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Title: Analytic solutions for locally optimal designs for gamma models having linear predictors without intercept
Author(s): Idais, Osama
Schwabe, RainerLook up in the Integrated Authority File of the German National Library
Issue Date: 2021
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-836936
Subjects: Generalized linear model
Optimal design
Gamma model
Intercept term
Abstract: The gamma model is a generalized linear model for gamma-distributed outcomes. The model is widely applied in psychology, ecology or medicine. Recently, Gaffke et al. (J Stat Plan Inference 203:199–214, 2019) established a complete class and an essentially complete class of designs for gamma models to obtain locally optimal designs in particular when the linear predictor includes an intercept term. In this paper we extend this approach to gamma models having linear predictors without intercept. For a specific scenario sets of locally D- and A-optimal designs are established. It turns out that the optimality problem can be transformed to one under gamma models with intercept leading to a reduction in the dimension of the experimental region. On that basis optimality results can be transferred from one model to the other and vice versa. Additionally by means of the general equivalence theorem optimality can be characterized formultiple regression by a system of polynomial inequalitieswhich can be solved analytically or by computer algebra. Thus necessary and sufficient conditions can be obtained on the parameter values for the local D-optimality of specific designs. The robustness of the derived designs with respect to misspecification of the initial parameter values is examined by means of their local D-efficiencies.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2020
Journal Title: Metrika
Publisher: Springer
Publisher Place: Berlin
Volume: 84
Issue: 1
Original Publication: 10.1007/s00184-019-00760-3
Page Start: 1
Page End: 26
Appears in Collections:Fakultät für Mathematik (OA)

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