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.

中文翻译：

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三参数逻辑模型的收缩估计

当考生可以猜出正确的答案时，三参数逻辑模型被广泛用于模拟对能力测试的反应，就像多项选择题的情况一样。然而，模型参数的弱可识别性导致估计的大可变性和似然函数数值最大化的收敛困难。为了克服这些问题，在本文中，我们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对猜测参数的脊型惩罚。然后通过各种方法选择调整参数：交叉验证、信息标准或使用经验贝叶斯方法。探索的第二种方法基于开发的方法，该方法通过调整后的分数方程来减少最大似然估计量的偏差。通过模拟研究和真实数据示例来研究这些方法的性能。