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Penalized joint maximum likelihood estimation applied to two parameter logistic item response models.

机译：惩罚联合最大似然估计应用于两个参数逻辑项目响应模型。

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摘要

Item response theory (IRT) models are a conventional tool for analyzing both small scale and large scale educational data sets, and they are also used for the development of high-stakes tests such as the Scholastic Aptitude Test (SAT) and the Graduate Record Exam (GRE). When estimating these models it is imperative that the data set includes many more examinees than items, which is a similar requirement in regression modeling where many more observations than variables are needed. If this requirement has not been met the analysis will yield meaningless results. Recently, penalized estimation methods have been developed to analyze data sets that may include more variables than observations. The main focus of this study was to apply LASSO and ridge regression penalization techniques to IRT models in order to better estimate model parameters. The results of our simulations showed that this new estimation procedure called penalized joint maximum likelihood estimation provided meaningful estimates when IRT data sets included more items than examinees when traditional Bayesian estimation and marginal maximum likelihood methods were not appropriate. However, when the IRT datasets contained more examinees than items Bayesian estimation clearly outperformed both penalized joint maximum likelihood estimation and marginal maximum likelihood.
机译：项目反应理论（IRT）模型是分析小型和大型教育数据集的常规工具，还用于开发高学历测试，例如学术能力测验（SAT）和研究生成绩考试（GRE）。在估计这些模型时，必须确保数据集包含的考生比项目多得多，这在回归建模中是类似的要求，在回归建模中，需要的观察数多于变量。如果未满足此要求，则分析将产生无意义的结果。近来，已经开发出惩罚估计方法来分析可能包括比观察更多的变量的数据集。这项研究的主要重点是将LASSO和岭回归惩罚技术应用于IRT模型，以便更好地估计模型参数。我们的模拟结果表明，当传统的贝叶斯估计和边际最大似然方法不适用时，当IRT数据集包含比被测者更多的项目时，这种称为惩罚联合最大似然估计的新估计程序将提供有意义的估计。但是，当IRT数据集包含的考生多于项目时，贝叶斯估计明显优于罚分联合最大似然估计和边际最大似然。

著录项

  • 作者

    Paolino, Jon-Paul.;

  • 作者单位

    Columbia University.;

  • 授予单位 Columbia University.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 72 p.
  • 总页数 72
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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