Summary

Fixes #2305.

When fit_regularized is called on discrete models (e.g., Logit, Probit, MNLogit, Poisson), the covariance parameter estimation in cov_params_func_l1 calls np.linalg.inv(-H_restricted) to invert the restricted Hessian matrix. If the data has perfect or quasi-perfect separation — where a predictor (or combination of predictors) perfectly predicts the outcome — the Hessian becomes singular and this inversion fails with a cryptic LinAlgError: Singular matrix message that gives users no guidance on the root cause.

Changes

• File: statsmodels/discrete/discrete_model.py
• Function: DiscreteModel.cov_params_func_l1
• Wrapped the np.linalg.inv(-H_restricted) call in a try/except np.linalg.LinAlgError block
• Re-raises the error with a descriptive message that:
  • Identifies the problem (singular Hessian, cannot invert)
  • Explains the likely causes (perfect separation, quasi-perfect separation, multicollinearity)
  • Suggests actionable remedies (check data for separation, remove redundant predictors, increase regularization alpha)

Before

numpy.linalg.LinAlgError: Singular matrix

After

numpy.linalg.LinAlgError: Hessian matrix is singular and cannot be inverted.
This is often caused by perfect or quasi-perfect separation in the data,
where one or more predictors perfectly predict the outcome, or by
multicollinearity among predictors. Consider checking your data for
separation, removing redundant predictors, or increasing the regularization
penalty (alpha).

Test plan

• Verify the error message is raised with the new descriptive text when fitting a logit model with perfectly separated data using fit_regularized
• Verify that normal fit_regularized usage (non-singular Hessian) is unaffected
• Run existing test suite: python -m pytest statsmodels/discrete/tests/ -x -q