This work proposes a 4-parameter factor analytic (4P FA) model for multi-item measurements composed of binary items as an extension to the dichotomized single latent variable FA model. We provide an analytical derivation of the relationship between the newly proposed 4P FA model and its counterpart in the item response theory (IRT) framework, the 4P IRT model. A Bayesian estimation method for the proposed 4P FA model is provided to estimate the four item parameters, the respondents' latent scores, and the scores cleaned of the guessing and inattention effects. The newly proposed algorithm is implemented in R and Python, and the relationship between the 4P FA and 4P IRT is empirically demonstrated using real datasets from admission tests and the assessment of anxiety.

翻译：本研究提出了一种针对二元项目组成的多项目测量的四参数因子分析（4P FA）模型，作为二值化单潜变量因子分析模型的扩展。我们通过解析推导建立了新提出的4P FA模型与其在项目反应理论（IRT）框架中的对应模型——四参数IRT（4P IRT）模型之间的关系。为估计四个项目参数、受访者的潜变量得分以及剔除猜测和疏忽效应后的净化得分，本文提供了针对所提出4P FA模型的贝叶斯估计方法。新提出的算法已在R和Python中实现，并通过入学考试和焦虑评估的实际数据集实证验证了4P FA与4P IRT模型之间的关系。