D-optimal Design for Regression Beta with Random Effect

Most of the research of design optimality is conducted on linear and generalized linear models. In applicable studies, in agriculture, social sciences, etc, usually in addition to fixed effects, there is also at least one random effect in the model. These models are known as mixed models. In this article, Beta regression model with a random intercept is considered as a mixed model and locally D-optimal design is calculated for simple and quadratic forms of the model and the trend of changes of optimal design points for different parameter values will be studied. For the simple model, a two point locally D-optimal design has been obtained for different parameter values and in the quadratic model, a three point locally D-optimal design has been acquired. Also, according to the efficiency criterion, these locally D-optimal designs are compared with the same designs. It was observed that the efficiency of optimal design, when the random intercept is not considered in the model is lower than the case in which the random effect is considered.