Estimation of Multiple Linear Regression Analysis Coefficients with Multicollinearity by Ridge Regression and Cuckoo Search

Abstract

The purpose of this study is to estimate the coefficients in multiple linear regression analysis that has multicollinearity problems by the method of Ridge Regression by Hoerl, Kennard and Baldwin compare with those method by the Cuckoo Search using Mean Squared Error (MSE) as the objective function. The efficiency criteria are MSE and Variance Inflation Factor (VIF). The comparison, using a simulation data composes of 3 independent variables with a sample size 30 and a real data set consists of 14 independent variables with 252 observations. In the Cuckoo Search Algorithms, 5, 10 and 15 iterations of searching r constant in ridge, 20 nests and 100, 500, 1,000, 5,000 and 10,000 repeated times are proposed. The result revealed that, the Ridge Regression by the Cuckoo Search with 15 iterations of searching r constant and 10,000 times of repetition gives the most appropriate regression coefficients. Moreover, those method by the Cuckoo Search also provides regression coefficients with lower MSE and VIF values than those method by Hoerl, Kennard and Baldwin in both data sets.