应用Stan软件包实现IRT模型的贝叶斯参数估计

Stan是一个新的用于估计指定统计模型的概率编程语言,它使用了强大而高效的汉密尔顿蒙特卡罗(Hamiltonian Monte Carlo,HMC)抽样算法,相比较传统的Gibbs抽样和Metropolis算法具有显著的效率提升.R软件包“rstan” 链接了R与Stan 2个软件,使得Stan可以借助R的计算环境运行.首先,该文通过3参数Logistic(3PL)模型代码介绍了Stan的程序语言; 其次,该文使用Stan计算2个评估模型-数据拟合的全新指标WAIC和LOO,为应用Stan进行IRT模型相关研究提供了有效的参考工具; 最后,该文还采用了2个真实数据分别考察了Stan在单维IRT模型和多维IRT模型参数估计中的运行表现.研究结果表明:采用一个新的贝叶斯统计软件Stan,通过2个实证研究验证了该方法的有效性与可行性,为国内学者应用Stan进行IRT模型相关研究提供了有效的参考资料.

Using Stan to Implement Bayesian Parameter Estimation of IRT Models

Stan,a new probabilistic programming language for specifying statistical models,implements the powerful and efficient Hamiltonian Monte Carlo(HMC)sampling algorithm,which is significantly more efficient than the traditional Gibbs sampling and Metropolis algorithms.R package "rstan" links R and Stan,enabling Stan to run with R environment.First,this article introduces the programming language of Stan through the three-parameter logistic(3PL)model code.Secondly,this paper administrates Stan to calculate two new criteria of model-data fitting:WAIC and LOO,which provides an effective reference for IRT model studies.Finally,two types of real data are performed to investigate the performance of Stan in parameter estimation of one-dimensional IRT model and multidimensional IRT model respectively.In conclusion,this paper utilizes a new Bayesian statistical software to estimate the effectiveness and feasibility of this method through two empirical studies,which provides effective references for domestic scholars to apply Stan in IRT model research.