A hybridized consistent Akaike type information criterion for regression models in the presence of multicollinearity

Consistent Akaike information criterion (CAIC) is an adjusted form of classical AIC. This criterion was developed by modifying the penalty. As a result, we propose a novel AIC type criterion, called CAIC (nα). The proposed criterion includes a dynamic parameter for controlling the penalty further. The distinctive feature of CAIC (nα) is to penalize multicollinearity level considering the information complexity measures. CAIC (nα) requires the α parameter, and in addition, a procedure is proposed to estimate α based on the information complexity of the regression model. Monte Carlo simulations and real data set examples demonstrate that CAIC (nα) performs better than classical information criteria for the potential multicollinearity problems.