Handling Multicollinearity; A Comparative Study Of The Prediction Performance Of Some Methods Based On Some Probabiltiy Distributions

摘要

This study used some probability distribution (Gamma, Beta and Chi-square distributions) to assess the performance of partial least square regression (PLSR), ridge regression (RR) and LASSO regression (LR) methods. Ordinary Least Squares may fail if the variables are almost collinear or related. As such, this methods (PLSR, RR, AND LR) were compared using simulated data that follows gamma, beta and chi-square distributions with number variables (P=4 and 10) and sample sizes (n=60 and 90). The comparison was carried out using Mean Square Log Error (MSLE), Mean Absolute Error (MAE) and R-Square (R2) which shows that the results of RR is better when P=4 and n=60 using gamma distribution, but using chi square distribution PLRS is better methods. Also, when P=4 and n=90, RR shows better results with both gamma and beta distributions but with chi square distribution all methods have equal predictive ability. However, at P=10 and n=60 RR performed better with both gamma and chi square distributions while when data follows beta distribution all distributions have equal predictive ability. RR shows better results at both gamma and chi square distributions when P=10 and n=90 while PLSR performed better with beta distribution.