Prediction with data from designed experimentation

Abstract

The intent of this study was to understand via simulation how data from designed experimentation for linear models can succeed in the prediction of individual values despite its relatively small size which renders data splitting for validation purposes nonviable. Another intent was to emphasize why, for a given level of precision, designed experimentation requires far many more runs for the prediction of individual values than it does for its more mundane use of mean prediction, and how this required number of runs can be determined via simulation as a function of the model validation method used. The results showed that prediction with designed data can be successful given its low tendency to overfitting and that model reduction can be detrimental to prediction which contrasts with the pursuit of a bias-variance tradeoff with undesigned data. As designed data increasingly resembles undesigned data, either by containing factors that have zero influence in the response, having high correlation among factors levels, and/or having small $n$ to $p$ ratio, model reduction becomes increasingly necessary for prediction.

Keywords:

• DOE
• Model reduction
• Model selection
• Information criteria