Methods for Increasing the Number of Experimental Points on a D-Optimal Design
DOI:
https://doi.org/10.17230/ingciencia.10.20.11Keywords:
Criteria of optimality, D-optimality, sensitivity function, non-linear models, lack-of-fit test.Abstract
The purpose of the optimum designs is to determine the optimal experimental conditions in terms of minimum variance of the estimated vector of parameters, so that statistical inferences can be generated as accurate as possible. This theory presupposes knowledge of the function relating the explanatory variables with the response variable. In this situation, usually get designs with support points as parameters in the model. Since p-point designs assume that the model function is known, these could not be optimal in some practical situations because they do not allow to test the goodness of fit of the assumed model [1]. In this paper we present a generalization of the methodology proposed by [2] to increase the number of support points in D-optimality criterion. An expression for the variance of the predicted response in terms of a constant will be provided, which allow to determine the points to be added to the D-optimal design. We propose a strategy for choosing delta. Finally we provide a pseudo-optimal design with (p + s) support points.
MSC: 62K05
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