2024/01/10 by Oldemar Rodŕıguez, Rodriguez, Oldemar
Computer Science · #Advanced Statistical Modeling Techniques #FOS: Computer and information sciences #Methodology (stat.ME) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2401.05471
openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a new approach to fit a linear regression for symbolic internal-valued variables, which improves both the Center Method suggested by Billard and Diday in \citeBillardDiday2000 and the Center and Range Method suggested by Lima-Neto, E.A. and De Carvalho, F.A.T. in \citeLima2008, Lima2010. Just in the Centers Method and the Center and Range Method, the new methods proposed fit the linear regression model on the midpoints and in the half of the length of the intervals as an additional variable (ranges) assumed by the predictor variables in the training data set, but to make these fitments in the regression models, the methods Ridge Regression, Lasso, and Elastic Net proposed by Tibshirani, R. Hastie, T., and Zou H in \citeTib1996, HastieZou2005 are used. The prediction of the lower and upper of the interval response (dependent) variable is carried out from their midpoints and ranges, which are estimated from the linear regression models with shrinkage generated in the midpoints and the ranges of the interval-valued predictors. Methods presented in this document are applied to three real data sets cardiologic interval data set, Prostate interval data set and US Murder interval data set to then compare their performance and facility of interpretation regarding the Center Method and the Center and Range Method. For this evaluation, the root-mean-squared error and the correlation coefficient are used. Besides, the reader may use all the methods presented herein and verify the results using the \tt RSDA package written in \tt R language, that can be downloaded and installed directly from \tt CRAN \citeRod2014.