algorithm, and discussed its application on psychology tests. Monte Carlo method was used to explore the feasibility of MCMC algorithm and to examine the estimation precision as well as the properties of three parameter logistic MIRT models. Besides, this study employed MIRT model to analyze Raven＇s Advanced Progressive Matrices test （RAPMT）. Three findings were presented： （1） The estimation precision of the self-developed program of three parameter logistic MIRT model was comparable with those reported by western studies, which demonstrated the validity of the self-developed program; （2） Along with the sample size and the number of item sample increased, the estimation precision and the robustness of MIRT parameter increased; but along with the number of the test dimension increased （e.g. from 3 to 5）, the estimation precision and the robustness of MIRT parameter decreased; （3） When applied the MIRT into the analysis of the RAPMT： （a） Most of the discrimination of the test items were very high. （b） The ability scores of the five dimensions of in the RAPMT were ranked ascendingly as CR, PP, FA, D3 and D2. Compare to the unidimensional item response theory （UIRT）, the ability scores of each dimensions reported by MIRT provided more abundant and valuable information for cognitive diagnosis. （c） The correlations between the five dimensions in the RAPMT were on the low to moderate levels.