Model comparison for generalized linear models with dependent observations

TL;DR

This paper introduces a quasi-Bayesian information criterion for generalized linear models with dependent data, extending classical BIC to handle misspecification and dependence, and proves its consistency.

Contribution

It proposes a new model selection criterion based on stochastic expansion of quasi-likelihood, extending BIC for dependent and potentially misspecified models, with theoretical consistency guarantees.

Findings

The criterion is consistent in selecting the true model.

Numerical examples demonstrate the effectiveness of the proposed method.

Real data analysis confirms practical applicability.

Abstract

The stochastic expansion of the marginal quasi-likelihood function associated with a class of generalized linear models is shown. Based on the expansion, a quasi-Bayesian information criterion is proposed that is able to deal with misspecified models and dependent data, resulting in a theoretical extension of the classical Schwarz's Bayesian information criterion. It is also proved that the proposed criterion has model selection consistency with respect to the optimal model. Some illustrative numerical examples and a real data example are presented.