Fox J-P
Department of Research Methodology, Measurement and Data Analysis, University of Twente, The Netherlands.
Br J Math Stat Psychol. 2005 May;58(Pt 1):145-72. doi: 10.1348/000711005X38951.
A structural multilevel model is presented where some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal polytomous response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel model. A Bayesian procedure Markov chain Monte Carlo (MCMC), to estimate all parameters simultaneously is presented. It is shown that certain model checks and model comparisons can be done using the MCMC output. The techniques are illustrated using a simulation study and an application involving students' achievements on a mathematics test and test results regarding management characteristics of teachers and principles.
本文提出了一种结构多层次模型，其中一些变量无法直接观测，而是通过测试或问卷进行测量。观测到的二分或有序多分类响应数据用于使用项目反应理论模型来测量潜在变量。潜在变量可以在多层次模型的任何层次上定义。本文提出了一种贝叶斯过程马尔可夫链蒙特卡罗（MCMC）方法，用于同时估计所有参数。结果表明，可以使用MCMC输出进行某些模型检验和模型比较。通过模拟研究和一个应用实例对这些技术进行了说明，该应用实例涉及学生在数学测试中的成绩以及关于教师和校长管理特征的测试结果。
