Gaussian variational estimation for multidimensional item response theory
Gaussian variational estimation for multidimensional item response theory
复制标题
多维项目响应理论的高斯变分估计
DOI：
10.1111/bmsp.12219
复制
发表时间：
2020
影响因子：
2.6
通讯作者：
Xu, Gongjun
中科院分区：
文献类型：
--
作者：
Cho, April E.;Wang, Chun;Zhang, Xue;Xu, Gongjun
多维项目反应理论（MIRT）广泛应用于教育和心理测试的评估和评价。它通过指定个体的多个潜在特征与其对测试项目的反应之间的函数关系来对个体反应模式进行建模。 MIRT 参数估计的一大挑战是，由于潜在变量结构，似然性涉及棘手的多维积分。已经提出了各种方法，涉及积分的直接数值近似或蒙特卡罗模拟。然而，众所周知，这些方法在高维度上计算要求较高，并且依赖于后验分布的采样数据点。我们提出了一种新的高斯变分期望最大化（GVEM）算法，该算法采用变分推理通过计算上可行的下界来近似难以处理的边际似然。此外，所提出的算法可用于评估探索性分析中潜在特征的维度。进行了仿真研究，以证明新 GVEM 算法与流行的替代 Metropolis-Hastings Robbins-Monro 算法相比的计算效率和估计精度。此外，还提出了理论结果，以建立新 GVEM 算法估计量的一致性。
Multidimensional item response theory (MIRT) is widely used in assessment and evaluation of educational and psychological tests. It models the individual response patterns by specifying a functional relationship between individuals' multiple latent traits and their responses to test items. One major challenge in parameter estimation in MIRT is that the likelihood involves intractable multidimensional integrals due to the latent variable structure. Various methods have been proposed that involve either direct numerical approximations to the integrals or Monte Carlo simulations. However, these methods are known to be computationally demanding in high dimensions and rely on sampling data points from a posterior distribution. We propose a new Gaussian variational expectation‐‐maximization (GVEM) algorithm which adopts variational inference to approximate the intractable marginal likelihood by a computationally feasible lower bound. In addition, the proposed algorithm can be applied to assess the dimensionality of the latent traits in an exploratory analysis. Simulation studies are conducted to demonstrate the computational efficiency and estimation precision of the new GVEM algorithm compared to the popular alternative Metropolis–Hastings Robbins–Monro algorithm. In addition, theoretical results are presented to establish the consistency of the estimator from the new GVEM algorithm.