B0722
Title: Using mixtures in seemingly unrelated linear regression models with non-normal errors
Authors: Giuliano Galimberti - University of Bologna (Italy) [presenting]
Gabriele Soffritti - University of Bologna (Italy)
Abstract: Seemingly unrelated regression equations (SURE) refers a set of equations for modelling the dependence of $D$ variables ($D \geq 1$) on one or more regressors in which the error terms in the different equations are allowed to be correlated. In such situations, the equations should be jointly considered. Most of the methods that have been developed to deal with SURE are based on the assumption that the distribution of the error terms is multivariate Gaussian. In order to allow departures from this assumption, the use of multivariate Gaussian mixtures is proposed. This approach has the advantage of capturing the effect of unobserved nominal regressors from the model and obtaining robust estimates of the regression coefficients when the distribution of the error terms is non-normal. Identifiability conditions for this new class of models are provided. The score vector and the hessian matrix of the corresponding log-likelihood function are derived. Maximum likelihood estimates for the unknown parameters are computed using an Expectation-Maximisation algorithm. In order to select the number of mixture components, the use of information criteria is suggested. The properties and the usefulness of the proposed methods are illustrated through the analysis of simulated and real datasets.
