Screening Strategies in the Presence of Interactions

Product and process improvement can involve a large number of factors that must be varied simultaneously. Understanding how factors interact is a key step in identifying those factors that have a substantial impact on the response. This article gives the first comprehensive assessment and comparison of screening strategies for interactions using two-level supersaturated designs, group screening, and a variety of data analysis methods including shrinkage regression and Bayesian methods. We develop novel methodology to allow application of Bayesian methods in two-stage group screening. Insights on using the strategies are provided through a variety of simulation scenarios and open issues are discussed. Supplementary materials are available online.

[1]  R. Dorfman.  The Detection of Defective Members of Large Populations , 1943 .

[2]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[3]  A. Sterrett.  On the Detection of Defective Members of Large Populations , 1957 .

[4]  G. Watson.  A Study of the Group Screening Method , 1961 .

[5]  K. H. Booth,et al.  Some Systematic Supersaturated Designs , 1962 .

[6]  William J. Hill,et al.  Discrimination Among Mechanistic Models , 1967 .

[7]  G. Wahba.  Smoothing noisy data with spline functions , 1975 .

[8]  Peter Craven,et al.  Smoothing noisy data with spline functions , 1978 .

[9]  R. Daniel Meyer,et al.  An Analysis for Unreplicated Fractional Factorials , 1986 .

[10]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

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

[12]  Accelerated weathering of marine fabrics , 1992 .

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

[14]  Dennis K. J. Lin,et al.  A new class of supersaturated designs , 1993 .

[15]  T. Hastie,et al.  [A Statistical View of Some Chemometrics Regression Tools]: Discussion , 1993 .

[16]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[17]  Changbao Wu,et al.  Construction of supersaturated designs through partially aliased interactions , 1993 .

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

[19]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[20]  W. DuMouchel,et al.  A simple Bayesian modification of D-optimal designs to reduce dependence on an assumed model , 1994 .

[21]  Dennis K. J. Lin.  Generating Systematic Supersaturated Designs , 1995 .

[22]  L. Breiman.  Better subset regression using the nonnegative garrote , 1995 .

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

[24]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[25]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[26]  Nam-Ky Nguyen.  An algorithmic approach to constructing supersaturated designs , 1996 .

[27]  A. O'Hagan,et al.  Kendall's Advanced Theory of Statistics, Vol. 2b: Bayesian Inference. , 1996 .

[28]  George E. P. Box,et al.  Follow-up designs to resolve confounding in multifactor experiments , 1996 .

[29]  William Li,et al.  Columnwise-pairwise algorithms with applications to the construction of supersaturated designs , 1997 .

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

[31]  E. George,et al.  APPROACHES FOR BAYESIAN VARIABLE SELECTION , 1997 .

[32]  Dennis K. J. Lin,et al.  On the identifiability of a supersaturated design , 1998 .

[33]  David R. Anderson,et al.  Model Selection and Multimodel Inference , 2003 .

[34]  K. Vijayan,et al.  Some Risks in the Construction and Analysis of Supersaturated Designs , 1999, Technometrics.

[35]  David M. Steinberg,et al.  Minimum aberration and model robustness for two‐level fractional factorial designs , 1999 .

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

[37]  Changbao Wu,et al.  FACTOR SCREENING AND RESPONSE SURFACE EXPLORATION , 2001 .

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

[39]  S. Lewis,et al.  Detection of interactions in experiments on large numbers of factors , 2001 .

[40]  Dennis K. J. Lin,et al.  Data analysis in supersaturated designs , 2002 .

[41]  Dennis K. J. Lin,et al.  Construction of mixed-level supersaturated design , 2002 .

[42]  Angela M. Dean,et al.  Comparison of group screening strategies for factorial experiments , 2002 .

[43]  Dennis K. J. Lin,et al.  A Two-Stage Bayesian Model Selection Strategy for Supersaturated Designs , 2002, Technometrics.

[44]  J. Charles Kerkering,et al.  Eliciting and Analyzing Expert Judgment, A Practical Guide , 2002, Technometrics.

[45]  Jack P. C. Kleijnen,et al.  Finding the Important Factors in Large Discrete-Event Simulation: Sequential Bifurcation and its Applications , 2003 .

[46]  Theodore T. Allen,et al.  Supersaturated Designs That Maximize the Probability of Identifying Active Factors , 2003, Technometrics.

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

[48]  Andy J. Keane,et al.  A Web-Based Knowledge Elicitation System (GISEL) for Planning and Assessing Group Screening Experiments for Product Development , 2004, J. Comput. Inf. Sci. Eng..

[49]  Yufeng Liu,et al.  k-Circulant Supersaturated Designs , 2004, Technometrics.

[50]  R. Tibshirani,et al.  On the “degrees of freedom” of the lasso , 2007, 0712.0881.

[51]  J. S. Hunter,et al.  Statistics for Experimenters: Design, Innovation, and Discovery , 2006 .

[52]  Bo Wahlberg,et al.  Construction and Analysis , 2005 .

[53]  Angela M. Dean,et al.  TWO-STAGE GROUP SCREENING IN THE PRESENCE OF NOISE FACTORS AND UNEQUAL PROBABILITIES OF ACTIVE EFFECTS , 2005 .

[54]  Jack P. C. Kleijnen,et al.  Screening for the important factors in large discrete-event simulation : Sequential bifurcation and its applications , 2006 .

[55]  D. Donoho.  For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

[56]  Jianqing Fan,et al.  Sure independence screening for ultrahigh dimensional feature space , 2006, math/0612857.

[57]  Barry L. Nelson,et al.  Controlled Sequential Bifurcation: A New Factor-Screening Method for Discrete-Event Simulation , 2006, Oper. Res..

[58]  William Li,et al.  Screening designs for model selection , 2006 .

[59]  Max D. Morris,et al.  An Overview of Group Factor Screening , 2006 .

[60]  Hugh A. Chipman,et al.  Prior Distributions for Bayesian Analysis of Screening Experiments , 2006 .

[61]  Hugh A. Chipman,et al.  Incorporating Prior Information in Optimal Design for Model Selection , 2007, Technometrics.

[62]  Wenbin Lu,et al.  Variable selection for proportional odds model , 2006 .

[63]  M. Yuan,et al.  On the non‐negative garrotte estimator , 2007 .

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

[65]  Kenny Q. Ye,et al.  Model discrimination—another perspective on model-robust designs , 2007 .

[66]  Dursun A. Bulutoglu,et al.  E(s2)-Optimal supersaturated designs with good minimax properties , 2007 .

[67]  Terence Tao,et al.  The Dantzig selector: Statistical estimation when P is much larger than n , 2005, math/0506081.

[68]  Angela M. Dean,et al.  Construction and analysis of Es2 efficient supersaturated designs , 2007 .

[69]  Runze Li,et al.  Tuning parameter selectors for the smoothly clipped absolute deviation method. , 2007, Biometrika.

[70]  David Brunson,et al.  A Critical Assessment of Two-Stage Group Screening Through Industrial Experimentation , 2008, Technometrics.

[71]  C. Robert.  Discussion of "Sure independence screening for ultra-high dimensional feature space" by Fan and Lv. , 2008 .

[72]  Dennis K. J. Lin,et al.  Bayesian D-optimal supersaturated designs , 2008 .

[73]  S. Pandey,et al.  What Are Degrees of Freedom , 2008 .

[74]  P. Bickel,et al.  Sparsity and the Possibility of Inference , 2008 .

[75]  Min-Qian Liu,et al.  Optimal mixed-level k-circulant supersaturated designs , 2008 .

[76]  B. Dejaegher,et al.  Supersaturated designs: set-ups, data interpretation, and analytical applications , 2008, Analytical and bioanalytical chemistry.

[77]  Weng Kee Wong,et al.  Recent developments in nonregular fractional factorial designs , 2008, 0812.3000.

[78]  Weng Kee Wong,et al.  The use of nonregular fractional factorial designs in combination toxicity studies. , 2009, Food and chemical toxicology : an international journal published for the British Industrial Biological Research Association.

[79]  Frederick Kin Hing Phoa,et al.  Analysis of Supersaturated Designs via Dantzig Selector , 2009 .

[80]  W. Wong,et al.  The need of considering the interactions in the analysis of screening designs , 2009 .

[81]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[82]  Roger Phan-Tan-Luu,et al.  Supersaturated design for screening factors influencing the preparation of sulfated amides of olive pomace oil fatty acids , 2009 .

[83]  A. Dean,et al.  An Overview of Two-level Supersaturated Designs with Cyclic Structure , 2009 .

[84]  Gareth M. James,et al.  DASSO: connections between the Dantzig selector and lasso , 2009 .

[85]  Thomas J. Santner,et al.  Design and analysis of computer experiments for screening input variables , 2010 .

[86]  Peter J. Bickel,et al.  Hierarchical selection of variables in sparse high-dimensional regression , 2008, 0801.1158.

[87]  Runze Li,et al.  Regularization Parameter Selections via Generalized Information Criterion , 2010, Journal of the American Statistical Association.

[88]  Dennis K. J. Lin,et al.  Screening for Fuel Economy: A Case Study of Supersaturated Designs in Practice , 2010 .

[89]  Christopher J. Marley,et al.  A comparison of design and model selection methods for supersaturated experiments , 2010, Comput. Stat. Data Anal..

[90]  Christopher J. Nachtsheim,et al.  A Class of Screening Designs Robust to Active Second-Order Effects , 2010 .

[91]  Derek Bingham,et al.  Simulated Annealing Model Search for Subset Selection in Screening Experiments , 2011, Technometrics.

[92]  Dennis K. J. Lin,et al.  ON CONSTRUCTION OF OPTIMAL MIXED-LEVEL SUPERSATURATED DESIGNS , 2011, 1105.3816.

[93]  Christopher J. Marley.  Screening experiments using supersaturated designs with application to industry , 2011 .

[94]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .