Joining models with commutative orthogonal block structure

Using the algebraic structure of COBS, based on Commutative Jordan algebras of symmetric matrices, and the Cartesian product we build up complex models from simpler ones through joining, in order to analyse together models obtained independently. This commutativity condition of COBS is a necessary and sufficient condition for the least square estimators, LSE, to be best linear unbiased estimators, BLUE, whatever the variance components. Since joining COBS we obtain new COBS, the good properties of estimators hold for the joined models.