Methods for Analyzing the 12 Run Plackett-Burman Design

Abstract

In the early stages of an experimental analysis it is often of interest to determine the most important factors. The main goal of this master thesis is to study and compare different methods for determining the active factors in a 12 run Plackett-Burman experiment. The methods discussed in this thesis are the Dantzig selector, a graphical Dantzig selector, a projection based Dantzig selector, the Lasso, a projection based method, the partial F-test, a graphical method using orthogonalization and the residual variance of fitted models. The methods were implemented in R and applied to data generated from a total of 15 different models. The form of these models vary in terms of the number of active factors and the presence of interaction effects. This diversity of models facilitate exposure of strengths, weaknesses and limitations of the methods. From the study conducted in this thesis it was confirmed that methods using the Dantzig selector perform significantly better for designs following the uniform uncertainty principle. The results produced by the Lasso were found to be relatively close to what was obtained by the Dantzig selector. Further, it was found that a combination of the projection based method, residual variance of fitted models and the graphical method using orthogonalization together form a highly valuable procedure for determining active factors.