Abstract:
The non-parametric Gaussian mixture of regressions (NPGMRs) model serves as a flexible
approach for the determination of latent heterogeneous regression relationships. This model assumes
that the component means, variances and mixing proportions are smooth unknown functions of
the covariates where the error distribution of each component is assumed to be Gaussian and
hence symmetric. These functions are estimated over a set of grid points using the Expectation-
Maximization (EM) algorithm to maximise the local-likelihood functions. However, maximizing
each local-likelihood function separately does not guarantee that the local responsibilities and
corresponding labels, obtained at the E-step of the EM algorithm, align at each grid point leading to
a label-switching problem. This results in non-smooth estimated component regression functions.
In this paper, we propose an estimation procedure to account for label switching by tracking the
roughness of the estimated component regression functions. We use the local responsibilities to
obtain a global estimate of the responsibilities which are then used to maximize each local-likelihood
function. The performance of the proposed procedure is demonstrated using a simulation study
and through an application using real world data. In the case of well-separated mixture regression
components, the procedure gives similar results to competitive methods. However, in the case of
poorly separated mixture regression components, the procedure outperforms competitive methods.
