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arXiv · 2412.00945

A Generalized Spatial Correlated Mean Component Model: Theory and Application to U.S. County Voting Data

N. A. Cruz·J. D. Toloza-Delgado·O. O. Melo
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Abstract

This paper introduces the generalized spatial correlated inverse mean component (GSCIMC), a flexible and computationally efficient framework for modeling spatial dependence in non-Gaussian data from the exponential family. We establish asymptotic properties of the proposed estimators, including consistency, asymptotic normality, and efficiency, and derive robust variance expressions that enable valid inference under heteroskedasticity or partial model misspecification. Through extensive simulation studies, we show that the GSCIMC estimator provides stable estimation, accurate inference, and reliable coverage across a wide range of spatial dependence structures and response distributions. An empirical analysis of U.S. county-level voting patterns in the 2020 presidential election illustrates the model's ability to identify spatial spillover effects while maintaining an interpretable regression framework, the proposed framework provides a practical and theoretically grounded tool for analyzing binary, count, or skewed continuous spatial responses. An open-source implementation is available in the spatemR package, facilitating the application of GSCIMC across disciplines such as environmental science, epidemiology, and regional economics.

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N. A. Cruz, J. D. Toloza-Delgado, O. O. Melo. 2026-09-21. A Generalized Spatial Correlated Mean Component Model: Theory and Application to U.S. County Voting Data. https://arxiv.org/abs/2412.00945

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