Omnichannel Media Mix Modelling (MMM) Lightweight Python Pipeline

Python functions for computing geometric carryover decay and non-linear diminishing returns saturation.

import numpy as np
import pandas as pd
from sklearn.linear_model import Ridge

def geometric_adstock(spend_series: np.ndarray, decay_rate: float = 0.6) -> np.ndarray:
    """Computes carryover effect across successive weeks."""
    adstocked = np.zeros_like(spend_series, dtype=float)
    adstocked[0] = spend_series[0]
    for t in range(1, len(spend_series)):
        adstocked[t] = spend_series[t] + decay_rate * adstocked[t-1]
    return adstocked

def hill_diminishing_returns(adstocked_spend: np.ndarray, K: float, S: float = 2.0) -> np.ndarray:
    """Models saturation curve where K is half-saturation spend."""
    return (adstocked_spend ** S) / (adstocked_spend ** S + K ** S)

def fit_mmm_model(X_transformed: np.ndarray, y_revenue: np.ndarray, alpha: float = 1.0):
    """Fits regularized Ridge regression to estimate channel coefficients."""
    model = Ridge(alpha=alpha, positive=True)
    model.fit(X_transformed, y_revenue)
    return model