Exploring the Performance of Methods to Deal Multicollinearity: Simulation and Real Data in Radiation Epidemiology Area

The issue of multicollinearity has long been acknowledged in statistical modelling; however, it is often untreated in the most of published papers. Indeed, the use of methods for multicollinearity correction is still scarce. One important reason is that despite many proposed methods, little is known about their strength or performance. We compare the statistical properties and performance of four main techniques to correct multicollinearity, i.e., Ridge Regression (R-R), Principal Components Regression (PC-R), Partial Least Squares Regression (PLS-R), and Lasso Regression (L-R), in both a simulation study and two real data examples used for modelling volumes of heart and Thyroid as a function of clinical and anthropometric parameters. We find that when the statistical approaches were used to address different levels of collinearity, we observed that R-R, PC-R and PLS-R appeared to have a somewhat similar behavior, with a slight advantage for the PLS-R. Indeed, in all implemented cases, the PLS-R always provided the smallest value of root mean square error (RMSE). When the degree of collinearity was moderate, low or very low, the L-R method had also somewhat similar performance to other methods. Furthermore, correction methods allowed us to provide stable and trustworthy parameter estimates for predictors in the modelling of heart and Thyroid volumes. Therefore, this work will contribute to highlighting performances of methods used only for situations ranging from low to very high multicollinearity.