Abstract
In the ordinal regression methods, the additive utility function is estimated by the pair-wise comparison of sample items. A single additive utility function is estimated explicitly in the ordinal regression, while a set of additive utility functions is implicitly estimated in the robust ordinal regression. While the ordinal regression method is efficient in the estimation but the result is rather myopic, the robust ordinal regression is not very efficient in the estimation but the result is robust. In this paper, we propose an intermediate approach between the ordinal and robust ordinal regression methods, called the interval ordinal regression method. We estimate an interval model for the additive utility function. We show that the estimation problem can be reduced to a mixed integer programming problem. An example is given.
