Graphical evaluation of the ridge-type robust regression estimators in mixture experiments.
ScientificWorldJournal 2014;
2014:806471. [PMID:
25202738 PMCID:
PMC4151492 DOI:
10.1155/2014/806471]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2014] [Revised: 07/17/2014] [Accepted: 07/31/2014] [Indexed: 11/24/2022] Open
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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