Answer tucker example 5

You have the following three cores.

In Go the variation is dispersed over many elements, and it is hard to see what elements are significant and how many should be accounted for in the interpretation. 

In Gd, we verify that the diagonal elements have increased. Note the large off-diagonal elements. More importantly, there is no clear cut between high important factor combinations and unimportants ones. There is a smooth and unclear transition between significant and non-significant core elements. 

In Gv, we can identify 5 clearly significant elements. And the gap between significant and non-significant core elements is  between 18.75 and 5.39. The optimization of variance-of-squares re-enforces the significant elements found in the initial core, yielding a core that is easier to interpret. 

With regards to verifying the orthogonality of the rotated and unrotated components matrices, it may be advisable to calculate the correlation matrices which should equal identity matrices in case of orthogonality. For the unrotated component matrices, and the transformation matrices from the core with optimal variance-of-squares, we may write this in MATLAB as: 

%Rotate the factors with optimal diagonality rotations 

Ad'*Ad, Bd'*Bd, Cd'*Cd
%Verify the original component matrices  

%Rotate the factors with optimal var-of-sq. rotations 

Av'*Av, Bv'*Bv, Cv'*Cv
%Verify the rotated component matrices