Use of ridge regression analysis in the multicollinearity in animal science

Abstract

Ridge and basic investment are analysis methods used to guide regression analysis, to make very convenient regression analysis. Although the least squares estimates are unbiased when multicollinearity occurs, the variances of the estimates can be quite far from their true values. Ridge and principal components regression standard errors are reduced by allowing one-level biased regression estimates. Therefore, when multicollinearity is present, the ridge regression method can be used as an alternative to the least squares method. In this study, it was aimed to develop a model that predicts various egg quality criteria obtained from 238 Lohmann LSL-white commercial laying hens at 46 weeks of age. Due to the multicollinearity between egg quality criteria, ridge regression analysis methods, which are alternatives to least squares regression, were applied and these two methods were compared for the same data set. The coefficient of determination (R2) and coefficient of variation were used as comparison criteria. According to these criteria, it was observed that the least squares (R2=0.876), ridge (R2=86.9) methods gave the best fit, respectively. As a result, it was concluded that it would be more accurate to use Ridge regression methods instead of using the least squares method in case of multicollinearity.