Maximum Likelihood Analysis for a Generalized Regession-Discontinuity Design

Abstract

The regression-discontinuity design (RDD) offers the possibility of making inferences about causal effects from observations on selected groups. The quasi-experimental groups are formed by dividing the scores of a premeasurement in two halves. The treatment effect is inferred from the differences between the regression of a postmeasurement on the premeasurement for the two groups. We discuss a generalized form of this design: (a) Apart from parallel shift of the regression lines, differences in variance and covariance are considered; (b) pretest and posttest may be multivariate; and (c) more than two groups may be involved in the design. Data from such a design are considered to have a truncated bivariate distribution. For the RDD, maximum likelihood parameter estimation procedures and tests of hypotheses are presented.