A Trivariate Geometric Classification of Decision Boundaries for Mixtures of Regressions

Mixtures of regressions play a prominent role in regression analysis when it is known the population of interest is divided into homogeneous and disjoint groups. This typically consists in partitioning the observational space into several regions through particular hypersurfaces called decision boundaries. A geometrical analysis of these surfaces allows to highlight properties of the used classifier. In particular, a geometrical classification of decision boundaries for the three most used mixtures of regressions (with fixed covariates, with concomitant variables and random covariates) was provided in case of one and two covariates, under Gaussian assumptions and in presence of only one real response variable. This work aims to extend these results to a more complex setting where three independent variables are considered.