Approximate and exact optimal designs for $$2^k$$ 2 k factorial experiments for generalized linear models via second order cone programming

Belmiro P. M. Duarte () and Guillaume Sagnol ()
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Belmiro P. M. Duarte: Instituto Politécnico de Coimbra, Instituto Superior de Engenharia de Coimbra
Guillaume Sagnol: Technische Universität Berlin

Statistical Papers, 2020, vol. 61, issue 6, No 20, 2737-2767

Abstract: Abstract Model-based optimal designs of experiments (M-bODE) for nonlinear models are typically hard to compute. The literature on the computation of M-bODE for nonlinear models when the covariates are categorical variables, i.e. factorial experiments, is scarce. We propose second order cone programming (SOCP) and Mixed Integer Second Order Programming (MISOCP) formulations to find, respectively, approximate and exact A- and D-optimal designs for $$2^k$$ 2 k factorial experiments for Generalized Linear Models (GLMs). First, locally optimal (approximate and exact) designs for GLMs are addressed using the formulation of Sagnol (J Stat Plan Inference 141(5):1684–1708, 2011). Next, we consider the scenario where the parameters are uncertain, and new formulations are proposed to find Bayesian optimal designs using the A- and log det D-optimality criteria. A quasi Monte-Carlo sampling procedure based on the Hammersley sequence is used for computing the expectation in the parametric region of interest. We demonstrate the application of the algorithm with the logistic, probit and complementary log–log models and consider full and fractional factorial designs.

Keywords: D-optimal designs; $$2^k$$ 2 k Factorial experiments; Exact designs; Second order cone programming; Generalized linear models; Quasi-Monte Carlo sampling; 62K05; 90C47 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00362-018-01075-7

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