Locally Modified D - Optimal Design for Logistic Models

Locally Modified D - Optimal Design for Logistic Models

Most of the criteria, have been developed to obtain the optimal designs are based on the variance of the model parameter estimates. However, in case of existence, for non-linear models, a closed form of the variance is not available or it is intractable. To overcome this problem, researchers follow an asymptotie: approach by sing the FishErr information to approximate the variance. The resulted asymptotic optimal design maybe invalid for small to moderate sample size. In this paper we introduce a modified D-optimality criterion by replacing the Cramer-Rao bound with Bhattacharyya bound in construction of the information matrix. We present the modified information matrix for a two parameters logistic model and obtain the locally modified D-optimal designs for different value of sample sizes. The results show that the optimal designs have been obtained from our modified approach perform more efficiently in term of variance parameter estimates.