Fast leave-one-cluster-out cross-validation by clustered Network Information Criteria (NICc)

This paper introduced a clustered estimator of the Network Information Criterion (NICc) to approximate leave-one-cluster-out cross-validated deviance, which can be used as an alternative to cluster-based cross-validation when modeling clustered data. Stone proved that Akaike Information Criterion (AIC) is an asymptotic equivalence to leave-one-observation-out cross-validation if the parametric model is true. Ripley pointed out that the Network Information Criterion (NIC) derived in Stone's proof, is a better approximation to leave-one-observation-out cross-validation when the model is not true. For clustered data, we derived a clustered estimator of NIC, referred to as NICc, by substituting the Fisher information matrix in NIC with its estimator that adjusts for clustering. This adjustment imposes a larger penalty in NICc than the unclustered estimator of NIC when modeling clustered data, thereby preventing overfitting more effectively. In a simulation study and an empirical example, we used linear and logistic regression to model clustered data with Gaussian or binomial response, respectively. We showed that NICc is a better approximation to leave-one-cluster-out deviance and prevents overfitting more effectively than AIC and Bayesian Information Criterion (BIC). NICc leads to more accurate model selection, as determined by cluster-based cross-validation, compared to AIC and BIC.