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：我们建议多变量概率分布, 以模拟二进制变量和连续变量之间的线性关联。 拟议的分布是先前开发的多变量二进制分布的自然延伸。 作为拟议分布的一种应用, 我们为连续变量和二进制变量的混合开发一个要素分析。 我们还讨论与要素分析相关的不适当解决方案。 作为避免不正确解决方案的处方, 我们提出一个限制, 即每个行要素载荷矩阵的矢量都有相同的规范。 我们通过分析真实数据集, 以数字方式验证了拟议要素分析和规范约束处方 。