Optimal Crossover Designs for Generalized Linear Models: An Application to Work Environment Experiment

We consider locally D-optimal crossover designs for generalized linear models. Three different types of responses were recorded in a work environment experiment conducted at Booking.com . These responses follow Poisson, beta and gamma distributions. The responses from the same subjects are naturally correlated. To capture the dependence among these observations, we use six different types of correlation structures. The optimal allocations of subjects to each treatment sequence are obtained by minimizing the objective function, which is the variance of direct treatment effect estimates. We show that optimal allocations are reasonably robust to a different choice of correlation structures. Although uniform allocations are widely used in practice, we establish these designs are sub-optimal under certain conditions.