Inequality Constraints in Regression Models to Symbolic Interval Variables

This paper introduces some approaches to fitting a constrained linear regression model to interval-valued data. The new methods show the importance of the range's information in their prediction performance and the use of inequality constraints to guarantee mathematical coherence between the predicted values of the lower bound (gamma
_Ui
) and the upper bound (ŷ
_Li
)-The authors also propose expressions to the goodness of fit measure called
determination coefficient
. The assessment of the proposed prediction methods is based on the estimation of the average behaviour of the
root mean square error
and of the
square of the correlation coefficient
in the framework of a Monte Carlo experiment with differents data sets configurations. Finally, the approaches proposed in this paper are applied in a real data-set.