Regression applied to symbolic interval-spatial data

Symbolic data analysis is a research area related to machine learning and statistics, which provides tools to describe geo-objects, and enables several types of variables to be dealt with, including interval type variables. Moreover, despite the recent progress in understanding symbolic data, there are no studies in the literature that address this type of data in the context of spatial data analysis. Thus, in this paper, we propose two different approaches of the spatial regression model for symbolic interval-valued data. The first fits a linear regression model on the minimum and maximum values of the interval values and the second fits a linear regression model on the center and range values of the interval. In order to evaluate the performance of these approaches, we have performed Monte Carlo simulations in which we calculated the mean value of the performance metric of the models analyzed. Furthermore, we also analyzed two applications involving real data. In the first, we examined the performance of the models in the Brazilian State of Pernambuco. In the second application, we analyzed the performance of the models for the Brazilian Northeastern region. Both applications were related to socioeconomic variables. We observed that in areas with less spatial variability, the interval spatial regression model performs better when compared with a usual method. When considering areas with a higher spatial variability, both ways presented similar results. Graphical abstract