Bayesian Model Selection Methods for Multilevel IRT Models: A Comparison of Five DIC‐Based Indices
Bayesian Model Selection Methods for Multilevel IRT Models: A Comparison of Five DIC‐Based Indices
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多级 IRT 模型的贝叶斯模型选择方法：五个基于 DIC 的指数的比较
DOI：
10.1111/jedm.12197
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发表时间：
2019
影响因子：
1.3
通讯作者：
N. Shi
中科院分区：
文献类型：
--
作者：
Xue Zhang;Jian Tao;Chun Wang;N. Shi
模型选择在任何统计分析中都很重要，主要目标是根据一定的标准，从给定数据的一组候选模型中找到首选的(或最简约的)模型。最近的一些文献使用偏差信息准则(DIC)在不同形式的多水平项目反应理论模型(MLIRT)中进行模型选择。大多数实践者使用WinBUGS来实现MLIRT模型的MCMC算法，而WinBUGS提供的默认版本的DIC只关注测量级别的参数。结果表明，该版本的DIC是不合适的。这项研究介绍了DIC的五个变种，作为MLIRT模型的一个模型选择指数。考虑到一个三层的多层IRT模型，形成了五种形式的DIC：仅根据测量模型计算的第一级条件DIC，这是WinBUGS等许多软件给出的指标；根据第二级模型计算的第二级边缘DIC和第二级联合DIC；以及从整个模型计算的顶级边缘DIC和顶级联合DIC。通过仿真研究，对五种模型选择指标的性能进行了评价。被操纵的因素包括组的数量、二级协变量的数量、顶级协变量的数量以及测量模型的类型(单参数与双参数)。考虑到计算的可行性和可解释性，在我们模拟的条件下，第二级联合DIC被推荐用于MLIRT模型。
Model selection is important in any statistical analysis, and the primary goal is to find the preferred (or most parsimonious) model, based on certain criteria, from a set of candidate models given data. Several recent publications have employed the deviance information criterion (DIC) to do model selection among different forms of multilevel item response theory models (MLIRT). The majority of the practitioners use WinBUGS for implementing MCMC algorithms for MLIRT models, and the default version of DIC provided by WinBUGS focused on the measurement‐level parameters only. The results herein show that this version of DIC is inappropriate. This study introduces five variants of DIC as a model selection index for MLIRT models with dichotomous outcomes. Considering a multilevel IRT model with three levels, five forms of DIC are formed: first‐level conditional DIC computed from the measurement model only, which is the index given by many software packages such as WinBUGS; second‐level marginalized DIC and second‐level joint DIC computed from the second‐level model; and top‐level marginalized DIC and top‐level joint DIC computed from the entire model. We evaluate the performance of the five model selection indices via simulation studies. The manipulated factors include the number of groups, the number of second‐level covariates, the number of top‐level covariates, and the types of measurement models (one‐parameter vs. two‐parameter). Considering the computational viability and interpretability, the second‐level joint DIC is recommended for MLIRT models under our simulated conditions.