Title: Total sum of squares decomposition for mixtures of regressions
Authors: Salvatore Ingrassia - University of Catania (Italy) [presenting]
Antonio Punzo - University of Catania (Italy)
Abstract: A three-term decomposition of the total sum of squares is proposed for mixtures of linear regressions whose parameters are estimated by maximum likelihood, via the expectation-maximization algorithm, under normally distributed errors in each mixture component. In particular, three types of mixtures of regressions are considered: with fixed covariates, with concomitant variables, and with random covariates. A ternary diagram is also suggested to make easier the joint interpretation of the three terms of the proposed decomposition. Furthermore, local and overall coefficients of determination are respectively defined to judge how well the model fits the data group-by-group but also taken as a whole. Artificial data are considered to find out more about the proposed decomposition, including violations of the model assumptions. Finally, an application to real data illustrates the use and the usefulness of these proposals.