Statistical Modelling 12 (2012), 257–277

A factor mixture analysis model for multivariate binary data

Silvia Cagnone
Department of Statistics,
University of Bologna
Bologna
Italy

Cinzia Viroli
Department of Statistics,
University of Bologna
via Belle Arti 41
I–40126 Bologna
Italy
eMail: cinzia.viroli@unibo.it

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.

Keywords:

model based clustering; latent trait analysis; EM algorithm

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