Using criterion-based model averaging in two-input multiple response surface methodology problems

Experimental designs in multiple response surface methodology (MRSM) often result in small sample size datasets with associated modelling and model selection problems. Classical model selection criteria are inefficient when using small sample size datasets while the model selection process has inherent uncertainties. Modelling of small sample size datasets below (10 + k), where k is the maximum number of regressors inclusive of the intercept, suffers from credibility problems. In this empirical paper, criterion-based frequentist model-averaging (CBFMA) is proposed as a solution to the small sample size problems of modelling MRSM datasets. We also compare the goodness of fit and prediction accuracy of using CBFMA models versus ordinary least squares (OLS) candidate models. Findings suggest that CBFMA models have good fitness to data and predictive accuracy. Also, the small sample size model selection criteria bias problem is improved on. However, in the MRSM context, CBFMA does not directly solve both criterion and response surface uncertainties, and averaged model estimators have mean squared errors that are greater than the best OLS candidate models.