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Optimum designs for nonlinear models with correlation structure: robustness study
Diseños óptimos para modelos no lineales con estructura de correlación: estudio de robustez
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Optimum designs for nonlinear models with correlation structure: robustness study. (2022). Revista EIA, 19(38), 3807 pp. 1-16. https://doi.org/10.24050/reia.v19i38.1529
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This article proposes a methodology to compare exact D-optimal designs when the assumption of incorrectness of the error term in the model is not fulfilled and four covariance structures are taken into consideration to model it. A simplified expression of the Fisher’s information matrix is found for the general case of correlated observations and is used in the four considered covariance structures.
With each covariance structure, the respective optimal design is found, known as the nominal design, and the robustness of the other optimal designs is evaluated by finding their efficiency in relation to the nominal design. It is concluded that the four optimal designs are competitive with respect to the other considered covariance structures, by observing a minimal loss of efficiency of each of these designs and showing that the optimal designs, at least with the considered covariance structures, are robust to the choice of the covariance structure. Additionally, it is shown, via simulation, that, with the optimal designs, under each covariance structure, good estimators are obtained for the model parameters when evaluating the magnitude of the coefficient of variation and the relative mean square error.
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