Paek Insu, Lin Zhongtian, Chalmers Robert Philip
Florida State University, Tallahassee, FL, USA.
Cambium Assessment, Inc., Washington, DC., USA.
Educ Psychol Meas. 2023 Apr;83(2):375-400. doi: 10.1177/00131644221096431. Epub 2022 May 16.
To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori (MMAP) and posterior standard error (PSE) are estimated. Confidence intervals (CIs) for these parameters and other parameters which did not take any priors were investigated with popular prior distributions, different error covariance estimation methods, test lengths, and sample sizes. A seemingly paradoxical result was that, when priors were taken, the conditions of the error covariance estimation methods known to be better in the literature (Louis or Oakes method in this study) did not yield the best results for the CI performance, while the conditions of the cross-product method for the error covariance estimation which has the tendency of upward bias in estimating the standard errors exhibited better CI performance. Other important findings for the CI performance are also discussed.
为了降低在期望最大化（MML-EM）估计方法下的边际极大似然估计中出现海伍德情况或估计2PL或3PL模型时不收敛的可能性，可以使用2PL模型中项目斜率参数的先验或3PL模型中伪猜测参数的先验，并估计边际极大后验（MMAP）和后验标准误差（PSE）。针对这些参数以及未采用任何先验的其他参数，使用流行的先验分布、不同的误差协方差估计方法、测验长度和样本量研究了置信区间（CI）。一个看似矛盾的结果是，当采用先验时，文献中已知较好的误差协方差估计方法（本研究中的路易斯或奥克斯方法）的条件并未产生CI性能的最佳结果，而在估计标准误差时具有向上偏差趋势的误差协方差估计的交叉乘积方法的条件却表现出更好的CI性能。还讨论了CI性能的其他重要发现。
