Influence of local values on cD-optimal designs for logistic models
Abstract
When experiments are designed, it is uncommon to use criteria to determine the treatments and number of replicates that should be conducted to properly estimate the parameters in the model under study. This is mainly due to a lack of knowledge of said criteria and, in many other cases, to the difficulty of interpreting them. Optimal designs try to overcome this difficulty by providing optimal experimental conditions and factor levels whose response should be evaluated in order to improve the quality of the statistical inference at a lower cost. Said designs also use optimality criteria, which are functions of the Fisher-information matrix. One of the most common estimation problems in nonlinear models is specifying local values for the parameters of the model, which is necessary to minimice the optimality criterion (King & Wong, 2000) [1]. This work examines the robustness of optimal designs obtained from logistic models when perturbations in the local values of the parameters are considered. The objective is to provide researchers with a wide range of action to select local values while guaranteeing that the efficiency of the resulting optimal designs is not considerably compromised compared to reference values. For that purpose, based on the data of an example, the efficiency of each resulting design was contrasted with the efficiency of unperturbed values. Furthermore, cD-optimal designs were created to estimate the logit variance. The impact of said perturbations on local cD-optimal designs resulted in an efficiency of approximately 70%, with a range of 0.04 of perturbation above the reference value.
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