F incorrect centering introduces artificial variation

Appendix 9.F Incorrect Centering Introduces Artificial Variation 

Consider a data set structured as a bilinear part plus a constant identical for all elements that is, all elements have the same common offset, as also shown in Equation (9.4). It might seem natural to remove this offset by initially subtracting the grand mean m from the data. However, this will not simplify the subsequent modeling of the data, and in fact, it obscures interpretation of the model, because such a centering leads to artificial mathematical components that also need to be modeled. 

To explain this, assume that X is perfectly described by a bilinear part plus a common offset 

Centering by removing the overall mean of all elements of X can be written 

Multi-way Analysis With Applications in the Chemical Sciences 

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