标题： 多变量概率分布用于类别和有序随机变量 显示英文标题

标题： Multivariate probability distribution for categorical and ordinal random variables

摘要： 我们为分类和有序随机变量提出一种多变量概率分布。 为此，我们结合格拉斯曼分布与分类和有序变量的虚拟编码。 为了实现分类和有序变量所需的虚拟变量共现概率，我们为格拉斯曼分布提出一种简洁的参数化方法，以确保概率分布的非负性。 作为所提分布的应用，我们开发了一种用于分类和有序变量的因素分析，并使用真实数据集验证了该模型的有效性。 显示英文摘要

摘要： We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the co-occurrence probabilities of dummy variables required for categorical and ordinal variables, we propose a parsimonious parameterization for the Grassmann distribution that ensures the positivity of probability distribution. As an application of the proposed distribution, we develop a factor analysis for categorical and ordinal variables and show the validity of the model using a real dataset.