D-optimal Designs for Multiple Poisson Regression Model with Random Coefficients

The majority of the Optimal design research has focused on linear models and binary data models. However, a couple of researches have recently called attention to Poisson regression models with random effects. In the present paper, we theoretically and numerically discuss the optimal designs for multiple Poisson regression model with random coefficients and two explanatory variables. Since there is no closed form for the information matrix, the quasiinformation approach is applied in order to nd the optimal designs in this study. Some special cases are illustrated and a new version of equivalence theorem is obtained.