We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As an application of the proposed distribution, we develop a factor analysis for a mixture of continuous and binary variables. We also discuss improper solutions associated with factor analysis. As a prescription to avoid improper solutions, we propose a constraint that each row vector of factor loading matrix has the same norm. We numerically validated the proposed factor analysis and norm constraint prescription by analyzing real datasets.

翻译：我们提出了一种多元概率分布，用于建模二元变量与连续变量之间的线性相关性。该分布是先前发展的多元二元分布的自然扩展。作为所提分布的应用，我们开发了针对连续与二元变量混合数据的因子分析方法。同时，我们讨论了因子分析中可能出现的非正常解问题。为避免此类非正常解，我们提出了因子载荷矩阵各行向量范数相等的约束条件。通过分析真实数据集，我们对所提出的因子分析方法及范数约束方案进行了数值验证。