Second Order Regression and Distance Analysis

Summary

This paper discusses alternative strategies in a data analytical situation where one would usually apply multiple regression analysis. The target units of the analysis are a set of predictor variables on the one hand and a criterion variable on the other hand. In the first place we move away from the multiple regression approach by allowing the influence of the predictor set to be channeled through a latent variable that does not have to fit in the predictor space. This technique will be shown to have certain distance properties. These properties are emphazised by introducing a loss function that is defined explicitly on the distances. A special feature of this loss function is that the result of the analysis might be multidimensional. An example is given that investigates the predictive properties.