TITLE:
A Practical Solution to the Small Sample Size Bias and Uncertainty Problems of Model Selection Criteria in Two-Input Process Multiple Response Surface Methodology Datasets
AUTHORS:
Domingo Pavolo, Delson Chikobvu
KEYWORDS:
Multiple Response Surface Methodology, All Possible Regressions, Model Selection Criteria, Data Matrices
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.1,
February
25,
2019
ABSTRACT: Multiple response surface methodology (MRSM) most often involves the
analysis of small sample size datasets which have associated inherent statistical
modeling problems. Firstly, classical model selection criteria in use are very
inefficient with small sample size datasets. Secondly, classical model selection
criteria have an acknowledged selection uncertainty problem. Finally, there is
a credibility problem associated with modeling small sample sizes of the order
of most MRSM datasets. This work focuses on determination of a solution to
these identified problems. The small sample model selection uncertainty problem
is analysed using sixteen model selection criteria and a typical two-input MRSM
dataset. Selection of candidate models, for the responses in consideration, is
done based on response surface conformity to expectation to deliberately avoid selection of models using the
problematic classical model selection criteria. A set of permutations of
combinations of response models with conforming response surfaces is
determined. Each combination is optimised and results are obtained using
overlaying of data matrices. The permutation of results is then averaged to
obtain credible results. Thus, a transparent multiple model approach is used to
obtain the solution which gives some credibility to the small sample size
results of the typical MRSM dataset. The conclusion is that, for a two-input
process MRSM problem, conformity of response surfaces can be effectively used
to select candidate models and thus the use of the problematic model selection
criteria is avoidable.