Title 



Optimal supersaturated designs
 
Author 



 
Abstract 



We consider screening experiments where an investigator wishes to study many factors using fewer observations. Our focus is on experiments with twolevel factors and a main effects model with intercept. Since the number of parameters is larger than the number of observations, traditional methods of inference and design are unavailable. In 1959, Box suggested the use of supersaturated designs and in 1962, Booth and Cox introduced measures for efficiency of these designs including E(s(2)), which is the average of squares of the offdiagonal entries of the information matrix, ignoring the intercept. For a design to be E(s(2))optimal, the main effect of every factor must be orthogonal to the intercept (factors are balanced), and among all designs that satisfy this condition, it should minimize E(s(2)). This is a natural approach since it identifies the most nearly orthogonal design, and orthogonal designs enjoy many desirable properties including efficient parameter estimation. Factor balance in an E(s(2))optimal design has the consequence that the intercept is the most precisely estimated parameter. We introduce and study UE(s(2))optimality, which is essentially the same as E(s(2))optimality, except that we do not insist on factor balance. We also provide a method of construction. We introduce a second criterion from a traditional design optimality theory viewpoint. We use minimization of bias as our estimation criterion, and minimization of the variance of the minimum bias estimator as the design optimality criterion. Using Doptimality as the specific design optimality criterion, we introduce Doptimal supersaturated designs. We show that Doptimal supersaturated designs can be constructed from Doptimal chemical balance weighing designs obtained by Galil and Kiefer (1980, 1982), Cheng (1980) and other authors. It turns out that, except when the number of observations and the number of factors are in a certain range, an UE(s(2))optimal design is also a Doptimal supersaturated design. Moreover, these designs have an interesting connection to Bayes optimal designs. When the prior variance is large enough, a Doptimal supersaturated design is Bayes Doptimal and when the prior variance is small enough, an UE(s(2))optimal design is Bayes Doptimal. While E(s(2))optimal designs yield precise intercept estimates, our study indicates that UE(s(2))optimal designs generally produce more efficient estimates for the main effects of the factors. Based on theoretical properties and the study of examples, we recommend UE(s(2))optimal designs for screening experiments.   
Language 



English
 
Source (journal) 



Journal of the American Statistical Association.  Washington, D.C.  
Publication 



Washington, D.C. : 2014
 
ISSN 



01621459
 
Volume/pages 



109:508(2014), p. 15921600
 
ISI 



000346797000021
 
Full text (Publishers DOI) 


  
