Evaluation of compound optimality criteria for Second Order Rotatable Designs constructed using balanced incomplete block design.

Abstract

The theory of optimal experimental designs is concerned with the construction of designs that are optimum with respect to some statistical criteria. These criteria include the alphabetic optimality criteria such as; D-, A-, E-, T-, G- and C- criterion. Compound optimality criteria are those that combine two or more alphabetic optimality criteria. Design optimality criteria have specific desired properties that are sufficient in one design and at the same time inadequate in another design. Thus, a compound optimality criterion gives a balance when any two or more alphabetic optimality criteria are combined. The purpose of this study was to obtain compound optimality criteria for second order rotatable designs constructed using Balanced Incomplete Block Designs (BIBDs). The objectives of the study were to determine C-optimality criteria for the designs with 32, 64 and 112 points in three, four and five dimensions respectively; to obtain compound optimality criteria and to evaluate the efficiencies for both the alphabetic and compound optimality criteria. The C- criterion was achieved through minimizing the variance of the information matrix, whereas the compound optimality criteria were obtained from the alphabetic criteria using the specified formulae. The efficiencies were determined by comparing the specific design optimality criteria to the optimal design Criterion. C optimality criteria for designs with 32, 64 and 112 points were obtained with the optimal values as 7197.76, 36.63 and 75.33 respectively. The compound optimality criteria CD-, DT- and CDT-criterion and the respective efficiencies for the selected points were evaluated. In conclusion, the compound optimality criteria obtained provided better design characteristics in terms of minimizing variances for parameter estimates and model selection. Efficiencies for compound optimality criteria were found to be higher relative to the corresponding alphabetic optimality criteria counterparts. The study recommended that compound optimality to be used in the selection of designs that are used in performing experiments in order to achieve optimal response. It recommends further research to be done on U- Criterion that combines D-criterion, A