Title: Using criterion-based model averaging in two-input MRSM problems: investigating cloning of an under-fitted response model
Authors: Domingo Pavolo; Delson Chikobvu
Addresses: Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, The University of the Free State, Bloemfontein, South Africa ' Department of Mathematical Statistics and Actuarial Sciences, Faculty of Natural and Agricultural Sciences, The University of the Free State, Bloemfontein, South Africa
Abstract: Cloning of an under-fitted parent ordinary least squares response model using model averaging to combine its genetic ordinary least squares models is presented and investigated as a solution to the model's problem of parametric bias and variability with the intention of improving prediction accuracy. The permutation of genetic models that is produced from the set of the under-fitted ordinary least squares model's independent variables is first determined. Sets of genetic models that combine to give the same functional form as the parent ordinary least squares model are then obtained and combined using criterion-based model averaging. The mean squared errors of the clones are very close to that of the parent ordinary least squares model but is always larger. The mean squared forecasted error suggest that most of the clones have better prediction accuracy than the ordinary least squares model. Combining the clones using criterion-based frequentist model averaging and arithmetic model averaging shows that the higher the number of clones combined using criterion-based frequentist model averaging the better the fitness to data than arithmetic model averaging while the higher the number of clones combined using arithmetic averaging the better the prediction accuracy.
Keywords: response surface cloning; multi-response surface methodology; ordinary least squares model; response models; all regressions modelling.
International Journal of Experimental Design and Process Optimisation, 2020 Vol.6 No.3, pp.201 - 233
Received: 11 May 2019
Accepted: 02 Dec 2019
Published online: 26 Feb 2021 *