Abstract: 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 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 described which are equal percent bias reducing. The methods discussed in Section 8 will probably be the most generally applicable in practice. These matching methods are based on the values of the sample best linear discriminant or define distance by the inverse of the sample covariance matrix.

INTRODUCTION

In an observational (non-randomized) study the objective is often to determine the effect of a dichotomous treatment variable (e.g., exposure to a specific drug) on several dependent variables (e.g., blood pressure, cholesterol levels). The treatment variable defines two populations of units, P1 (e.g., subjects given the drug) and P2 (subjects not given the drug). Since the treatments were not randomly assigned to the units, estimating the effect of the treatment variable on the dependent variables using random samples from P1 and P2 may be quite biased.