B1053
Title: Multicollinearity in treatment evaluation: A comparison between Lp-norm and least squares estimators
Authors: Massimiliano Giacalone - University of Campania Luigi Vanvitelli (Italy)
Eugenia Nissi - University G d Annunzio Chieti Pescara (Italy)
Massimiliano Giacalone - University of Campania Luigi Vanvitelli (Italy) [presenting]
Abstract: Multicollinearity is one of the most important issues in multiple regression analysis. It has a key role, especially in the assessment of treatment effects within the regression setting. Under multicollinearity ordinary least squares (OLS) method produces unstable coefficient estimates and the associate standard errors are severely inflated. In the context of treatment effect evaluation, collinearity does not allow for identifying the net contribution of the treatment effect from those deriving from control variables. In this framework, the regression theory is based on specific assumptions concerning the set of error random variables. In particular, when errors are uncorrelated and have a constant variance, the OLS estimators produce the best, linear unbiased estimates (BLUE) among all linear estimators. If the Gauss-Markov assumptions fail, alternative methods than OLS should be employed instead. A novel Lpmin approach is proposed, based on Lp-norm estimation, that is an adaptive robust procedure useful when the residual distribution assumptions deviate from normality. Lp-norm regression with Lpmin solution produces more efficient estimates of the model parameters than those generated by the OLS method, especially in the presence of multicollinearity. In order to show the better results provided by the Lpmin method a simulation study and a real-data application are finally presented.
