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Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming

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dc.contributor.author Wong, Weng Kee
dc.contributor.author Zhou, Julie
dc.date.accessioned 2019-01-17T18:07:35Z
dc.date.copyright 2018 en_US
dc.date.issued 2018
dc.identifier.citation Wong, W.K., Yin, Y. & Zhou, J. (2018). Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming. Journal of Computational and Graphical Statistics, 1-33. https://doi.org/10.1080/10618600.2018.1476250 en_US
dc.identifier.uri https://doi.org/10.1080/10618600.2018.1476250
dc.identifier.uri https://dspace.library.uvic.ca//handle/1828/10520
dc.description.abstract We use semidefinite programming (SDP) to find a variety of optimal designs for multi-response linear models with multiple factors, and for the first time, extend the methodology to find optimal designs for multi-response nonlinear models and generalized linear models with multiple factors. We construct transformations that (i) facilitate improved formulation of the optimal design problems into SDP problems, (ii) enable us to extend SDP methodology to find optimal designs from linear models to nonlinear multi-response models with multiple factors and (iii) correct erroneously reported optimal designs in the literature caused by formulation issues. We also derive invariance properties of optimal designs and their dependence on the covariance matrix of the correlated errors, which are helpful for reducing the computation time for finding optimal designs. Our applications include finding A-, As-, c-, and D-optimal designs for multi-response multi-factor polynomial models, locally c- and D-optimal designs for a bivariate Emax response model and for a bivariate Probit model useful in the biosciences. en_US
dc.description.sponsorship This research work was partially supported by Discovery Grants from the Natural Science and Engineering Research Council of Canada. The research of Wong was partially supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639. en_US
dc.language.iso en en_US
dc.publisher Journal of Computational and Graphical Statistics en_US
dc.subject A-optimality en_US
dc.subject c-Optimality en_US
dc.subject Generalized linear model en_US
dc.subject Invariance property en_US
dc.subject Multi-response model en_US
dc.subject Semidefinite programming en_US
dc.title Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming en_US
dc.type Postprint en_US
dc.description.scholarlevel Faculty en_US
dc.description.reviewstatus Reviewed en_US
dc.description.embargo 2019-09-01


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