Multivariate Matching Methods That are Equal Percent Bias Reducing, I: Some Examples

Multivariate matching methods are commonly used in the behavioral and medical sciences in an attempt to control bias when randomization is not feasible. Some examples of multivariate matching methods are discussed in Althauser and Rubin (1970) and Cochran and Rubin (1973), but otherwise seem to have received little attention in the literature. Here, we present examples of multivariate matching methods that will yield the same percent reduction in bias for each matching variable for a variety of underlying distributions. Eleven distributional cases are considered, and for each one, matching methods are defined which are equal percent bias reducing. Methods discussed in Section 8, which are based on the values of the estimated best linear discriminant or which define distance by a sample based inner-product, will probably be the most generally applicable in practice.