rho-uncertainty 0.1.1

Correcting inference in SAR models for rho-estimation uncertainty

rho-uncertainty

Correcting inference in spatial autoregressive (SAR) models for the estimation uncertainty in ρ.

The standard plug-in procedure treats ρ̂ as known, producing standard errors that are systematically too small. This package provides two corrections:

• VIF (instant, closed-form): captures 40-67% of the true correction
• SANI (seconds, numerical): captures ~98% of the true correction

Installation

pip install rho-uncertainty

Or download rho_uncertainty.py directly and place it in your working directory.

Usage with PySAL/spreg

from spreg import ML_Lag
model = ML_Lag(y, X, w=w)

from rho_uncertainty import correct
correct(model)           # prints corrected regression table
correct(model, 'sani')   # higher accuracy (~10s)

Usage with raw matrices

from rho_uncertainty import rho_test

# W: spatial weights (n x n), X: design matrix (n x p, with intercept)
# y: dependent variable (n,), rho_hat: estimated rho
result = rho_test(W, X, y, rho_hat=0.3)

Quick VIF-only correction

from rho_uncertainty import vif_correction

factor = vif_correction(W, X, rho_hat)
se_corrected = se_naive * factor

Example output

======================================================================
  SAR Regression with Rho-Uncertainty Correction
======================================================================
  Dependent variable: crime
  n = 49,  p = 3,  rho_hat = 0.4159
  Method: VIF

      Variable      Coef  SE(naive)    SE(VIF)    t(VIF)   p-value
  -----------------------------------------------------------------
        income    0.4795     0.1587     0.1597    3.0020    0.0043  ***
         hoval   -0.0760     0.1583     0.1589   -0.4784    0.6346
  -----------------------------------------------------------------
  Average variance inflation: +1.07%
======================================================================

How it works

The VIF captures only 40-67% of the true variance correction due to a structural limitation called phantom substitution. SANI bypasses this through Rao-Blackwellized numerical integration.

Requirements

• Python >= 3.8
• NumPy >= 1.20
• SciPy >= 1.7

License

MIT