Goal Programming Formulations For A Comparative Analysis Of Scalar Norms And Ordinal Vs. Ratio Data

Abstract

Goal programming has proven a valuable mathematical programming form in a number of venues. There has been a similar rapid growth in interest in data mining, where a variety of different data types are encountered. This paper applies goal programming formulations to compare relative performance of L1, L2, and L∞ norms as well as ordinal and ratio data types in a dynamic predictive environment. The models are applied to compare relative accuracy and stability in forecasting a professional athletic environment. Results confirm that ratio data provide more accurate forecasts than ordinal data. Responsiveness to error can be good and bad in prediction. Too much response to outlying events makes the predictor “nervous” and unreliable. L1 metric models are much easier and faster to solve, but involve higher levels of ambiguity than nonlinear models. L1 metric models also were more responsive to changes, but correspondingly tend to be more affected by unexpected outcomes.