Consider a linear regression model: $$y = β_0 + β_1X_1 + β_2X_2 + ... + β_kX_k + ε$$ where $R^2 = 1 - (SSR/SST)$.

I would like to determine the contribution of a factor $i$ (call it $R^2_i$) into the total $R^2$ such that $R^2_1$ + $R^2_2$ + ... +$R^2_k$ = $R^2$, because I want to know the impact of each factor into the total variance.

One methodology, called Shapley-Owen Decomposition, exists that performs that. The problem is that it is very computational heavy because it takes $2^k$ number of computations for each factor. It can be done pretty fast on Python when $k$ is small, but when $k$ is large, it is impossible.

My personal application is to decompose the $R^2$ into factors when $k$ is like 15-20 AND I want to do it using rolling-basis, because I want to see how the contributions change over time (which naturally means more computations).

I am wondering what efficient methodologies are out there to achieve my goal. A reference to academic paper/application would be appreciated. Thank you very much.


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