SOME NEW CLASSIFICATION-BASED RIDGE PARAMETERS IN LINEAR REGRESSION MODELS

Abstract

Multicollinearity problem influences the Ordinary Least Square Estimator in that it produces inefficient parameter estimates of linear regression model. The ridge regression estimator is one of the alternatives which produces efficient estimates. However, the efficiency of the ridge estimator depends on the choice of ridge parameter, 𝑘. This thesis examined some generalized ridge parameters and introduced the concept of kind into the existing classification (that is, forms and types). The different forms considered are Fixed Maximum (FM), Varying Maximum (VM), Arithmetic Mean (AM), Geometric Mean (GM), Harmonic Mean (HM) Median (ME) and Mid-Range, the various types are Original (O), Reciprocal (R), Square Root (SR), Reciprocal of Square Root (RSR), Pth Root and Reciprocal of Pth Root and the various kinds Original (O), Reciprocal (R), Square Root (SR), Reciprocal of Square Root (RSR), Pth Root and Reciprocal of Pth Root. These classifications resulted into proposing some other techniques of Ridge parameter estimation. Investigation of the existing and proposed ridge parameters were done by conducting 1000 Monte-Carlo experiments on a linear regression with three (3) and seven (7) explanatory variables under six (6) levels of multicollinearity (𝜌=0.8,0.9,0.95,0.99,0.999,0.9999) four (4) levels of error variance (𝜎2=0.25,1,25,100) and five sample sizes (n = 10, 20, 30, 40, 50). It is intended to identify the ridge parameters that would give efficient estimates. Results from simulation study and real life data application show that some newly proposed ridge parameters such as the Original kind of Arithmetic mean form of Pth Root type of Fayose and Ayinde (2019) generalized ridge are among the most frequently efficient estimators. Also, the performances of these estimators are dependent on the sample sizes of the data, number of independent variables and the level of multicollinearity.