On the Equivalence of Doehlert and Equiradial Designs in Modeling the GDP Growth of Nigerian Economy

Abstract

The study ‘on the equivalence of Doehlert and Equiradial Designs in modeling the GDP growth of Nigerian economy’ was studied using quadratic model. Second-order designs were used in the analyses with radius of 1.0 and they include; Doehlert, Inscribed and Equiradial Designs. These designs were considered with additions of centre points from 1 to 5 inclusive. The study evaluated the equivalence of Doehlert and Equiradial Designs and proposed an equivalence equation of Doehlert Design (DD) and Equiradial Design (ED) with A-optimality. It was revealed that A-optimality of DD and that of ED decreases as the centre points increases. The proposed measure revealed that the two designs were equivalent and when the A-optimality of one of the designs is known, the A-optimality of the other can be obtained and verse versa. It was also revealed that the equiradial design for n=6 with 1 centre point is better than the doehlert design. The sum of square error value of equiradial design is less than that of doehlert design by 0.000222, while the doehlert design was found better than the inscribed design by 0.052816. As the centre points increases, it was observed that the sum of square errors of these designs increased significantly. It was therefore recommended among others, that the proposed Equivalence Equation of A-optimality can be used in obtaining the A-optimality of Doehlert Design when that of Equiradial Design is known and verse versa.