Simulated Annealing Model Search for Subset Selection in Screening Experiments

The analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large, the number of trials is small, and there are constraints on model structure. Common subset selection methods do not perform well in this setting. We propose a new approach particularly well suited to screening. The method uses an intentionally nonconvergent stochastic search to generate a large set of well-fitting models, each with the same number of variables. Model selection is then viewed as a feature extraction problem from this set. An easy-to-use graphical method and an automatic approach are proposed to determine the best models. Computer code and additional supplementary materials are available online.

[1]  A. Atkinson.  Subset Selection in Regression , 1992 .

[2]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[3]  Yi Lin,et al.  An Efficient Variable Selection Approach for Analyzing Designed Experiments , 2007, Technometrics.

[4]  E. George,et al.  Journal of the American Statistical Association is currently published by American Statistical Association. , 2007 .

[5]  Hugh A. Chipman,et al.  Fast Model Search for Designed Experiments with Complex Aliasing , 1998 .

[6]  Hugh Chipman,et al.  Bayesian variable selection with related predictors , 1995, bayes-an/9510001.

[7]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[8]  C. F. Jeff Wu,et al.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2000 .

[9]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[10]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

[11]  K. Dowsland.  Some experiments with simulated annealing techniques for packing problems , 1993 .

[12]  R. Plackett,et al.  THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS , 1946 .

[13]  Mu Zhu,et al.  Darwinian Evolution in Parallel Universes: A Parallel Genetic Algorithm for Variable Selection , 2006, Technometrics.

[14]  H. Chipman,et al.  A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing , 1997 .

[15]  Mark A. Wolters.  Using oversized models to find active variables in screening experiments , 2007 .

[16]  W. D. Ray.  Informed Assessments: An Introduction to Information, Entropy and Statistics , 1996 .

[17]  Changbao Wu,et al.  Analysis of Designed Experiments with Complex Aliasing , 1992 .