GENERALIZED RIDGE REGRESSION: MULTI-RIDGE AND INVERSE-RIDGE METHODS WITH AND WITHOUT MULTICOLLINEARITY

Abstract

The study presented Mult-, and Inverse-ridge regressions for data with or without multicollinearity for certain shrinkage factors. The study considered data of GDP of Nigeria as response, while exchange, unemployment, inflation and foreign direct investment were used as the predictors. The data were tested for outlier using Grubb’s test and the VIF, condition number, correlation and t-values were used to assess how the OLS and Ridge regressions were related with the proposed mult-and inverse-ridge regressions. The study revealed that whether or not, there is outlier or multicollinearity in a data set, the mult or inverse-ridge gives the same estimate of model parameters with the respective shrinkage factors of 1.000006 and 0.999999. These methods, overcame the barrier of testing for outlier or multicollinearity in a data set, it is advised that instead of testing, use any of the methods, Ridge, Sub-Ridge, Multi-Ridge and Inverse-Ridge methods with their respective shrinkage penalty. The OLS was not condemned, rather, it was used as the basis for judging these proposed methods.