Alatent Gaussian mixturemodel to classify ordinal data is proposed. The observed categorical variables are considered as a discretization of an underlying finite mixture of Gaussians. The model is estimated within the expectation-maximization (EM) framework maximizing a pairwise likelihood. This allows us to overcome the computational problems arising in the full maximum likelihood approach due to the evaluation of multidimensional integrals that cannot be written in closed form. Moreover, a method to cluster the observations on the basis of the posterior probabilities in output of the pairwise EM algorithm is suggested. The effectiveness of the proposal is shown comparing the pairwise likelihood approach with the full maximum likelihood and the maximum likelihood for continuous data ignoring the ordinal nature of the variables. The comparison is made by means of a simulation study; applications to real data are provided.

Ranalli, M., Rocci, R. (2014). Mixture models for ordinal data: a pairwise likelihood approach. STATISTICS AND COMPUTING, -- [10.1007/s11222-014-9543-4].

Mixture models for ordinal data: a pairwise likelihood approach

ROCCI, ROBERTO
2014-01-01

Abstract

Alatent Gaussian mixturemodel to classify ordinal data is proposed. The observed categorical variables are considered as a discretization of an underlying finite mixture of Gaussians. The model is estimated within the expectation-maximization (EM) framework maximizing a pairwise likelihood. This allows us to overcome the computational problems arising in the full maximum likelihood approach due to the evaluation of multidimensional integrals that cannot be written in closed form. Moreover, a method to cluster the observations on the basis of the posterior probabilities in output of the pairwise EM algorithm is suggested. The effectiveness of the proposal is shown comparing the pairwise likelihood approach with the full maximum likelihood and the maximum likelihood for continuous data ignoring the ordinal nature of the variables. The comparison is made by means of a simulation study; applications to real data are provided.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore SECS-S/01 - Statistica
English
Con Impact Factor ISI
Finite mixture models, Composite likelihood, EM algorithm, Ordinal data
Ranalli, M., Rocci, R. (2014). Mixture models for ordinal data: a pairwise likelihood approach. STATISTICS AND COMPUTING, -- [10.1007/s11222-014-9543-4].
Ranalli, M; Rocci, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/129382
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