AIC and BIC penalise model complexity by counting parameters. But parameters are not equally informative. When predictors are correlated, the effective complexity is lower than the parameter count, and AIC/BIC choose the wrong model. nomocomp replaces the parameter count with the exact log-determinant of the observed Fisher information, correcting model rankings without approximation.
When two predictors carry similar information, adding both barely increases model complexity. But AIC/BIC penalise both equally. This can reverse the correct model ranking, especially when correlation is high (above 0.7) and sample size is moderate.
nomocomp extracts the observed Fisher information matrix from each fitted model and computes the log-determinant. This is the exact fibre-volume correction: it measures the effective dimension of each model, accounting for the actual shape of the likelihood surface.
import statsmodels.api as sm
from nomocomp import GeometricModelComparator
# Fit two competing models
model_a = sm.OLS(y, X_small).fit()
model_b = sm.OLS(y, X_large).fit()
# Compare with geometry
comp = GeometricModelComparator()
result = comp.compare([model_a, model_b],
labels=["small", "large"])
print(result.summary())
# Shows: geometric ranking, AIC ranking, BIC ranking,
# whether geometry reverses AIC/BIC, fibre volumesAt correlation 0.9 or above with n = 60+, the geometric comparator identifies the true model in 99-100% of seeds. AIC: 16%. BIC: 6%.
Collinearity phase diagram over 56 cells (correlation 0.0 to 0.99, sample size 20 to 200), 200 seeds each. The geometric correction reverses AIC/BIC where it matters most.
When predictors are independent, AIC and BIC already work well. The geometric correction agrees with them. It helps where they fail, not everywhere.
pip install nomocompRequires: nomogeo >= 0.4.0, numpy, statsmodels.
cd nomocomp && python -m pytest tests/ -qCovers extraction, comparison, ranking reversal, and conservation diagnostics.