The Residual Information Criterion, Corrected

TL;DR

This paper identifies a flaw in the original residual information criterion (RIC) for regression model selection, demonstrating it always favors the saturated model, and proposes a corrected version to address this issue.

Contribution

The paper reveals the flaw in the original RIC based on residual likelihood and introduces a corrected RIC to improve model selection accuracy.

Findings

Original RIC always selects the saturated model

Residual likelihood is unsuitable for defining information criteria

Proposed corrected RIC improves model selection

Abstract

Shi and Tsai (JRSSB, 2002) proposed an interesting residual information criterion (RIC) for model selection in regression. Their RIC was motivated by the principle of minimizing the Kullback-Leibler discrepancy between the residual likelihoods of the true and candidate model. We show, however, under this principle, RIC would always choose the full (saturated) model. The residual likelihood therefore, is not appropriate as a discrepancy measure in defining information criterion. We explain why it is so and provide a corrected residual information criterion as a remedy.