Department of Research Methodology, Measurement and Data Analysis, University of Twente, P.O. Box 217, 7500 AE , Enschede, The Netherlands.
Tilburg University, Tilburg, The Netherlands.
Psychometrika. 2017 Dec;82(4):979-1006. doi: 10.1007/s11336-017-9577-6. Epub 2017 Aug 29.
Two marginal one-parameter item response theory models are introduced, by integrating out the latent variable or random item parameter. It is shown that both marginal response models are multivariate (probit) models with a compound symmetry covariance structure. Several common hypotheses concerning the underlying covariance structure are evaluated using (fractional) Bayes factor tests. The support for a unidimensional factor (i.e., assumption of local independence) and differential item functioning are evaluated by testing the covariance components. The posterior distribution of common covariance components is obtained in closed form by transforming latent responses with an orthogonal (Helmert) matrix. This posterior distribution is defined as a shifted-inverse-gamma, thereby introducing a default prior and a balanced prior distribution. Based on that, an MCMC algorithm is described to estimate all model parameters and to compute (fractional) Bayes factor tests. Simulation studies are used to show that the (fractional) Bayes factor tests have good properties for testing the underlying covariance structure of binary response data. The method is illustrated with two real data studies.
引入了两种边际单参数项目反应理论模型，通过整合潜在变量或随机项目参数。结果表明，两种边际响应模型都是具有复合对称协方差结构的多元（概率单位）模型。使用（分数）贝叶斯因子检验评估了关于潜在协方差结构的几个常见假设。通过测试协方差分量评估单维因子（即局部独立性假设）和差异项目功能的支持。通过使用正交（Helmert）矩阵转换潜在响应，获得常见协方差分量的后验分布。该后验分布定义为移位逆伽马分布，从而引入默认先验和平衡先验分布。在此基础上，描述了一种 MCMC 算法来估计所有模型参数并计算（分数）贝叶斯因子检验。模拟研究表明，（分数）贝叶斯因子检验对于检验二项反应数据的潜在协方差结构具有良好的特性。该方法通过两个真实数据研究进行了说明。
