Model selection for extended quasi-likelihood models in small samples

Area of Science:

• Statistics
• Statistical Modeling
• Econometrics

Background:

• Model selection is crucial in statistical analysis, especially with generalized linear models.
• Existing criteria like AIC may exhibit bias in small sample sizes.
• Accurate model selection ensures reliable inference and prediction.

Purpose of the Study:

• To introduce and evaluate a corrected Akaike Information Criterion (AICc) for small sample model selection.
• To assess the performance of AICc against other criteria in extended quasi-likelihood and logistic regression models.
• To provide a more nearly unbiased estimator for expected Kullback-Leibler information.

Main Methods:

• Development of the small sample criterion (AICc).
• Comparison of AICc with Akaike Information Criterion (AIC), Pregibon's Cp*, and Hosmer et al.'s Cp criteria.
• Monte Carlo simulations were used to evaluate performance in logistic regression.

Main Results:

• AICc provides a more nearly unbiased estimator for expected Kullback-Leibler information compared to AIC.
• AICc demonstrates superior model selection performance over AIC, Cp*, and Hosmer et al.'s Cp in small samples.
• Monte Carlo results confirm AICc's effectiveness for logistic regression models.

Conclusions:

• AICc is a valuable tool for model selection in small sample situations.
• The criterion offers improved accuracy and reduced bias in estimating model fit.
• AICc is recommended for selecting extended quasi-likelihood and logistic regression models with limited data.