多维测验项目参数的估计：基于SEM与MIRT方法的比较

作者简要回顾了SEM框架下分类数据因素分析(CCFA)模型和MIRT框架下测验题目和潜在能力的关系模型, 对两种框架下的主要参数估计方法进行了总结。通过模拟研究, 比较了SEM框架下WLSc和WLSMV估计方法与MIRT框架下MLR和MCMC估计方法的差异。研究结果表明：(1) WLSc得到参数估计的偏差最大, 且存在参数收敛的问题; (2)随着样本量增大, 各种项目参数估计的精度均提高, WLSMV方法与MLR方法得到的参数估计精度差异很小, 大多数情况下不比MCMC方法差; (3)除WLSc方法外, 随着每个维度测验题目的增多参数估计的精度逐渐增高; (4)测验维度对区分度参数和难度参数的影响较大, 而测验维度对项目因素载荷和阈值的影响相对较小; (5)项目参数的估计精度受项目测量维度数的影响, 只测量一个维度的项目参数估计精度较高。另外文章还对两种方法在实际应用中应该注意的问题提供了一些建议。

Item Parameter Estimation for Multidimensional Measurement: Comparisons of SEM and MIRT Based Methods

Traditional 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) under the multidimensional response model. Popular categorical item factor analysis models and estimation methods found in the structural equation modeling and item response theory literatures are presented. The Monte Carlo simulation studies are conducted and revealed: (1) Similar parameter estimates have been obtained of Modified weighted least squares for categorical data method (WLSMV) from the structural equation model (SEM) framework and adoptive Restricted Maximum Likelihood (MLR) and Markov chain Monte Carlo (MCMC) methods from the multidimensional item response theory (MIRT) framework. Even with a small sample and the item response theory (IRT) estimates converted to SEM parameters, the WLSMV, MLR, and MCMC results are strikingly similar. But in small sample size and long test, weighted least squares for categorical data (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 precision of the estimators enhances as the quantity of the sample increases, and the differences between WLSMV and MLR are very trivial, and the precisions of WLSMV and MLR methods are not worse than that of the MCMC method in most conditions. (3) The precision of item factor loading and of item difficulty parameter is influenced by the test length, and the precision of item discrimination and of item difficulty parameter is influenced by the number of test dimension. (4) The precision of the estimators decreases as the number of dimensions measured by the item increases, especially for item discrimination and item factor loading parameter. Both SEM and 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.