Regression Models for Symbolic Interval-Valued Variables

This paper presents new approaches to fit regression models for symbolic internal-valued variables, which are shown to improve and extend the center method suggested by Billard and Diday and the center and range method proposed by Lima-Neto, E.A.and De Carvalho, F.A.T. Like the previously mentioned methods, the proposed regression models consider the midpoints and half of the length of the intervals as additional variables. We considered various methods to fit the regression models, including tree-based models, K-nearest neighbors, support vector machines, and neural networks. The approaches proposed in this paper were applied to a real dataset and to synthetic datasets generated with linear and nonlinear relations. For an evaluation of the methods, the root-mean-squared error and the correlation coefficient were used. The methods presented herein are available in the the RSDA package written in the R language, which can be installed from CRAN.