A New Analysis Strategy for Designs With Complex Aliasing

Abstract

Nonregular designs are popular in planning industrial experiments for their run-size economy. These designs often produce partially aliased effects, where the effects of different factors cannot be completely separated from each other. In this article, we propose applying an adaptive lasso regression as an analytical tool for designs with complex aliasing. Its utility compared to traditional methods is demonstrated by analyzing real-life experimental data and simulation studies.

Keywords:

• Adaptive lasso
• Regression
• Run-size economy
• Variable selection

Supplementary Materials

Introductions to the Dantzig selector, the LARS algorithm, and the Nonnegative Garotte, as well as additional details of the simulation results along with a complete list of data generating processes, are provided in the supplementary materials. Figures 1 and 2 are taken from these results.

Notes

Acknowledgments

The authors would like to thank the editor, an associate editor, and the reviewers for comments and suggestions that substantially improved the manuscript. They also thank Dr. C. F. Jeff Wu for his helpful suggestions. They are thankful to Ms. Samantha Cao as well for her comments.

Notes

1 The interested reader may refer to the review paper by Xu, Phoa, and Wong (2009) for the development of research on nonregular designs.

2 Part of the interaction effects matrix X₂ and the complete alias matrix L are given in the Appendix.

3 These specifications are similar to the motivating cast fatigue example, where the data can be thought of as being generated from the model $Y=A+\mathit{AB}+ϵ$ with A and AB having coefficients with absolute value close to 0.5 and model SD close to 0.25.

4 Following Wu and Hamada (2009, p. 287), we define the quadratic effect of a three-level factor as being proportional to $(y_2-y_1)-(y_1-y_0)$ where y₀, y₁, and y₂ represent the observations at levels 0, 1, and 2, respectively.