Bridging Item Response Theory and Factor Analysis: A Four-Parameter Mixture-Dichotomized Model with Bayesian Estimation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912459714985984 |
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| author | Pavlech, Ján Martinková, Patrícia |
| author_facet | Pavlech, Ján Martinková, Patrícia |
| contents | Item Response Theory (IRT) and Factor Analysis (FA) are two major frameworks used to model multi-item measurements of latent traits. While the relationship between two-parameter IRT models and dichotomized FA models is well established, IRT models with additional parameters have lacked corresponding FA formulations. This work introduces a four-parameter factor analytic (4P FA) model for multi-item measurements composed of binary items, building on the traditional dichotomized single-factor FA model. We derive the relationship between the proposed 4P FA model and its counterpart in the IRT framework, the 4P IRT model. A Bayesian estimation method is developed to estimate the four item parameters, the respondents' latent scores, and the scores adjusted for guessing and inattention effects. The proposed algorithm is implemented in R and Python, and the relationship between the 4P FA and 4P IRT models is empirically examined using two real datasets: a standardized admission test and a psychological anxiety inventory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bridging Item Response Theory and Factor Analysis: A Four-Parameter Mixture-Dichotomized Model with Bayesian Estimation Pavlech, Ján Martinková, Patrícia Methodology Item Response Theory (IRT) and Factor Analysis (FA) are two major frameworks used to model multi-item measurements of latent traits. While the relationship between two-parameter IRT models and dichotomized FA models is well established, IRT models with additional parameters have lacked corresponding FA formulations. This work introduces a four-parameter factor analytic (4P FA) model for multi-item measurements composed of binary items, building on the traditional dichotomized single-factor FA model. We derive the relationship between the proposed 4P FA model and its counterpart in the IRT framework, the 4P IRT model. A Bayesian estimation method is developed to estimate the four item parameters, the respondents' latent scores, and the scores adjusted for guessing and inattention effects. The proposed algorithm is implemented in R and Python, and the relationship between the 4P FA and 4P IRT models is empirically examined using two real datasets: a standardized admission test and a psychological anxiety inventory. |
| title | Bridging Item Response Theory and Factor Analysis: A Four-Parameter Mixture-Dichotomized Model with Bayesian Estimation |
| topic | Methodology |
| url | https://arxiv.org/abs/2407.04071 |