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Locally ϕp-optimal designs for generalized linear models with a single-variable quadratic polynomial predictor

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  • Hsin-Ping Wu
  • John Stufken

Abstract

Finding optimal designs for generalized linear models is a challenging problem. Recent research has identified the structure of optimal designs for generalized linear models with single or multiple unrelated explanatory variables that appear as first-order terms in the predictor. We consider generalized linear models with a single-variable quadratic polynomial as the predictor under a popular family of optimality criteria. When the design region is unrestricted, our results establish that optimal designs can be found within a subclass of designs based on a small support with symmetric structure. We show that the same conclusion holds with certain restrictions on the design region, but in other cases a larger subclass may have to be considered. In addition, we derive explicit expressions for some D-optimal designs.

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  • Hsin-Ping Wu & John Stufken, 2014. "Locally ϕp-optimal designs for generalized linear models with a single-variable quadratic polynomial predictor," Biometrika, Biometrika Trust, vol. 101(2), pages 365-375.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:2:p:365-375.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast071
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    Cited by:

    1. Kao, Ming-Hung & Khogeer, Hazar, 2021. "Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    2. McGree, J.M., 2017. "Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 207-225.

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