spmixw 0.2.0

Bayesian Spatial Panel Data Models with Convex Combinations of Weight Matrices

spmixw

Bayesian Spatial Panel Data Models with Convex Combinations of Weight Matrices.

Python port of the R package spmixW, implementing Bayesian Markov chain Monte Carlo (MCMC) estimation of spatial panel data models including Spatial Autoregressive (SAR), Spatial Durbin Model (SDM), Spatial Error Model (SEM), Spatial Durbin Error Model (SDEM), and Spatial Lag of X (SLX) specifications with fixed effects.

Status

v0.1.0 (current): All standard panel models — OLS, SAR, SDM, SEM, SDEM, SLX — plus formula interface, model comparison via log-marginal likelihoods, and simulate_panel() for reproducible DGPs.

v0.2 (planned): Convex combinations of multiple weight matrices, following Debarsy and LeSage (2021).

v0.3 (planned): Bayesian Model Averaging (BMA) over subsets of weight matrices.

Installation

pip install spmixw

Quick start

import numpy as np
from spmixw import simulate_panel, spmodel, make_knw

# Generate weight matrix from random coordinates
rng = np.random.default_rng(42)
coords = rng.uniform(size=(80, 2))
W = make_knw(coords, k=5)

# Simulate from a SAR DGP
panel = simulate_panel(
    N=80, T=10, W=W, rho=0.5,
    beta=[1.0, -0.5], seed=42,
)

# Estimate using formula interface
res = spmodel(
    "y ~ x1 + x2",
    data=panel, W=W, model="sar",
    id="region", time="year",
    effects="twoway",
    ndraw=8000, nomit=2000, seed=42,
)

print(res)
print(res.tidy())
print(res.glance())

Models supported

Model	Function	Spatial parameter	Formula interface
OLS	ols_panel()	none	model="ols"
SAR	sar_panel()	ρ (lag)	model="sar"
SDM	sdm_panel()	ρ (lag)	model="sdm"
SEM	sem_panel()	λ (error)	model="sem"
SDEM	sdem_panel()	λ (error)	model="sdem"
SLX	slx_panel()	none	model="slx"

All models support fixed-effects specifications ("none", "region", "time", "twoway") and optional heteroscedastic errors via the Geweke (1993) Student-t mixture.

Model comparison

from spmixw import compare_models

comp = compare_models(
    "y ~ x1 + x2",
    data=panel, W=W,
    id="region", time="year", effects="twoway",
)
print(comp)
#   model  log_marginal  probability
# 0   SLX    -3587.68      0.0000
# 1   SDM    -3503.57      0.9817
# 2  SDEM    -3528.06      0.0183

License

GPL-3.0-or-later

References

• Debarsy, N. and LeSage, J.P. (2021). "Bayesian model averaging for spatial autoregressive models based on convex combinations of different types of connectivity matrices." Journal of Business & Economic Statistics, 40(2), 547-558. doi:10.1080/07350015.2020.1840993
• LeSage, J.P. and Pace, R.K. (2009). Introduction to Spatial Econometrics. Taylor & Francis/CRC Press.
• LeSage, J.P. (2020). "Fast MCMC estimation of multiple W-matrix spatial regression models and Metropolis-Hastings Monte Carlo log-marginal likelihoods." Journal of Geographical Systems, 22(1), 47-75.
• Geweke, J. (1993). "Bayesian Treatment of the Independent Student-t Linear Model." Journal of Applied Econometrics, 8(S1), S19-S40.