Bootstrap-adjusted quasi-likelihood information criteria for mixed model selection

We propose two model selection criteria relying on the bootstrap approach, denoted by QAICb1 and QAICb2, in the framework of linear mixed models. Similar to the justification of Akaike Information Criterion (AIC), the proposed QAICb1 and QAICb2 are proved as asymptotically unbiased estimators of the Kullback–Leibler discrepancy between a candidate model and the true model. However, they are defined on the quasi-likelihood function instead of the likelihood and are proven to be asymptotically equivalent. The proposed selection criteria are constructed by the quasi-likelihood of a candidate model and a bias estimation term in which the bootstrap method is adopted to improve the estimation for the bias caused by using the candidate model to estimate the true model. The simulations across a variety of mixed model settings are conducted to demonstrate that the proposed selection criteria outperform some other existing model selection criteria in selecting the true model. Generalized estimating equations (GEE) are utilized to calculate QAICb1 and QAICb2 in the simulations. The effectiveness of the proposed selection criteria is also demonstrated in an application of Parkinson's Progression Markers Initiative (PPMI) data.