Constrained Regression Estimates of Technology Effects on Fuel Economy

This article reviews some practical aspects of linear regression modeling explicitly incorporating knowledge about the signs and ordering of the regression parameters. Statistical properties of equality and inequality constrained estimators are presented. This constrained methodology is applied to the problem of estimating the potential impact of specified technologies on motor vehicle fuel economy utilizing a data base consisting of over two thousand model year 1988–1990 cars and trucks. These estimates are compared with those obtained from an ordinary least squares analysis and with those obtained from a Bayesian analysis. The computational aspects of constrained least squares estimators are discussed. The problem can be formulated as a quadratic programming problem, transformed to a linear complementarity problem, and subsequently solved using available software in the Statistical Analysis System (SAS) Interactive Matrix Language. Depending on the nature of the constraints, the problem may be solved using a non-linear regression model procedure in SAS. The necessary transformation and mappings to accommodate these computational approaches are described.