Alternative weighting schemes for linear prediction

An important problem in applied research is the prediction of scores on a criterion from scores on a set of predictors. Typically, least squares regression is employed. However, in the small sample sizes seen frequently in applied settings, least squares regression is generally unstable. In this paper, the regression methods of equal weights, principal components, first principal component, equal weighting of components, and factor analysis are compared to least squares regression. For small to moderate samples drawn from the class of applied situations simulated here, equal weights regression is superior to the other methods studied.