Revuelta Javier, Ximénez Carmen
Department of Psychology, Autonoma University of MadridMadrid, Spain.
Front Psychol. 2017 Jun 16;8:961. doi: 10.3389/fpsyg.2017.00961. eCollection 2017.
This article introduces Bayesian estimation and evaluation procedures for the multidimensional nominal response model. The utility of this model is to perform a nominal factor analysis of items that consist of a finite number of unordered response categories. The key aspect of the model, in comparison with traditional factorial model, is that there is a slope for each response category on the latent dimensions, instead of having slopes associated to the items. The extended parameterization of the multidimensional nominal response model requires large samples for estimation. When sample size is of a moderate or small size, some of these parameters may be weakly empirically identifiable and the estimation algorithm may run into difficulties. We propose a Bayesian MCMC inferential algorithm to estimate the parameters and the number of dimensions underlying the multidimensional nominal response model. Two Bayesian approaches to model evaluation were compared: discrepancy statistics (DIC, WAICC, and LOO) that provide an indication of the relative merit of different models, and the standardized generalized discrepancy measure that requires resampling data and is computationally more involved. A simulation study was conducted to compare these two approaches, and the results show that the standardized generalized discrepancy measure can be used to reliably estimate the dimensionality of the model whereas the discrepancy statistics are questionable. The paper also includes an example with real data in the context of learning styles, in which the model is used to conduct an exploratory factor analysis of nominal data.
本文介绍了多维名义响应模型的贝叶斯估计和评估程序。该模型的作用是对由有限数量的无序响应类别组成的项目进行名义因子分析。与传统因子模型相比，该模型的关键之处在于，在潜在维度上每个响应类别都有一个斜率，而不是将斜率与项目相关联。多维名义响应模型的扩展参数化需要大样本进行估计。当样本量适中或较小时，其中一些参数在经验上可能难以识别，并且估计算法可能会遇到困难。我们提出了一种贝叶斯MCMC推理算法来估计多维名义响应模型的参数和潜在维度的数量。比较了两种用于模型评估的贝叶斯方法：提供不同模型相对优劣指示的差异统计量（DIC、WAICC和LOO），以及需要对数据进行重采样且计算量更大的标准化广义差异度量。进行了一项模拟研究来比较这两种方法，结果表明标准化广义差异度量可用于可靠地估计模型的维度，而差异统计量则存在问题。本文还包括一个在学习风格背景下的真实数据示例，其中该模型用于对名义数据进行探索性因子分析。
