Bootstrap-based model selection criteria for beta regressions

TL;DR

This paper introduces two bootstrap-based model selection criteria, BQCV and 632QCV, for beta regressions, demonstrating their effectiveness in small samples through simulations and empirical application.

Contribution

The paper proposes novel bootstrap-based criteria for model selection in beta regressions, improving small sample performance over traditional AIC-based methods.

Findings

Proposed criteria outperform AIC in small samples

Simulation results show better model selection accuracy

Empirical application validates practical usefulness

Abstract

The Akaike information criterion (AIC) is a model selection criterion widely used in practical applications. The AIC is an estimator of the log-likelihood expected value, and measures the discrepancy between the true model and the estimated model. In small samples the AIC is biased and tends to select overparameterized models. To circumvent that problem, we propose two new selection criteria, namely: the bootstrapped likelihood quasi-CV (BQCV) and its 632QCV variant. We use Monte Carlo simulation to compare the finite sample performances of the two proposed criteria to those of the AIC and its variations that use the bootstrapped log-likelihood in the class of varying dispersion beta regressions. The numerical evidence shows that the proposed model selection criteria perform well in small samples. We also present and discuss and empirical application.