Bayesian D-optimal design for logistic regression model with exponential distribution for random intercept

Nowadays, generalized linear models have many applications. Some of these models which have more applications in the real world are the models with random effects; that is, some of the unknown parameters are considered random variables. In this article, this situation is considered in logistic regression models with a random intercept having exponential distribution. The aim is to obtain the Bayesian D-optimal design; thus, the method is to maximize the Bayesian D-optimal criterion. For the model was considered here, this criterion is a function of the quasi-information matrix that depends on the unknown parameters of the model. In the Bayesian D-optimal criterion, the expectation is acquired in respect of the prior distributions that are considered for the unknown parameters. Thus, it will only be a function of experimental settings (support points) and their weights. The prior distribution of the fixed parameters is considered uniform and normal. The Bayesian D-optimal design is finally calculated numerically by R3.1.1 software.