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

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dc.contributor.authorWong, Weng Kee
dc.contributor.authorZhou, Julie
dc.date.accessioned2019-01-17T18:07:35Z
dc.date.copyright2018en_US
dc.date.issued2018
dc.description.abstractWe 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.embargo2019-09-01
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThis 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.identifier.citationWong, 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/10.1080/10618600.2018.1476250en_US
dc.identifier.urihttps://doi.org/10.1080/10618600.2018.1476250
dc.identifier.urihttp://hdl.handle.net/1828/10520
dc.language.isoenen_US
dc.publisherJournal of Computational and Graphical Statisticsen_US
dc.subjectA-optimality
dc.subjectc-Optimality
dc.subjectGeneralized linear model
dc.subjectInvariance property
dc.subjectMulti-response model
dc.subjectSemidefinite programming
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleOptimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programmingen_US
dc.typePostprinten_US

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