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.
翻译：我们提出了一种适用于分类和顺序随机变量的多元概率分布。为此，我们结合Grassmann分布和分类和顺序变量的虚拟编码。为了实现分类和顺序变量所需的虚拟变量的共同出现概率，我们提出了一种Grassmann分布的简洁参数化方法，确保概率分布的正性。作为所提出的分布的应用，我们开发了一种适用于分类和顺序变量的因子分析，并使用真实数据集展示了该模型的有效性。
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