A modelling framework for regression with collinearity

This study addresses a fundamental, yet overlooked, gap between standard theory and empirical modelling practices in the OLS regression model y=Xβ+u with collinearity. In fact, while an estimated practice is desired to have stability efficiency its “individual estimates”, y itself has no capacity identify control collinearity X hence including selection process (MSP) would fill this unless controlled view of sampling theory. paper, first introducing new concept “empirically effective modelling” (EEM), we propose our EEM methodology (EEM-M) as integrated two MSPs data (yo,X) given. The MSP uses only, called XMSP, pre-selects class D models individually inefficiency-controlled collinearity-controlled estimates, where corresponding controlling variables are chosen from predictive error each estimate. Next, defining inefficiency-collinearity risk index for model, partial ordering introduced onto set compare without using yo, better-ness admissibility discussed. second commonly used that (yo,X), evaluates total performance whole by such AIC, BIC, etc. select optimal D. Third, materialize algorithms proposed.