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Original Articles

Constructing Efficient Experimental Designs for Generalized Linear Models

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Pages 2827-2845 | Received 23 Aug 2013, Accepted 20 May 2014, Published online: 12 Dec 2014

References

  • Abdelbasit, K.M., Plackett, R.L. (1983). Experimental design for binary data. Journal of the American Statistical Association 78(381):90–98.
  • Atkinson, A.C., Donev, A.N. (1989). The construction of exact D-optimum experimental designs with application to blocking response surface designs. Biometrika 76(3):515–526.
  • Atkinson, A.C., Donev, A.N., Tobias, R.D. (2007). Optimum Experimental Designs with SAS. Vol. 34. Oxford: Oxford University Press.
  • Box, G.E., Lucas, H.L. (1959). Design of experiments in non-linear situations. Biometrika, 77–90.
  • Broudiscou, A., Leardi, R., Phan-Tan-Luu, R. (1996). Genetic algorithm as a tool for selection of D-optimal design. Chemometrics and Intelligent Laboratory Systems 35(1):105–116.
  • Chaloner, K., Larntz, K. (1989). Optimal Bayesian design applied to logistic regression experiments. Journal of Statistical Planning and Inference 21(2):191–208.
  • Chaloner, K., Verdinelli, I. (1995). Bayesian experimental design: A review. Statistical Science 10(3):273–304.
  • Chowdhury, K.K., Gijo, E.V., Raghavan, R. (2000). Quality improvement through design of experiments: A case study. Quality Engineering 12(3):407–416.
  • Christopher, V.I., George, M.A. (2011). Whole-plot exchange algorithms for constructing D-optimal multistratum designs. Communications in Statistics - Simulation and Computation 40(7):1030–1042.
  • Cook, R.D., Nachtsheim, C.J. (1980). A comparison of algorithms for constructing exact D-optimal designs. Technometrics 22(3):315–324.
  • Dror, H.A., Steinberg, D.M. (2006). Robust experimental design for multivariate generalized linear models. Technometrics 48(4):520–529.
  • Fedorov, V.V. (1969). Theory of Optimal Experiments. Preprint No. 7 LSM. Izd-vo, Moscow: Moscow State University.
  • Fedorov, V.V. (1971). Theory of Optimal Experiments. New York: Academic Press.
  • Ford, I., Torsney, B., Wu, C.J. (1992). The use of a canonical form in the construction of locally optimal designs for non-linear problems. Journal of the Royal Statistical Society, Series B, 54(2):569–583.
  • Gotwalt, C.M., Jones, B.A., Steinberg, D.M. (2009). Fast computation of designs robust to parameter uncertainty for nonlinear settings. Technometrics 51(1):88–95.
  • Haines, L.M. (1987). The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models. Technometrics 29(4):439–447.
  • Heredia-Langner, A., Carlyle, W.M., Montgomery, D.C., Borror, C.M., Runger, G.C. (2003). Genetic algorithms for the construction of D-optimal designs. Journal of Quality Technology 35(1):28–46.
  • Khuri, A.I., Mukherjee, B., Sinha, B.K., Ghosh, M. (2006). Design issues for generalized linear models: A review. Statistical Science 21(3):376–399.
  • Kiefer, J. (1959). Optimum experimental designs. Journal of the Royal Statistical Society, Series B, 272–319.
  • Kiefer, J. (1961). Optimum designs in regression problems, II. The Annals of Mathematical Statistics, 298–325.
  • Kiefer, J., Wolfowitz, J. (1959). Optimum designs in regression problems. The Annals of Mathematical Statistics, 271–294.
  • Li, W.W., Wu, J. C.F. (1997). Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics 39(2):171–179.
  • Mathew, T., Sinha, B.K. (2001). Optimal designs for binary data under logistic regression. Journal of Statistical Planning and Inference 93(1):295–307.
  • McCullagh, P., Nelder, J. A. (1989). Generalized Linear Models, 2nd ed., Chapman & Hall CRC Monographs on Statistics & Applied Probability, Taylor & Francis.
  • Meyer, R.K., Nachtsheim, C.J. (1988). Simulated annealing in the construction of exact optimal design of experiments. American Journal of Mathematical and Management Sciences 8(3–4):329–359.
  • Meyer, R.K., Nachtsheim, C.J. (1995). The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37(1):60–69.
  • Mitchell, T.J. (1974). An algorithm for the construction of “D-optimal” experimental designs. Technometrics 16(2):203–210.
  • Mitchell, T.J., Miller Jr, F.L. (1970). Use of design repair to construct designs for special linear models. Math. Div. Ann. Progr. Oak Ridge National Laboratory, Oak Ridge, TN, USA. Report (ORNL-4661), 130–131.
  • Monroe, E.M., Pan, R., Anderson-Cook, C.M., Montgomery, D.C., Borror, C.M. (2011). A generalized linear model approach to designing accelerated life test experiments. Quality and Reliability Engineering International 27(4):595–607.
  • Monroe, E.M., Rong, P., Anderson-Cook, C.M., Montgomery, D.C., Borror, C.M. (2010). Sensitivity analysis of optimal designs for accelerated life testing. Journal of Quality Technology 42(2):121–135.
  • Myers, R.H., Montgomery, D.C., Vining, G.G., Robinson, T.J. (2012). Generalized Linear Models: With Applications in Engineering and the Sciences. Vol. 791. Hoboken, NJ:John Wiley and Sons.
  • Nelder, J.A., Baker, R.J. (1972). Generalized Linear Models. John Wiley and Sons, Inc.
  • Nguyen, N.K. (1993). An algorithm for constructing optimal resolvable incomplete block designs: An algorithm. Communications in Statistics-Simulation and Computation 22(3):911–923.
  • Nguyen, N.K., Miller, A.J. (1992). A review of some exchange algorithms for constructing discrete D-optimal designs. Computational Statistics and Data Analysis 14(4):489–498.
  • Sitter, R.R., Torsney, B. (1995). Optimal designs for binary response experiments with two design variables. Statistica Sinica 5:405–419.
  • Vahl, C. I., Miliken, G. A. (2011). Whole plot exchange algorithms for constructing D-optimal multistratum designs. Communications in Statistics-Simulation and Computation 40(7):1030–1042.
  • Vuchkov, I.N., Damgaliev, D.L., Donev, A.N. (1989). Generation of D-optimal designs in a finite design space. Communications in Statistics-Simulation and Computation 18(1):319–337.
  • Welch, W.J. (1984). Computer-aided design of experiments for response estimation. Technometrics 26(3):217–224.
  • Welch, W.J. (1982). Branch-and-bound search for experimental designs based on D optimality and other criteria. Technometrics 24(1):41–48.
  • Woods, D.C. (2010). Robust designs for binary data: Applications of simulated annealing. Journal of Statistical Computation and Simulation 80(1):29–41.
  • Woods, D.C., Lewis, S.M., Eccleston, J.A., Russell, K.G. (2006). Designs for generalized linear models with several variables and model uncertainty. Technometrics 48(2):284–292.
  • Wynn, H.P. (1970). The sequential generation of D-optimum experimental designs. The Annals of Mathematical Statistics 41(5):1655–1664.

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