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

• 成果类型: Article
• 署名作者: Wu, Hsin-Ping; Stufken, John
• 署名单位: University System of Georgia; University of Georgia
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast071
• 发表日期: 2014
• 页码: 365375
• 关键词: la garza phenomenon; binary data; regression-models; nonlinear models

摘要

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.