Ridge Least Absolute Deviation Performance in Addressing Multicollinearity and Different Levels of Outlier Simultaneously

Abstract

If there is multicollinearity and outliers in the data, the inference about parameter estimation in the LS method will deviate due to the inefficiency of this method in estimating. To overcome these two problems simultaneously, it can be done using robust regression, one of which is ridge least absolute deviation method. This study aims to evaluate the performance of the ridge least absolute deviation method in surmounting multicollinearity in divers sample sizes and percentage of outliers using simulation data. The Monte Carlo study was designed in a multiple regression model with multicollinearity (ρ=0.99) between variables and and outliers 10%, 20%, 30% on response variables with different sample sizes (n = 25, 50,75,100,200; =0, and β=1 otherwise). The existence of multicollinearity in the data is done by calculating the correlation value between the independent variables and the VIF value. Outlier detection is done by using boxplot. Parameter estimation was carried out using the RLAD and LS methods. Furthermore, a comparison of the MSE values of the two methods is carried out to see which method is better in overcoming multicollinearity and outliers. The results showed that RLAD had a lower MSE than LS. This signifies that RLAD is more precise in estimating the regression coefficients for each sample size and various outlier levels studied.