心理科学

心理科学 ›› 2012, Vol. 35 ›› Issue (2): 441-445.

• 统计与测量 • 上一篇    下一篇

单维项目因素分析：CCFA与IRT估计方法的比较

刘红云1,李美娟1,2,骆方1,李小山3   

  1. 1. 北京师范大学
    2.
    3. 北京师范大学心理学院
  • 收稿日期:2010-10-21 修回日期:2011-05-13 出版日期:2012-03-20 发布日期:2012-03-20
  • 通讯作者: 骆方
  • 基金资助:
    国家自然科学基金青年基金项目

Unidimensional Item Factor Analysis: A Comparison of Categorical Confirmation Factor Analysis and Item Response Theory

  • Received:2010-10-21 Revised:2011-05-13 Online:2012-03-20 Published:2012-03-20
  • Contact: Fang Luo

摘要： 当观测指标变量为二分分类数据时，传统的因素分析方法不再适用。作者简要回顾了SEM框架下的分类数据因素分析模型和IRT框架下的测验题目和潜在能力的关系模型，并对两种框架下主要采用的参数估计方法进行了总结。通过两个模拟研究，比较了SEM框架下GLSc和MGLSc估计方法与IRT框架下MML/EM估计方法的差异。研究结果表明：（1）三种方法中，GLSc得到参数估计的偏差最大，MGLSc和MML/EM估计方法相差不大；（2）随着样本量增大，各种项目参数估计的精度均提高；（3）项目因素载荷和难度估计的精度受测验长度的影响；（4）项目因素载荷和区分度估计的精度受总体因素载荷（区分度）高低的影响；（5）测验项目中阈值的分布会影响参数估计的精度，其中受影响最大的是项目区分度。（6）总体来看，SEM框架下的项目参数估计精度较IRT框架下项目参数估计的精度高。此外，文章还将两种方法在实际应用中应该注意的问题提供了一些建议。

关键词: 参数估计, 分类数据, 验证性因素分析, 项目反应理论

Abstract: The factor analysis models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a brief review and synthesis of the item factor analysis estimation literature for categorical data (e.g., 0-1 type response scales). Popular categorical item factor analysis models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Two Monte Carlo simulation studies are conducted and revealed: (1) Similar parameter estimates have been obtained from the SEM and IRT parameterizations. Even with a small sample and the IRT estimates converted to SEM parameters, the MWLSc, and MML/EM results are strikingly similar. But in small sample size and long test, WLSc did not obtain the convergence parameter estimations, although in short test, WLSc estimates have been obtained, the estimates are consistently more discrepant than those produced by the other estimation techniques. (2) The precise of the estimators enhances as the quantity of the sample increases. (3) The precise of item factor load and of item difficulty parameter is influenced by the test length. (4) The precise of item factor load and of item discrimination parameter is influenced by the size of the whole factor load (discrimination). (5) The distribution of the threshold of test item affects the precise of the parameter estimate, and item discrimination is the most sensitive parameter to the threshold. (6) In whole, the precise of item parameter estimate in SEM framework is higher than that in IRT framework. Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems encountered in almost all empirical social science research fields. The authors conclude with considerations for categorical item factor analysis and give some advice for applied researchers.

Key words: parameter estimation, categorical data, confirmatory factor analysis, item response theory