Factor analysis for a mixture of continuous and binary random variables

TL;DR

This paper introduces a new multivariate distribution for modeling correlations between binary and continuous variables and develops a factor analysis method for such mixed data, addressing issues of improper solutions with a norm constraint.

Contribution

It extends multivariate binary distributions to include continuous variables and proposes a factor analysis method with a norm constraint to prevent improper solutions.

Findings

Validated the proposed factor analysis on real datasets.

Demonstrated effectiveness of the norm constraint in avoiding improper solutions.

Showed the model captures correlations between mixed variable types.

Abstract

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.