41 research outputs found
D-optimal Factorial Designs under Generalized Linear Models
Generalized linear models (GLMs) have been used widely for modelling the mean
response both for discrete and continuous random variables with an emphasis on
categorical response. Recently Yang, Mandal and Majumdar (2013) considered full
factorial and fractional factorial locally D-optimal designs for binary
response and two-level experimental factors. In this paper, we extend their
results to a general setup with response belonging to a single-parameter
exponential family and for multi-level predictors.Comment: 16 pages, 1 figur
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d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response
Identifying optimal designs for generalized linear models with a binary response can be a challengingtask, especially when there are both discrete and continuous independent factors in the model. Theoreticalresults rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions.In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particleswarm optimization, to find a variety of D-optimal approximate and exact designs for experiments withdiscrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficientlyfind locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigaterobustness properties of the d-QPSO algorithm-generated designs to variousmodel assumptions andprovide real applications to design a bio-plastics odor removal experiment, an electronic static experiment,and a 10-factor car refueling experiment. Supplementary materials for the article are available online
-SELC: Optimization by sequential elimination of level combinations using genetic algorithms and Gaussian processes
Identifying promising compounds from a vast collection of feasible compounds
is an important and yet challenging problem in the pharmaceutical industry. An
efficient solution to this problem will help reduce the expenditure at the
early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu
and Johnson [Technometrics 48 (2006) 273--283] proposed the SELC algorithm.
Although powerful, it fails to extract substantial information from the data to
guide the search efficiently, as this methodology is not based on any
statistical modeling. The proposed approach uses Gaussian Process (GP) modeling
to improve upon SELC, and hence named -SELC. The performance of
the proposed methodology is illustrated using four and five dimensional test
functions. Finally, we implement the new algorithm on a real pharmaceutical
data set for finding a group of chemical compounds with optimal properties.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS199 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Software for Implementing the Sequential Elimination of Level Combinations Algorithm
Genetic algorithms (GAs) are a popular technology to search for an optimum in a large search space. Using new concepts of forbidden array and weighted mutation, Mandal, Wu, and Johnson (2006) used elements of GAs to introduce a new global optimization technique called sequential elimination of level combinations (SELC), that efficiently finds optimums. A SAS macro, and MATLAB and R functions are developed to implement the SELC algorithm.