A factor mixture analysis model for multivariate binary data

TL;DR

This paper introduces a novel latent variable model for multivariate binary data that combines factor analysis with mixture modeling to enable dimension reduction and clustering within heterogeneous populations.

Contribution

It replaces Gaussian assumptions with a finite mixture of Gaussians for factors, allowing simultaneous dimension reduction and clustering in binary data analysis.

Findings

Model effectively reduces dimensions in binary data.

Performs accurate clustering in the latent space.

Demonstrated through simulations and real data applications.

Abstract

The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite mixture of multivariate Gaussians. The aim of the proposed model is twofold: it allows to achieve dimension reduction when the data are dichotomous and, simultaneously, it performs model based clustering in the latent space. Model estimation is obtained by means of a maximum likelihood method via a generalized version of the EM algorithm. In order to evaluate the performance of the model a simulation study and two real applications are illustrated.