Hi @bashtage,
Over the last couple of months, we (mostly @schroedk) have spent quite a bit of time developing a faster demeaning algorithm for fixed effects regression that works particularly well for poorly-connected fixed effects (as e.g. in worker firm panels with little mobility). The core idea is to replace the diagonal preconditioner that linearmodels current LSMR implementation uses with an additive Schwarz preconditioner.
For some fixed effects structures, this new preconditioner works much better than diagonal LSMR:
We have Python bindings published to PyPi as within_py that has a pretty simple API. Here is how you'd fit a simple FWL problem:
beta_true = np.array([1.0, -2.0, 0.5])
X = np.random.randn(n, 3)
y = X @ beta_true + np.random.randn(n)
result = solve_batch(fe, np.column_stack([y, X]))
y_tilde, X_tilde = result.demeaned[:, 0], result.demeaned[:, 1:]
beta_hat = np.linalg.lstsq(X_tilde, y_tilde, rcond=None)[0]
print(np.round(beta_hat, 4)) # [ 0.9982 -2.006 0.5005]
If you are curious how the solver works, we have written up details here and here.
Would you be interested to try this out as a second, optional solver for the AbsoringLS backend? If yes, I'd set up a draft PR in the next days / weeks.
Best, Alex
Hi @bashtage,
Over the last couple of months, we (mostly @schroedk) have spent quite a bit of time developing a faster demeaning algorithm for fixed effects regression that works particularly well for poorly-connected fixed effects (as e.g. in worker firm panels with little mobility). The core idea is to replace the diagonal preconditioner that
linearmodelscurrent LSMR implementation uses with an additive Schwarz preconditioner.For some fixed effects structures, this new preconditioner works much better than diagonal LSMR:
We have Python bindings published to PyPi as
within_pythat has a pretty simple API. Here is how you'd fit a simple FWL problem:If you are curious how the solver works, we have written up details here and here.
Would you be interested to try this out as a second, optional solver for the
AbsoringLSbackend? If yes, I'd set up a draft PR in the next days / weeks.Best, Alex