A General Structure for the Class of Mixed Linear Models

The object of this p~per is to present a general structure for mixed models which can be used to unify a large number of linear models often encountered in agricultural research work. Researchers often encounter special cases of these models under such diverse conditions that they fail to recognize the links to a common structure. ConSequently, in practice it is not unusual to find very special ad-hock analyses being developed when approaches based on well established general theory exist. The gains from this unification are two-fold. A general structure provides a basis that can be used in developing models that are appropriate for specific applications and it provides a framework within which computer programmers can develop software that can be used to perform relatively sophisticated analyses without unreasonable difficulty. The classical example here is the wide variety of least-squares analyses that are now routinely performed using commonly available linear regression packages. These calculations are almost invariably based on the fixed effects or Model I (Eisenhart, 1947) assumptions with independent identically distributed random errors. There is a need for similar tools for Model II, the random effects model and the large class of mixed models.