连续型和二元混合随机变量的因子分析
Factor analysis for a mixture of continuous and binary random variables
摘要：
我们提出了一个多元概率分布模型的线性相关性之间的二元和连续变量。建议的分布是一个自然的扩展，以前开发的多元二进制分布。作为建议的分布的应用，我们开发了一个连续和二元变量的混合物的因子分析。我们还讨论了与因子分析相关的不适当的解决方案。作为避免不适当解的一种方法，我们提出了一个约束条件，即因子加载矩阵的各行向量具有相同的范数。通过对真实数据集的分析，对提出的因子分析和范数约束方法进行了数值验证.
英文摘要：
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.
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