Deriving a randomization-based mixed model

Brien and Bailey (2006, section 7) describe how to derive a randomization-based mixed model for an experiment. This is equivalent to the procedure described for deriving the decomposition table, except that Brien and Bailey a) allow for the augmentation of the model by including any term thought important, even if not justified by the randomization, b) recognise that aliased and confounded terms will have to be omitted for the mixed model algorithm to succeed, and c) suggest that the parameterization of the fixed and/or random terms may need to be varied to obtain a better model for the data. Also, terms involving pseudofactors are unlikely to be necessary. Brien and Demétrio (2009) employ these principles in extending this method to cover longitudinal experiments