A Class of Linear Multiple Regression Techniques for Ordered Attributes

Abstract

A class of linear multiple regression techniques is discussed, in which the order of magnitude is constrained, among regression coefficients. Each of the predictor variables is a qualitative variate having some categories which are on an ordinal scale. The criterion variable is quantitative. The problem is to solve a quadratic programming problem, in which the objective function is the residual sum of the squares of regression, and the constraints are linear ones imposed on the regression coefficients. Under some conditions for the observed data, the problem can be solved numerically. This technique works effectively for some types of regression analysis.