Robust Fitting for Generalized Additive Models for Location, Scale and Shape

TL;DR

This paper introduces a robust fitting approach for GAMLSS models that mitigates the impact of outliers and deviations from likelihood assumptions, improving estimation stability and smoothing parameter selection.

Contribution

It proposes a general robustification method for GAMLSS, including robust smoothing parameter selection and a novel median downweighting criterion for non-linear effects.

Findings

Robust methods outperform traditional likelihood-based approaches in simulations.

Automatic smoothing parameter selection is effective with the extended Fellner-Schall method.

The approach demonstrates good performance in brain imaging data analysis.

Abstract

The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such assumption are known to mislead any likelihood-based inference and can hinder penalization schemes meant to ensure some degree of smoothness for non-linear effects. We propose a general approach to achieve robustness in fitting GAMLSSs by limiting the contribution of observations with low log-likelihood values. Robust selection of the smoothing parameters can be carried out either by minimizing information criteria that naturally arise from the robustified likelihood or via an extended Fellner-Schall method. The latter allows for automatic smoothing parameter selection and is particularly advantageous in applications with multiple smoothing parameters. We also address the challenge of tuning robust estimators for models with non-linear effects by proposing a novel median downweighting proportion criterion. This enables a fair comparison with existing robust estimators for the special case of generalized additive models, where our estimator competes favorably. The overall good performance of our proposal is illustrated by further simulations in the GAMLSS setting and by an application to functional magnetic resonance brain imaging using bivariate smoothing splines.