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Bayesian explanatory additive IRT models
British Journal of Mathematical and Statistical Psychology ( IF 2.6 ) Pub Date : 2021-06-05 , DOI: 10.1111/bmsp.12245
Patrick Mair 1 , Kathrin Gruber 2
Affiliation  

In this article we extend the framework of explanatory mixed IRT models to a more general class called explanatory additive IRT models. We do this by augmenting the linear predictors in terms of smooth functions. This development offers many new modeling options such as the inclusion of nonlinear covariate effects, the specification of various temporal and spatial dependency patterns, and parameter partitioning across covariates. We use integrated nested Laplace approximation (INLA) for accurate and computationally efficient estimation of the parameters. Uninformative, weakly informative, and informative prior settings for the hyperparameters are discussed. Running time experiments and Monte Carlo parameter recovery simulations are performed in order to study the accuracy and computational efficiency of INLA when applied to the proposed explanatory additive IRT model class. Using a real-life dataset, a variety of application scenarios is explored, and the results are compared with classical maximum likelihood estimation when possible. R code is included in the supplemental materials to allow readers to fully reproduce the examples computed in the paper.

中文翻译:

贝叶斯解释性加性 IRT 模型

在本文中,我们将解释性混合 IRT 模型的框架扩展到更通用的类,称为解释性加性 IRT 模型。我们通过在平滑函数方面增加线性预测变量来做到这一点。这一发展提供了许多新的建模选项,例如包含非线性协变量效应、各种时间和空间依赖模式的规范以及跨协变量的参数划分。我们使用集成嵌套拉普拉斯近似 (INLA) 来准确和计算有效地估计参数。讨论了超参数的非信息性、弱信息性和信息性先验设置。运行时间实验和蒙特卡洛参数恢复模拟是为了研究 INLA 在应用于所提出的解释性加性 IRT 模型类时的准确性和计算效率。使用现实生活中的数据集,探索各种应用场景,并在可能的情况下将结果与经典的最大似然估计进行比较。补充材料中包含 R 代码,以使读者能够完全重现论文中计算的示例。
更新日期:2021-06-05
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