The four-parameter logistic model (4PLM) has recently attracted much interest in various applications. Motivated by recent studies that re-express the four-parameter model as a mixture model with two levels of latent variables, this paper develops a new expectation-maximization (EM) algorithm for marginalized maximum a posteriori estimation of the 4PLM parameters. The mixture modelling framework of the 4PLM not only makes the proposed EM algorithm easier to implement in practice, but also provides a natural connection with popular cognitive diagnosis models. Simulation studies were conducted to show the good performance of the proposed estimation method and to investigate the impact of the additional upper asymptote parameter on the estimation of other parameters. Moreover, a real data set was analysed using the 4PLM to show its improved performance over the three-parameter logistic model.

中文翻译：

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混合建模框架下四参数逻辑模型的边缘化最大后验估计。

四参数逻辑模型 (4PLM) 最近在各种应用中引起了极大的兴趣。受最近将四参数模型重新表示为具有两个潜在变量水平的混合模型的研究的启发，本文开发了一种新的期望最大化 (EM) 算法，用于对 4PLM 参数进行边缘化最大后验估计。4PLM 的混合建模框架不仅使所提出的 EM 算法在实践中更容易实现，而且还提供了与流行的认知诊断模型的自然联系。进行了仿真研究以显示所提出的估计方法的良好性能，并研究附加上渐近线参数对其他参数估计的影响。而且，