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| Rosenbaum, Paul R. and Donald B. Rubin, "The Central Role of the Propensity Score in Observational Studies for Causal Effects", Biometrika, Vol. 70, No. 1 (April 1983), pp. 41-55. Abstract: The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates. Applications include: (i) matched sampling on the univariate propensity score, which is a generalization of discriminant matching, (ii) multivariate adjustment by subclassification on the propensity score where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations, and (iii) visual representation of multivariate covariance adjustment by a two-dimensional plot. Keywords: Covariance adjustment, direct adjustment, discriminant matching, matched sampling, nonrandomized study, standardization, stratification, subclassification. Books Referenced in this Paper: (what is this?)
This worked rather nicely for us recently when we constructed a multi-Logit default probability model based on financial ratios. We tested whether ratios based on GAAP accounting statements were essentially the same as comparable ratios based on IFRS accounting statements (with the notion that we might pool them). --G.M.Gupton Download paper (535K PDF) 16 pages
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