The efficiency factorization multiplier for the Watson efficiency in partitioned linear models: Some examples and a literature review

We consider partitioned linear models where the model matrix X=(X1:X2)X=(X1:X2) has full column rank, and concentrate on the special case where X1′X2=0 when we say that the model is orthogonally partitioned. We assume that the underlying covariance matrix is positive definite and introduce the efficiency factorization multiplier which relates the total Watson efficiency of ordinary least squares to the product of the two subset Watson efficiencies. We illustrate our findings with several examples and present a literature review.