Department of Economics and Statistics, University of Udine, Italy.
Br J Math Stat Psychol. 2021 Nov;74(3):591-609. doi: 10.1111/bmsp.12241. Epub 2021 Mar 18.
The three-parameter logistic model is widely used to model the responses to a proficiency test when the examinees can guess the correct response, as is the case for multiple-choice items. However, the weak identifiability of the parameters of the model results in large variability of the estimates and in convergence difficulties in the numerical maximization of the likelihood function. To overcome these issues, in this paper we explore various shrinkage estimation methods, following two main approaches. First, a ridge-type penalty on the guessing parameters is introduced in the likelihood function. The tuning parameter is then selected through various approaches: cross-validation, information criteria or using an empirical Bayes method. The second approach explored is based on the methodology developed to reduce the bias of the maximum likelihood estimator through an adjusted score equation. The performance of the methods is investigated through simulation studies and a real data example.
三参数逻辑模型广泛用于当考生可以猜测正确答案时（如多项选择题）模拟能力测试的反应。然而，该模型参数的弱可识别性导致估计值的变异性较大，并且在数值最大化似然函数时会出现收敛困难。为了解决这些问题，本文探索了各种收缩估计方法，主要有两种方法。首先，在似然函数中引入了猜测参数的岭型惩罚。然后通过各种方法选择调整参数：交叉验证、信息准则或使用经验贝叶斯方法。探索的第二种方法是基于通过调整评分方程来减少最大似然估计偏差的方法学。通过模拟研究和实际数据示例来研究方法的性能。
