Construction of Locally D-Optimal Design for Poisson Regression Model Using Recursive Algorithm

Abstract

Designing optimum experiment for nonlinear models is generally challenging due to the dependence of design support point on the unknown parameter(s) value(s). For a locally optimal design, the unknown parameters are replaced by a guess value; if the guesses are not so close to the actual parameter(s) value(s), the resulting design may not be optimal, robust and efficient. One possible way to salvage the situation is to identify a subclass of designs with a simple format, so that one can restrict considerations to this subclass for any optimality problem. With a simple format, it would be relatively easy to derive an optimal design, analytically or numerically. In this paper, we identified a subclass of design with relatively simple format and use functional approach based on implicit function theorem to construct locally D-optimal design for Poisson regression model. The result showed the dependence of optimal design points on values of unknown parameters and on the bound of the design interval. Also the design proved to be minimally supported (saturated) at two design points including B, the upper boundary point. Furthermore, the lower support point was shown to be approximated by a convergent power series using recursive algorithm.

Keywords: D-optimal Design, Fisher Information Matrix, Functional Approach, Minimally Supported/Saturated Design, Poisson Regression Model, Tylor Series.


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