Comparison of fast regression algorithms in large datasets

The aim is to compare the performances of fast regression methods, namely dimensional reduction of correlation matrix (DRCM), nonparametric dimensional reduction of correlation matrix (N-DRCM), variance inflation factor (VIF) regression, and robust VIF (R-VIF) regression in the presence of multicollinearity and outliers problems. In all simulation-scenarios, all the target variables were chosen for final models using four methods. The DRCM and N-DRCM are the methods that reach the final model in the shortest time, respectively. The time to reach the final model using R-VIF regression was approximately twice shorter than that of VIF regression. In each method, as the number of variables and the level of outliers increased, the time taken to reach the final model increased. When the level of multicollinearity and the number of variables (p > 500) increased, the times to reach the final models using DRCM in datasets with outliers were slightly shorter than the those of N-DRCM. The largest numbers of noise variables were selected to the model using DRCM and N-DRCM, but the least number of them were selected to the model using the R-VIF regression. The RMSE values obtained using DRCM, N-DRCM and VIF regression were similar in each scenario. As a result of the real dataset, the final model selected using R-VIF regression had the highest R2. It also had the lowest RMSE value among those obtained with other approaches excluding VIF regression. As such, the R-VIF regression method demonstrated a better performance than the others in all datasets.