J. D. Toloza-Delgado | Searcharxiv

arXiv2026

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

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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arXiv2024

Joint spatial modeling of mean and non-homogeneous variance combining semiparametric SAR and GAMLSS models for hedonic prices

In the context of spatial econometrics, it is very useful to have methodologies that allow modeling the spatial dependence of the observed variables and obtaining more precise predictions of both the mean and the variability of the response variable, something very useful in territorial planning and public policies. This paper proposes a new methodology that jointly models the mean and the variance. Also, it allows to model the spatial dependence of the dependent variable as a function of covariates and to model the semiparametric effects in both models. The algorithms developed are based on generalized additive models that allow the inclusion of non-parametric terms in both the mean and the variance, maintaining the traditional theoretical framework of spatial regression. The theoretical developments of the estimation of this model are carried out, obtaining desirable statistical properties in the estimators. A simulation study is developed to verify that the proposed method has a remarkable predictive capacity in terms of the mean square error and shows a notable improvement in the estimation of the spatial autoregressive parameter, compared to other traditional methods and some recent developments. The model is also tested on data from the construction of a hedonic price model for the city of Bogota, highlighting as the main result the ability to model the variability of housing prices, and the wealth in the analysis obtained.

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