Karabatsos George, Walker Stephen G
College of Education, University of Illinosis-Chicago, 60607, USA.
Br J Math Stat Psychol. 2009 Feb;62(Pt 1):1-20. doi: 10.1348/000711007X246237. Epub 2007 Sep 27.
In this paper we argue that model selection, as commonly practised in psychometrics, violates certain principles of coherence. On the other hand, we show that Bayesian nonparametrics provides a coherent basis for model selection, through the use of a 'nonparametric' prior distribution that has a large support on the space of sampling distributions. We illustrate model selection under the Bayesian nonparametric approach, through the analysis of real questionnaire data. Also, we present ways to use the Bayesian nonparametric framework to define very flexible psychometric models, through the specification of a nonparametric prior distribution that supports all distribution functions for the inverse link, including the standard logistic distribution functions. The Bayesian nonparametric approach provides a coherent method for model selection that can be applied to any statistical model, including psychometric models. Moreover, under a 'non-informative' choice of nonparametric prior, the Bayesian nonparametric approach is easy to apply, and selects the model that maximizes the log likelihood. Thus, under this choice of prior, the approach can be extended to non-Bayesian settings where the parameters of the competing models are estimated by likelihood maximization, and it can be used with any psychometric software package that routinely reports the model log likelihood.
在本文中，我们认为心理测量学中常用的模型选择方法违反了某些一致性原则。另一方面，我们表明贝叶斯非参数方法通过使用在抽样分布空间上具有广泛支持的“非参数”先验分布，为模型选择提供了一个一致的基础。我们通过对实际问卷数据的分析，阐述了贝叶斯非参数方法下的模型选择。此外，我们还介绍了通过指定支持逆链接的所有分布函数（包括标准逻辑分布函数）的非参数先验分布，利用贝叶斯非参数框架来定义非常灵活的心理测量模型的方法。贝叶斯非参数方法为模型选择提供了一种一致的方法，可应用于任何统计模型，包括心理测量模型。此外，在非参数先验的“无信息”选择下，贝叶斯非参数方法易于应用，并选择使对数似然最大化的模型。因此，在先验的这种选择下，该方法可以扩展到通过似然最大化估计竞争模型参数的非贝叶斯设置中，并且可以与任何常规报告模型对数似然的心理测量软件包一起使用。
