Evaluating modified generalized information criterion in presence of multicollinearity

When there are many explanatory variables in the regression model, there is a chance that some of these are intercorrelated. This is where the problem of multicollinearity creeps in due to which precision and accuracy of the coefficients is marred, and the quest to find the best model becomes tedious. To tackle such a situation, Model selection criteria are applied for selecting the best model that fits the data. Current study focuses on the evaluation of the four unmodified and four modified versions of generalized information criteria—Akaike Information Criterion, Schwarz's Bayes Information Criteria, Hannan-Quinn Information Criterion, and Akaike Information Criterion corrected for small samples. A simulation study using SAS software was carried out in order to compare the unmodified and modified versions of the generalized information criteria and to discover the best version amongst the four modified model selection criteria, for identifying the best model, when the collinearity assumption is violated. For the proposed simulation, two samples of size 50 and 100, for three explanatory variables X₁, X₂, and X₃, are drawn from Normal distribution. Two situations of collinearity violations between X₁ and X₂ are looked into, first when ρ = 0.6 and second when ρ = 0.8. The outcomes of the simulations are displayed in the tables along with visual representations. The results revealed that modified versions of the generalized information criteria are more sensitive in identifying models marred with high multicollinearity as compared to the unmodified generalized information criteria.