Designs for Generalized Linear Models With Several Variables and Model Uncertainty

David C. Woods · John A Eccleston · K. G. Russell

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Optimal Experimental Design Methods Statistical Methods and Bayesian Inference Advanced Statistical Methods and Models

Abstract

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

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References

1972Theory of optimal experiments 1995Bayesian Experimental Design: A Review 1990Minimax and maximin distance designs 2000The Theory of the Design of Experiments 1989Optimal Bayesian design applied to logistic regression experiments 1980A Comparison of Algorithms for Constructing Exact D-Optimal Designs 1999Model-Oriented Design of Experiments 1975The Design of Experiments for Discriminating Between two Rival Models

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2006Robust Experimental Design for Multivariate Generalized Linear Models 2009Fast Computation of Designs Robust to Parameter Uncertainty for Nonlinear Settings 2008Sequential Experimental Designs for Generalized Linear Models 2016Bayesian Design of Experiments Using Approximate Coordinate Exchange 2008Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity 2009D-OPTIMAL DESIGNS FOR POISSON REGRESSION MODELS

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