This is a special case of a balanced random intercepts model with a compound symmetric covariance matrix and one single covariate which is constant for all replicates. An example, is time, which is the same for all subjects. Maximum likelihood estimation has been performed. In this case the mathematics exist in a closed formula (Demidenko, 2013, pg. 67-69).
Authors: Michail Tsagris and Manos Papadakis