Bootstrap-based model selection criteria for beta regressions

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.