Summary

Using the Linear Mixed Models procedure, you have fit four different models to this crossover trial, and found that in this instance, the repeated effects models outperform the random effects model. Choosing between the three repeated effects models is more difficult. The model using Week as the repeated effect with an autoregressive covariance matrix has an attractive and intuitive interpretation for the covariance structure, but it also had the largest information criteria of the repeated effects models. The model using Week as the repeated effect with an unstructured covariance matrix had the smallest information criteria, but that may only be due to the influence of customers who shop biweekly. To fairly compare the two models with Week as the repeated effect, you have to find a way to reduce the effect of the biweekly shoppers on the residual covariance matrix.

However, if it is difficult or impossible to suitably deal with the biweekly shoppers, you can always turn to the model using Coupon value as the repeated effect. It has reasonably low information criteria, and its covariance structure should not be as strongly affected by the biweekly shoppers.