🤖 AI Summary
Four-parameter item response theory (4P-IRT) lacks a corresponding factor analysis (FA) counterpart, hindering unified latent variable modeling and systematic correction of response biases—namely, guessing and inattention—for binary items.
Method: This paper introduces the four-parameter factor analysis (4P-FA) model, establishing its analytical equivalence to 4P-IRT for the first time. We develop an identifiable Bayesian inference framework that jointly estimates all four item parameters and bias-corrected person-specific latent traits, implemented efficiently in R/Python.
Contribution/Results: Empirical applications to real-world college admission and anxiety assessment data demonstrate that 4P-FA accurately disentangles and corrects for guessing and inattention effects, substantially improving the validity and interpretability of latent trait estimation. By bridging the theoretical gap between IRT and FA, this work provides a novel paradigm for response-bias modeling in psychometrics.
📝 Abstract
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.