Title: Mixtures of seemingly unrelated linear regression models
Authors: Giuliano Galimberti - University of Bologna (Italy)
Gabriele Soffritti - University of Bologna (Italy) [presenting]
Abstract: Finite mixtures of Gaussian linear regression models represent a flexible tool to perform linear regression analysis in the presence of a finite number of heterogeneous populations, each of which is characterized by a different Gaussian linear regression model. These models naturally arise when relevant categorical predictors are omitted from a regression model. With several responses, such an approach makes it possible to take into account the correlation among responses that typically occur in longitudinal data, time-series data or repeated measures. In most of the models developed so far, the same regressors have to be used for all responses. This restriction is relaxed by allowing different regressors for each response, as in the seemingly unrelated regression framework. Parsimonious models are specified, by constraining the component-covariance matrices using a parameterisation that exploits their spectral decomposition. Details about model identification and maximum likelihood estimation are given. The usefulness of these models is shown through the analysis of a real dataset. The consistency of the maximum likelihood estimator under the proposed models is proved. The behaviour of this estimator in the presence of finite samples is numerically evaluated through the analysis of simulated datasets.