BUG: Test the rank of the IV inputs after scaling the columns

[inchang-ing]

Addresses case 3 of #823.

The rank checks in _validate_inputs call matrix_rank on the raw regressor and instrument matrices. matrix_rank thresholds the singular values relative to the largest one, so columns on very different scales look rank deficient even when they are not:

z = rng.standard_normal((500, 2))
x = z @ [1.0, 1.0] + rng.standard_normal(500)
y = 1 + 0.5 * x + rng.standard_normal(500)

IV2SLS(y, np.ones((500, 1)), x, z * [1.0, 1e13]).fit()
# ValueError: instruments [exog instruments]  do not have full column rank

Change

Both rank checks now scale the columns to unit length first, so the result does not depend on the units of the variables. A column that is exactly 0 cannot be scaled and is still detected as linearly dependent.

This is only the third case of #823; the LIML kappa cases (1 and 2) are untouched, since they need the relative-residual test and the joint change to the scaling of kappa.

Tests

• Added test_instr_rank_check_is_scale_invariant in tests/iv/test_model.py; it fits the model with an instrument scaled by 1e13 and compares the estimates with the unscaled ones.
• linearmodels/tests/iv/: 9522 passed, 2400 skipped.
• ruff check and numpydoc lint pass on the changed files.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.68%. Comparing base (89c3487) to head (cb1d80c).

Additional details and impacted files

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##             main     #850   +/-   ##
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  Coverage   99.68%   99.68%           
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  Files         199      199           
  Lines       37851    37861   +10     
  Branches     2433     2433           
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+ Hits        37730    37742   +12     
+ Misses         53       51    -2     
  Partials       68       68           

Flag	Coverage Δ
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subtractor	99.67% <100.00%> (+<0.01%)	⬆️

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[inchang-ing]

Gentle ping on this one — CI is green (15/15) and it is a small, self-contained bug fix. Would appreciate a review when you get a chance. Thanks!

[bashtage]

I'm not a fan of this. the regression is in the scale of the original columns, and if they are poorly scaled the numerics of the regression may be problematic. A rank check in the same scale as the regression should help protect the user from these numeric problems. What do you think?