I have been doing some reading on factor models. In the literature it mentions that when creating a portfolio that maximises particular attributes it may lead to unwanted bias to other factors. I understand this part.
So they create 'true' factor scores which clean a factor of the influences of all the other factors. It mentions the use of cross-sectional regressions to simultaneously remove these side effects. It is this part I am unsure of. I do not know how they are 'cleaning' their factors and if this is a standard practise?
A variable is decomposed into the true variable and the parts that are shared with other common variables. This is done using the residual variable methodology.