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 augmentatio...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 onedimensional 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.展开更多
主要研究四参数Logistic项目反应理论框架下潜在回归模型系数的贝叶斯变量选择方法。潜在回归模型是项目反应模型的扩展,该模型以学生潜在能力为响应变量,以观测变量(人口学特征、心理特质等)为解释变量建立回归模型。首先,通过将四参数...主要研究四参数Logistic项目反应理论框架下潜在回归模型系数的贝叶斯变量选择方法。潜在回归模型是项目反应模型的扩展,该模型以学生潜在能力为响应变量,以观测变量(人口学特征、心理特质等)为解释变量建立回归模型。首先,通过将四参数Logistic模型嵌入线性回归模型内,建立潜在回归模型;其次,通过对潜在回归系数引入Laplace、Horseshoe和Horseshoe+三类收缩先验,进行参数估计和变量选择;最后,通过模拟实验,与传统Metropolis-Hasting算法进行比较,以评估Hamiltonian Monte Carlo抽样方法的性能,实验结果表明,所采用的Hamiltonian Monte Carlo估计方法比Metropolis-Hasting算法更高效、更灵活。采用PISA-2018数据集开展实证研究,验证了所提出潜在回归模型及估计方法的有效性与实用性。展开更多
基金supported by theNationalNatural Science Foundation of China[grant number 12271168]the 111 Project of China[grant number B14019].
文摘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 onedimensional 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.
文摘主要研究四参数Logistic项目反应理论框架下潜在回归模型系数的贝叶斯变量选择方法。潜在回归模型是项目反应模型的扩展,该模型以学生潜在能力为响应变量,以观测变量(人口学特征、心理特质等)为解释变量建立回归模型。首先,通过将四参数Logistic模型嵌入线性回归模型内,建立潜在回归模型;其次,通过对潜在回归系数引入Laplace、Horseshoe和Horseshoe+三类收缩先验,进行参数估计和变量选择;最后,通过模拟实验,与传统Metropolis-Hasting算法进行比较,以评估Hamiltonian Monte Carlo抽样方法的性能,实验结果表明,所采用的Hamiltonian Monte Carlo估计方法比Metropolis-Hasting算法更高效、更灵活。采用PISA-2018数据集开展实证研究,验证了所提出潜在回归模型及估计方法的有效性与实用性。
