Identifying Mixtures of Regression Equations by the SAR procedure

A procedure for identifying data heterogeneity when fitting regression models is presented. The method is based on the SAR procedure, developed by Peña and Tiao (2002), and has three steps. First, the sample is cleaned for large outliers by using a discrepancy measure based on predictive ordinates. Second, observations are split into small homogeneous groups by using a link function derived from cross validation predictive distributions. Third, these small groups are then iteratively enlarged by incorporating observations homogeneous to those in the group. In this way the possible piece-wise regression equations are found. Examples are shown to illustrate the performance of the procedure for finding mixtures of regressions due to the presence of outliers or to switching regression models. A Monte Carlo study of the power of the proposed procedure is presented.