A NEW APPROACH FOR THE CONSTRUCTION OF D-OPTIMAL DESIGN IN LINEAR REGRESSION MODEL

Abstract

The optimal design approach is a powerful and flexible way to generate efficient experimental designs. It is a sub-field in statistics that provide the theory of construction of research designs that are as efficient as possible at minimum cost. Efficiency of the research design in the case of linear models refers to the accuracy of the estimates of the model parameters. Algorithmic techniques for computing optimal designs have continued to be needful in optimal experimental design field. General exchange algorithms and their modifications are more frequently used methods in literature for computing D-Optimal designs. However, they are not always suitable and efficient to compute optimal designs since their procedures are limited by their computational requirements. This study therefore focuses on the development of a new, efficient and robust Computer Algorithm that will efficiently construct optimal designs for linear models based on the D-optimality criterion. The new algorithm developed uses new and suitable strategies and procedures to obtain the initial design, find improved search directions and attain rapid convergence. Starting from an initial point X(1), the new algorithm finds a sequence of points X(2), X(3)...... by using suitable iterative procedure. The algorithm uses the convergence criterion ||CTX(K)|| < ε to test for optimality, where ε is a small number, C is a vector and CT is the transpose of the vector C. Furthermore, in this research a web based Computer application program suitable for the computation of efficiency of designs was developed. The Web Application was developed using a server side programming tool called PHP and a client side tool called JavaScript. The program developed has the capability to compare the quality or efficiencies of two or more designs. The output generated by the Program revealed that the D-Optimal Design is 241.101 % more A-efficient, 145.73% more D-efficient and 55.06% more G-efficient than the initial Design considered.