Restricting principal component analysis

In principal component analysis there is no prior restriction on which variables are included in a component.

I wonder if there is a method which has such a restriction. That is, if the original variables are $X_1,...,X_p$, I want to use only $X_1,...,X_i$ for the first component, $X_j,...X_m$ for the second, etc.

The purpose would be to give an "exact" interpretation of the components. E.g. having variables describing physical and cognitive performances, PCA may give components containing both physical and cognitive variables. However, I want components made of only one type of variables, so as to have a pure physical component and a pure cognitive one.

• just perform two independent PCAs, one on each variable type – g3o2 Feb 11 '18 at 11:10