InteractiveFixedEffects Example

A compact factor-model helper for balanced panels

InteractiveFixedEffects is the no-covariate factor-model helper behind the panel tooling. It is not a full treatment-effect estimator by itself; it estimates a balanced-panel decomposition with additive unit/time structure and interactive latent factors. That makes it useful for inspecting whether a panel has low-rank structure before using matrix-completion or factor-style causal designs.

1 Simulate A Factor Panel

import matplotlib.pyplot as plt
import numpy as np

from crabbymetrics import InteractiveFixedEffects

np.set_printoptions(precision=4, suppress=True)

rng = np.random.default_rng(4403)

n_units = 40
n_periods = 32
rank = 2
time = np.arange(n_periods)

alpha = rng.normal(scale=0.5, size=n_units)
xi = 0.04 * time + 0.35 * np.sin(time / 5.0)
loadings = rng.normal(size=(n_units, rank))
factors = np.vstack(
    [
        np.sin(np.linspace(0.0, 2.4 * np.pi, n_periods)),
        np.cos(np.linspace(0.0, 1.8 * np.pi, n_periods)),
    ]
)

Y_signal = alpha[:, None] + xi[None, :] + loadings @ factors
Y = Y_signal + rng.normal(scale=0.10, size=Y_signal.shape)

print("Y shape:", Y.shape)
print("signal variance:", round(float(np.var(Y_signal)), 4))
print("noise variance:", round(float(np.var(Y - Y_signal)), 4))

Y shape: (40, 32)
signal variance: 1.0483
noise variance: 0.0106

2 Fit The Factor Model

model = InteractiveFixedEffects(rank=2, force=3)
model.fit(Y)
summary = model.summary()
Y_hat = model.predict()

rmse = np.sqrt(np.mean((Y - Y_hat) ** 2))
signal_rmse = np.sqrt(np.mean((Y_signal - Y_hat) ** 2))
print("fit RMSE against noisy panel:", round(float(rmse), 4))
print("fit RMSE against latent signal:", round(float(signal_rmse), 4))
print("summary keys:", sorted(summary))

fit RMSE against noisy panel: 0.0951
fit RMSE against latent signal: 0.0392
summary keys: ['alpha', 'factor', 'fit', 'force', 'loading', 'mu', 'rank', 'residuals', 'vnt', 'xi']

fig, axes = plt.subplots(1, 3, figsize=(13, 4.0), constrained_layout=True)

for ax, matrix, title in [
    (axes[0], Y, "Observed Panel"),
    (axes[1], Y_hat, "Fitted Factor Panel"),
    (axes[2], Y - Y_hat, "Residuals"),
]:
    im = ax.imshow(matrix, aspect="auto", cmap="viridis")
    ax.set_title(title)
    ax.set_xlabel("Period")
    ax.set_ylabel("Unit")
    fig.colorbar(im, ax=ax, shrink=0.78)

plt.show()

InteractiveFixedEffects is intentionally narrow: fit(y), predict(), and summary(). For causal estimation with treatment timing, use the higher-level HorizontalPanelRidge, SyntheticDID, or MatrixCompletion pages, which all own the absorbing-treatment matrix contract.