Graphical Evaluation of the Ridge-Type Robust Regression Estimators in Mixture Experiments

Abstract

In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set.

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“…In ordinary least squares, the estimation of model parameters becomes unstable when there is a high correlation among features. 31) Ridge regression addresses this issue by introducing an L2 regularization term, constraining the magnitude of model parameters, and effectively mitigating problems associated with collinearity. 32) Ridge Regression is insensitive to outliers and at the cost of sacrificing some information and reducing precision, yields regression coefficients that are more realistic and reliable.…”