Efficient Full Information Maximum Likelihood Estimation for Multidimensional IRT Models. Research Report. ETS RR-09-03.
Efficient Full Information Maximum Likelihood Estimation for Multidimensional IRT Models. Research Report. ETS RR-09-03.
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多维 IRT 模型的高效全信息最大似然估计。
DOI：
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发表时间：
2009
期刊：
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通讯作者：
F. Rijmen
中科院分区：
文献类型：
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作者：
F. Rijmen
多维项目反应理论（IRT）模型的最大边际似然估计一直受到能力分布多维积分计算的阻碍。然而，研究者往往对潜在变量之间的条件依赖关系有一个特定的假设。利用这些关系可以产生更有效的估计算法。一个著名的例子是双因素模型，其中每个项目测量一个一般维度和K个其他维度中的一个，Gibbons和Hedeker（1992）表明，全信息最大似然估计只需要在二维积分上进行积分。在本文中，展示了如何将Gibbons和Hedeker（1992）的方法放入图形模型框架中。图形模型框架的优点是，通过将算法应用于统计模型的图形表示，可以以全自动的方式推导出有效的估计方案。这使得该方法相当普遍地适用，并且不再涉及繁琐的手工推导。通过将该方法应用于具有二阶维的多维IRT模型，证明了该方法的通用性。结果表明，这种模型的全信息最大似然估计也只需要求二维积分。
Maximum marginal likelihood estimation of multidimensional item response theory (IRT) models has been hampered by the calculation of the multidimensional integral over the ability distribution. However, the researcher often has a specific hypothesis about the conditional (in)dependence relations among the latent variables. Exploiting these relations may result in more efficient estimation algorithms. A well-known example is the bi-factor model, in which each item measures a general dimension and one of K other dimensions, for which Gibbons and Hedeker (1992) showed that full information maximum likelihood estimation only requires the integration over two-dimensional integrals. In this paper, it is shown how the approach of Gibbons and Hedeker (1992) can be placed into a graphical model framework. The advantage of the graphical model framework is that efficient estimation schemes can be derived in a fully automatic way by applying algorithms to the graphical representation of a statistical model. This renders the approach fairly generally applicable, and tedious derivations by hand are no longer involved. The generality of the approach is demonstrated by applying it to a multidimensional IRT model with a second order dimension. It turns out that full information maximum likelihood estimation for such a model also requires the evaluation of two-dimensional integrals only.