An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models
In this paper, we propose a Bayesian PG-INLA algorithm which is tailored to both one-dimensional and multidimensional 2-PL IRT models. The proposed PG-INLA algorithm utilizes a computationally efficient data augmentation strategy via the Pólya-Gamma variables, which can avoid low computational effic...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-01-01
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| Series: | Statistical Theory and Related Fields |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/24754269.2024.2442174 |
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| author | Xiaofan Lin Yincai Tang |
| author_facet | Xiaofan Lin Yincai Tang |
| author_sort | Xiaofan Lin |
| collection | DOAJ |
| description | In this paper, we propose a Bayesian PG-INLA algorithm which is tailored to both one-dimensional and multidimensional 2-PL IRT models. The proposed PG-INLA algorithm utilizes a computationally efficient data augmentation strategy via the Pólya-Gamma variables, which can avoid low computational efficiency of traditioanl Bayesian MCMC algorithms for IRT models with a logistic link function. Meanwhile, combined with the advanced and fast INLA algorithm, the PG-INLA algorithm is both accurate and computationally efficient. We provide details on the derivation of posterior and conditional distributions of IRT models, the method of introducing the Pólya-Gamma variable into Gibbs sampling, and the implementation of the PG-INLA algorithm for both one-dimensional and multidimensional cases. Through simulation studies and an application to the data analysis of the IPIP-NEO personality inventory, we assess the performance of the PG-INLA algorithm. Extensions of the proposed PG-INLA algorithm to other IRT models are also discussed. |
| format | Article |
| id | doaj-art-0842f78bdb8e43528f51b90958698208 |
| institution | Kabale University |
| issn | 2475-4269 2475-4277 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Statistical Theory and Related Fields |
| spelling | doaj-art-0842f78bdb8e43528f51b909586982082025-01-21T15:06:54ZengTaylor & Francis GroupStatistical Theory and Related Fields2475-42692475-42772025-01-0111310.1080/24754269.2024.2442174An efficient PG-INLA algorithm for the Bayesian inference of logistic item response modelsXiaofan Lin0Yincai Tang1KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of ChinaKLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, People's Republic of ChinaIn this paper, we propose a Bayesian PG-INLA algorithm which is tailored to both one-dimensional and multidimensional 2-PL IRT models. The proposed PG-INLA algorithm utilizes a computationally efficient data augmentation strategy via the Pólya-Gamma variables, which can avoid low computational efficiency of traditioanl Bayesian MCMC algorithms for IRT models with a logistic link function. Meanwhile, combined with the advanced and fast INLA algorithm, the PG-INLA algorithm is both accurate and computationally efficient. We provide details on the derivation of posterior and conditional distributions of IRT models, the method of introducing the Pólya-Gamma variable into Gibbs sampling, and the implementation of the PG-INLA algorithm for both one-dimensional and multidimensional cases. Through simulation studies and an application to the data analysis of the IPIP-NEO personality inventory, we assess the performance of the PG-INLA algorithm. Extensions of the proposed PG-INLA algorithm to other IRT models are also discussed.https://www.tandfonline.com/doi/10.1080/24754269.2024.2442174Item response theorytwo-parameter logistic modelPólya-GammaGibbs samplerintegrated nested Laplace approximation |
| spellingShingle | Xiaofan Lin Yincai Tang An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models Statistical Theory and Related Fields Item response theory two-parameter logistic model Pólya-Gamma Gibbs sampler integrated nested Laplace approximation |
| title | An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models |
| title_full | An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models |
| title_fullStr | An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models |
| title_full_unstemmed | An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models |
| title_short | An efficient PG-INLA algorithm for the Bayesian inference of logistic item response models |
| title_sort | efficient pg inla algorithm for the bayesian inference of logistic item response models |
| topic | Item response theory two-parameter logistic model Pólya-Gamma Gibbs sampler integrated nested Laplace approximation |
| url | https://www.tandfonline.com/doi/10.1080/24754269.2024.2442174 |
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