Linear Programming Computational Procedures for Ordinal Regression

The ordinal regression problem is an extension to the standard multiple regression problem in terms of assuming only ordinal properties for the dependent variable (rank order of preferred brands in a product class, academic ranks for students in a class, etc.) while retaining the interval scale assumption for independent (or predictor) variables. The linear programming formulation for obtaining the regression weights for ordinal regression, developed in an earlier paper, is outlined and computational improvements and alternatives which utilize the special structure of this linear program are developed and compared for their computational efficiency and storage requirements. A procedure which solves the dual of the original linear programming formulation by the dual simplex method with upper bounded variables, in addition to utilizing the special structure of the constraint matrix from the point of view of storage and computation, performs the best in terms of both computational efficiency and storage requirements. Using this special procedure, problems with 100 observations and 4 independent variables take less than 1/2 minute, on an average, on the IBM 360/67. Results also show that the linear programming solution procedure for ordinal regression is valid — the correlation coefficient between “true” and predicted values for the dependent variable was greater than .9 for most of the problems tested.