Abstract

The general problem of forming composite variables from components is prevalent in many types of research. A major aspect of this problem is the weighting of components. Assuming that composites are a linear function of their components, composites formed by using standard linear regression are compared to those formed by simple unit weighting schemes, i.e., where predictor variables are weighted by 1.0. The degree of similarity between the two composites, expressed as the minimum possible correlation between them, is derived. This minimum correlation is found to be an increasing function of the intercorrelation of the components and a decreasing function of the number of predictors. Moreover, the minimum is fairly high for most applied situations. The predictive ability of the two methods is compared. For predictive purposes, unit weighting is a viable alternative to standard regression methods because unit weights: are not estimated from the data and therefore do not “consume” degrees of freedom; are “estimated” without error ; cannot reverse the “true” relative weights of the variables. Predictive ability of the two methods is examined as a function of sample size and number of predictors. It is shown that unit weighting will be superior to regression in certain situations and not greatly inferior in others. Various implications for using unit weighting are discussed and applications to several decision making situations are illustrated