Generalized spatial autoregressive model

TL;DR

The paper introduces the GSAR model, a flexible and computationally feasible spatial autoregression approach for non-normal data, with theoretical validation and practical application to voting patterns.

Contribution

It extends existing spatial models to handle a wider range of distributions, improving statistical properties and applicability.

Findings

GSAR outperforms standard models in capturing spatial autocorrelation.

Theoretical results confirm convergence, efficiency, and consistency.

Empirical application demonstrates improved inference in voting data.

Abstract

This paper presents the generalized spatial autoregression (GSAR) model, a significant advance in spatial econometrics for non-normal response variables belonging to the exponential family. The GSAR model extends the logistic SAR, probit SAR, and Poisson SAR approaches by offering greater flexibility in modeling spatial dependencies while ensuring computational feasibility. Fundamentally, theoretical results are established on the convergence, efficiency, and consistency of the estimates obtained by the model. In addition, it improves the statistical properties of existing methods and extends them to new distributions. Simulation samples show the theoretical results and allow a visual comparison with existing methods. An empirical application is made to Republican voting patterns in the United States. The GSAR model outperforms standard spatial models by capturing nuanced spatial autocorrelation and accommodating regional heterogeneity, leading to more robust inferences. These findings underline the potential of the GSAR model as an analytical tool for researchers working with categorical or count data or skewed distributions with spatial dependence in diverse domains, such as political science, epidemiology, and market research. In addition, the R codes for estimating the model are provided, which allows its adaptability in these scenarios.