Weighted Statistical A-optimal Designs for Two-variable Poisson Regression Model with Application to Fertility Studies

Abstract

This research extends design optimization to model involving count data. A two-variable Poisson regression model was investigated for A-optimality on a constrained design space and the weights of the optimal design points were obtained. The constructed designs were verified to be A-optimal at 4-point design through the general equivalence theorem. The efficiency of the constructed optimal design was found to be 100% A-efficient. The concept of weighted optimal designs for Poisson regression model was applied to fertility studies. Approximate A-optimal design weights of educational level of women were obtained for each marriage duration period with respect to their places of residence. The study revealed that the numbers of women with secondary education and above were found to be consistently more than that of women with no education, lower primary education and upper primary education, respectively for all the marriage duration periods considered and at each place of residence. The only exclusion is the marriage duration of 0–4 years at Suva where the proportion of women with no education was more than other educational levels.

Keywords:    A-optimality, Design Point, Fisher Information Matrix, Imperialist Competitive Algorithm, Poisson Regression Model.