Seminario
A COMPOSITE LIKELIHOOD APPROACH TO CLUSTER ORDINAL DATA
Prof. Roberto Rocci - Università degli Studi di Roma "Tor Vergata"
Lunedì 20 Marzo 2017, Aula 101, ore 15.30
Abstract: A latent Gaussian mixture model to classify ordinal data is discussed. 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 composite 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 output of the composite EM algorithm is suggested.
Some extensions of the model are also discussed: the case where some variables are continuous and the case where some noise variables/dimensions mask the clustering structure. In the latter, the noise dimensions are detected considering the variables underlying the ordinal data to be linear combinations of two independent sets of second-order latent variables where only one contains the information about the clustering structure.
The effectiveness of the proposals is shown comparing the composite 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 on real and simulated data sets.