Marginal mean weighting through stratification: a generalized method for evaluating multivalued and multiple treatments with nonexperimental data

Psychol Methods. 2012 Mar;17(1):44-60. doi: 10.1037/a0024918. Epub 2011 Aug 15.


Propensity score matching and stratification enable researchers to make statistical adjustment for a large number of observed covariates in nonexperimental data. These methods have recently become popular in psychological research. Yet their applications to evaluations of multi-valued and multiple treatments are limited. The inverse-probability-of-treatment weighting method, though suitable for evaluating multi-valued and multiple treatments, often generates results that are not robust when only a portion of the population provides support for causal inference or when the functional form of the propensity score model is misspecified. The marginal mean weighting through stratification (MMW-S) method promises a viable nonparametric solution to these problems. By computing weights on the basis of stratified propensity scores, MMW-S adjustment equates the pretreatment composition of multiple treatment groups under the assumption that unmeasured covariates do not confound the treatment effects given the observed covariates. Analyzing data from a weighted sample, researchers can estimate a causal effect by computing the difference between the estimated average potential outcomes associated with alternative treatments within the analysis of variance framework. After providing an intuitive illustration of the theoretical rationale underlying the weighting method for causal inferences, the article demonstrates how to apply the MMW-S method to evaluations of treatments measured on a binary, ordinal, or nominal scale approximating a completely randomized experiment; to studies of multiple concurrent treatments approximating factorial randomized designs; and to moderated treatment effects approximating randomized block designs. The analytic procedure is illustrated with an evaluation of educational services for English language learners attending kindergarten in the United States.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Analysis of Variance
  • Causality
  • Child
  • Data Interpretation, Statistical
  • Humans
  • Learning
  • Longitudinal Studies / statistics & numerical data
  • Models, Statistical*
  • Models, Theoretical
  • Program Evaluation / methods
  • Program Evaluation / statistics & numerical data*
  • Propensity Score
  • Randomized Controlled Trials as Topic / statistics & numerical data
  • Research Design
  • Selection Bias
  • Statistics, Nonparametric*
  • Vocabulary