Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology, where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants' responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.

因子分析是一种用于评估多变量依赖性和相互依赖性的灵活技术。除了作为用于降低多元数据维度的探索性工具之外，它还可以估计在实际问题中通常具有有趣的理论解释的共同因素。然而，标准因子分析仅适用于对变量进行缩放的情况，这通常是不合适的，例如，在从心理学领域的问卷调查中获得的数据中，变量通常是分类的。在此框架中，我们提出了一种用于分析多元有序和无序多分类数据的因子模型。推理过程是通过马尔可夫链蒙特卡罗方法在贝叶斯方法下完成的。提出了两项​​蒙特卡罗模拟研究，以研究该方法在估计偏差、精度和因素数量评估方面的性能。我们还说明了所提出的方法来分析参与者对动机状态问卷数据集的反应，该数据集是为了研究实验室和现场环境中的情绪而开发的。