Title: A possible solution to the label-switching problem in fitting nonparametric mixture of regressions
Authors: Sphiwe Skhosana - University of Pretoria (South Africa) [presenting]
Frans Kanfer - University of Pretoria (South Africa)
Sollie Millard - University of Pretoria (South Africa)
Abstract: A nonparametric mixture of regressions (NMR), where the component regression functions have an unknown functional form but are assumed to be smooth functions of the covariate, provide a flexible approach to the analysis of heterogeneous regression relationships. The nonparametric regression functions are typically estimated over a set of grid points using local likelihood estimation via the Expectation-Maximization (EM) algorithm. However, maximizing each local likelihood function does not guarantee that the component labels will match at each grid point. We, therefore, have a potential label-switching problem. We propose a possible solution to the label switching problem which relies on the smoothness assumption of the nonparametric regression functions. Since the component labels at each grid point contain similar information about the data, we simultaneously maximize the local likelihood functions for each set of component labels and consider, as our final model, the solution that results in the smoothest component regression functions.