E-optimal Experimental Designs for Poisson Regression Models in Two and Three Variables

Abstract

In the context of generalized linear models, most of the recent studies were on logistic regression models and many of them focussed on optimal experimental designs with concentration on D-optimality. In this research, two- and three-variable Poisson regression models were considered for E-optimization on restricted design space [0, 1]. The two-variable Poisson regression model was not optimal at 3-design points, but was found to be E-optimal at 4-design points (1, 1), (0, 0), (0, 1) and (1, 0) with equal design weights of 0.25. The three-variable Poisson regression model was E-optimal at 4-design points (0, 0, 1), (0, 1, 0), (1, 1, 1) and (1, 0, 0) with each design point having design weights of 0.25. The prediction error variance (PEV) for the two-variable Poisson regression model is 0.35 and that of the three-variable Poisson regression model is 0.68. From this research, the two-variable Poisson regression model is preferred to the three-variable Poisson regression model because of smaller PEV.

Keywords: E-optimality; Fisher Information Matrix; Poisson Regression Model; Prediction Error Variance