When and when not to use optimal model averaging

TL;DR

This paper critically examines optimal model averaging methods, highlighting their limitations in addressing model selection uncertainty and proposing their use as complementary tools in machine learning and causal inference.

Contribution

It clarifies the role of risk-minimizing model averaging estimators, emphasizing their utility beyond traditional model selection, especially in machine learning and causal analysis.

Findings

Risk-minimizing estimators do not fully address model selection uncertainty.

Model averaging can be a useful tool for causal parameter identification.

Simulation studies demonstrate the practical implications of these insights.

Abstract

Traditionally model averaging has been viewed as an alternative to model selection with the ultimate goal to incorporate the uncertainty associated with the model selection process in standard errors and confidence intervals by using a weighted combination of candidate models. In recent years, a new class of model averaging estimators has emerged in the literature, suggesting to combine models such that the squared risk, or other risk functions, are minimized. We argue that, contrary to popular belief, these estimators do not necessarily address the challenges induced by model selection uncertainty, but should be regarded as attractive complements for the machine learning and forecasting literature, as well as tools to identify causal parameters. We illustrate our point by means of several targeted simulation studies.