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Modeling Dependence Structures for Response Times in a Bayesian Framework

机译:在贝叶斯框架中为响应时间建立依赖关系模型

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摘要

A multivariate generalization of the log-normal model for response times is proposed within an innovative Bayesian modeling framework. A novel Bayesian Covariance Structure Model (BCSM) is proposed, where the inclusion of random-effect variables is avoided, while their implied dependencies are modeled directly through an additive covariance structure. This makes it possible to jointly model complex dependencies due to for instance the test format (e.g., testlets, complex constructs), time limits, or features of digitally based assessments. A class of conjugate priors is proposed for the random-effect variance parameters in the BCSM framework. They give support to testing the presence of random effects, reduce boundary effects by allowing non-positive (co)variance parameters, and support accurate estimation even for very small true variance parameters. The conjugate priors under the BCSM lead to efficient posterior computation. Bayes factors and the Bayesian Information Criterion are discussed for the purpose of model selection in the new framework. In two simulation studies, a satisfying performance of the MCMC algorithm and of the Bayes factor is shown. In comparison with parameter expansion through a half-Cauchy prior, estimates of variance parameters close to zero show no bias and undercoverage of credible intervals is avoided. An empirical example showcases the utility of the BCSM for response times to test the influence of item presentation formats on the test performance of students in a Latin square experimental design.
机译:在创新的贝叶斯建模框架内,提出了对数正态模型的响应时间的多元概括。提出了一种新颖的贝叶斯协方差结构模型(BCSM),其中避免了随机效应变量的包含,而其隐含依赖性直接通过加性协方差结构建模。由于例如测试格式(例如,测试,复杂结构),时间限制或基于数字的评估功能,因此可以对复杂的依赖关系进行联合建模。针对BCSM框架中的随机效应方差参数,提出了一类共轭先验。它们为测试随机效应的存在提供了支持,通过允许使用非正(协)方差参数来减少边界效应,甚至为非常小的真实方差参数提供了精确的估计。 BCSM下的共轭先验导致有效的后验计算。为了在新框架中选择模型,讨论了贝叶斯因子和贝叶斯信息准则。在两个仿真研究中,显示了MCMC算法和贝叶斯因子的令人满意的性能。与通过半Cauchy先验进行参数扩展相比,方差参数的估计接近于零显示没有偏差,并且避免了可信区间的覆盖不足。一个经验示例展示了BCSM在响应时间上的效用,以测试项目展示格式对拉丁方实验设计中学生测试成绩的影响。

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