Optimal designs for generalized linear models

1992 ◽  
Vol 1 (2) ◽  
pp. 183-202 ◽  
Author(s):  
J. Burridge ◽  
P. Sebastiani
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Optimal Designs

scholarly journals Algebraic geometry of Poisson regression

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
Thomas Kahle ◽  
Kai-Friederike Oelbermann ◽  
Rainer Schwabe
Keyword(s):  
Algebraic Geometry ◽  
Generalized Linear Models ◽  
Poisson Regression ◽  
Linear Models ◽  
Optimal Designs ◽  
Local Optimality ◽  
Unknown Parameters ◽  
Explanatory Variables ◽  
Saturated Design ◽  
Poisson Counts

Designing experiments for generalized linear models is difficultbecause optimal designs depend on unknown parameters.  Here weinvestigate local optimality.  We propose to study for a given designits region of optimality in parameter space.  Often these regions aresemi-algebraic and feature interesting symmetries.  We demonstratethis with the Rasch Poisson counts model.  For any given interactionorder between the explanatory variables we give a characterization ofthe regions of optimality of a special saturated design. This extendsknown results from the case of no interaction.  We also give analgebraic and geometric perspective on optimality of experimentaldesigns for the Rasch Poisson counts model using polyhedral andspectrahedral geometry.

Optimal designs for generalized linear models with biased response

Metrika ◽  
2008 ◽  
Vol 70 (2) ◽  
pp. 225-237
Author(s):  
I. Ortiz ◽  
I. Martínez ◽  
C. Rodríguez ◽  
Y. del Águila
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Optimal Designs

scholarly journals Equivariance and Invariance for Optimal Designs in Generalized Linear Models Exemplified by a Class of Gamma Models

2021 ◽  
Vol 15 (4) ◽  
Author(s):  
Osama Idais ◽  
Rainer Schwabe
Keyword(s):  
Design Of Experiments ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Group Actions ◽  
Optimal Designs ◽  
Linear Component ◽  
Model Structure ◽  
Location Parameters ◽  
Locally Optimal Designs ◽  
Experimental Region

AbstractThe main intention of the present work is to outline the concept of equivariance and invariance in the design of experiments for generalized linear models and to demonstrate its usefulness. In contrast with linear models, pairs of transformations have to be employed for generalized linear models. These transformations act simultaneously on the experimental settings and on the location parameters in the linear component. Then, the concept of equivariance provides a tool to transfer locally optimal designs from one experimental region to another when the nominal values of the parameters are changed accordingly. The stronger concept of invariance requires a whole group of equivariant transformations. It can be used to characterize optimal designs which reflect the symmetries resulting from the group actions. The general concepts are illustrated by models with gamma distributed response and a canonical link. There, for a given transformation of the experimental settings, the transformation of the parameters is not unique and may be chosen to be nonlinear in order to fully exploit the model structure. In this case, we can derive invariant maximin efficient designs for the D- and the IMSE-criterion.

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