Optimal Designs: for a Beta GLM with Two Predictors

This book covers the construction of optimal experimental designs for Beta regression models using two predictors without interaction term. D-criterion is used as basis of optimality. Keeping in view the analytical complexity of the problem First Order Exchange Algorithm has been used to obtain locally optimal designs. These designs have been constructed under different conditions of parameter values, like positive, negative and mixture of positive and negative values. Robustness of optimal designs under parameter misspecification has also been investigated; and designs have been compared with commonly used equi-weighted designs in order to study the gain in efficiency. Use of the Efficient Rounding Procedure for obtaining exact designs by rounding off the design weights has been discussed and demonstrated through examples. The optimal designs for a variety of parameter settings are provided in appendices. These designs may be used in real life situations where appropriate.

Shahid Latif is a Lecturer in Statitics and is doing Ph.D. in Applied Statistics. His areas of interest are Experimental Designs and Regression Analysis. Dr. Muhammad Zafar Yab is a Professor of Statistics at Lahore Leads University, Lahore, Pakistan. He is the author of many research papers and is supervising M.Phil. and Ph.D. students.