Title: Analysis of longitudinal interval censored data using finite mixture of multivariate Student-t distributions
Authors: Christian Galarza - State University of Campinas (Brazil) [presenting]
Victor Hugo Lachos Davila - University of Connecticut (United States)
Abstract: Mixture models are based on the assumption of normality (symmetry) and thus are sensitive to outliers, heavy-tailed and skewness. Besides, these kind of data can be subject to some upper and/or lower detection limits because of the restriction of experimental apparatus. For such data structures, we present a proposal to deal with these issues simultaneously by propose an interval censored regression based on finite mixtures of multivariate Student-$t$ distributions. This approach allows us to model data with great flexibility, accommodating multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analytically simple yet efficient EM-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the multivariate truncated Student-$t$ distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimators is presented. Results obtained from the analysis of a part of Signal Tandmobiel data, which contains observed intervals of teeth emergence for 4430 Flemish children resulting from a longitudinal project, is reported to demonstrate the effectiveness of the proposed methodology.