Calculate the relative contribution of different factors to a response variable using R² decomposition. Use when you need to quantify how much each factor explains the variance of an outcome.
npxskills add benchflow-ai/skillsbench--skill contribution-analysisLoading…
Contribution analysis quantifies how much each factor contributes to explaining the variance of a response variable. This skill focuses on R² decomposition method.
When you have multiple correlated variables that belong to different categories:
import pandas as pd
import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression
from factor_analyzer import FactorAnalyzer
# Step 1: Combine ALL variables into one matrix
pca_vars = ['Var1', 'Var2', 'Var3', 'Var4', 'Var5', 'Var6', 'Var7', 'Var8']
X = df[pca_vars].values
y = df['ResponseVariable'].values
# Step 2: Standardize
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
# Step 3: Run ONE global PCA on all variables together
fa = FactorAnalyzer(n_factors=4, rotation='varimax')
fa.fit(X_scaled)
scores = fa.transform(X_scaled)
# Step 4: R² decomposition on factor scores
def calc_r2(X, y):
model = LinearRegression()
model.fit(X, y)
y_pred = model.predict(X)
ss_res = np.sum((y - y_pred) ** 2)
ss_tot = np.sum((y - np.mean(y)) ** 2)
return 1 - (ss_res / ss_tot)
full_r2 = calc_r2(scores, y)
# Step 5: Calculate contribution of each factor
contrib_0 = full_r2 - calc_r2(scores[:, [1, 2, 3]], y)
contrib_1 = full_r2 - calc_r2(scores[:, [0, 2, 3]], y)
contrib_2 = full_r2 - calc_r2(scores[:, [0, 1, 3]], y)
contrib_3 = full_r2 - calc_r2(scores[:, [0, 1, 2]], y)
The contribution of each factor is calculated by comparing the full model R² with the R² when that factor is removed:
Contribution_i = R²_full - R²_without_i
contributions = {
'Category1': contrib_0 * 100,
'Category2': contrib_1 * 100,
'Category3': contrib_2 * 100,
'Category4': contrib_3 * 100
}
dominant = max(contributions, key=contributions.get)
dominant_pct = round(contributions[dominant])
with open('output.csv', 'w') as f:
f.write('variable,contribution\n')
f.write(f'{dominant},{dominant_pct}\n')
| Issue | Cause | Solution |
|---|---|---|
| Negative contribution | Suppressor effect | Check for multicollinearity |
| Contributions don't sum to R² | Normal behavior | R² decomposition is approximate |
| Very small contributions | Factor not important | May be negligible driver |
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