DeMars Christine E, Satkus Paulius
James Madison University, Harrisonburg, VA, USA.
Graduate Management Admission Council, Reston, VA, USA.
Educ Psychol Meas. 2024 Aug;84(4):691-715. doi: 10.1177/00131644231203688. Epub 2023 Oct 30.
Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal maximum estimation. In this study, using sample sizes of 1,000 or smaller, not using priors often led to extreme, implausible parameter estimates. Applying prior distributions to the -parameters alleviated the estimation problems with samples of 500 or more; for the samples of 100, priors on both the -parameters and -parameters were needed. Estimates were biased when the mode of the prior did not match the true parameter value, but the degree of the bias did not depend on the strength of the prior unless it was extremely informative. The root mean squared error (RMSE) of the -parameters and -parameters did not depend greatly on either the mode or the strength of the prior unless it was extremely informative. The RMSE of the -parameters, like the bias, depended on the mode of the prior for .
边际极大似然法是项目反应理论模型的一种常见估计方法，它本质上并非贝叶斯方法。然而，由于估计困难，在估计三参数逻辑斯蒂模型（3PL模型）时，尤其是小样本情况下，贝叶斯先验常常应用于似然函数。对于边际极大似然估计中先验的选择，关注较少。在本研究中，当样本量为1000或更小的时候，不使用先验常常会导致极端的、不合理的参数估计。对参数应用先验分布缓解了500及以上样本量的估计问题；对于100的样本量，参数和参数都需要先验。当先验的众数与真实参数值不匹配时，估计会有偏差，但偏差程度并不取决于先验的强度，除非先验信息非常丰富。参数和参数的均方根误差（RMSE）并不很大程度上取决于先验的众数或强度，除非先验信息非常丰富。参数的RMSE，与偏差一样，取决于参数的先验众数。
