8.4 Steps in Matching

  1. Select distance measure
    • Exact matching (same covariates values)
    • One-dimensional summary measure (Mahalanobis35, P-score)
    • Caliper: “One strategy to avoid poor matches is to impose a caliper and only to select a match if it is within the caliper.” (Stuart 2010, 10)
      • Describes the bandwidth that matches are allowed to have, e.g., for a unit aged 42 we could accept someone between 40 and 44 or between 30 and 54
  2. Matching method (see Sävje, Higgins, and Sekhon 2016, 5, fig.1)
    • Nearest neighbor matching (1:1 or k:1 nearest neighbor, optimal matching36, replacement37)
    • Subclassification38, full matching39 and weighting40
  3. Assessing balance
    • Compare multivariate covariate distribution
    • Practice: one-dimensional measures (std. difference in means, variance ratio etc)
    • Repeat prior steps until balance is good
  4. Analysis of outcome based on matched sample (estimate regression)

References

Sävje, F, M J Higgins, and J S Sekhon. 2016. “Generalized Full Matching.”

Stuart, E A. 2010. “Matching Methods for Causal Inference: A Review and a Look Forward.” Stat. Sci.

  1. As outlined by Stuart (2010, 10) the variance-covariance matrices on the basis of which we calculate the distances change depending on whether we are interested in the average treatment effect on the treated (ATT) or the average treatment effect (ATE).↩

  2. “One complication of simple (‘greedy’) nearest neighbormatching is that the order in which the treated subjects are matched may change the quality of the matches. Optimal matching avoids this issue by taking into account the overall set of matches when choosing individual matches, minimizing a global distance measure (Rosenbaum, 2002).” (Stuart 2010, 10)↩

  3. “Matching with replacement can often decrease bias because controls that look similar to many treated individuals can be used multiple times. This is particularly helpful in settings where there are few control individuals comparable to the treated individuals (e.g., Dehejia and Wahba, 1999). Additionally, when matching with replacement the order in which the treated individuals are matched does not matter. However, inference becomes more complex when matching with replacement, because the matched controls are no longer independent - some are in the matched sample more than once and this needs to be accounted for in the outcome analysis, for example by using frequency weights. When matching with replacement it is also possible that the treatment effect estimate will be based on just a small number of controls; the number of times each control is matched should be monitored.” (Stuart 2010, 11)↩

  4. “Subclassification forms groups of individuals who are similar,for example as defined by quintiles of the propensity score distribution.” (Stuart 2010, 11)↩

  5. “A more sophisticated form of subclassification, full matching, selects the number of subclasses automatically (Rosenbaum, 1991; Hansen, 2004; Stuart and Green,2008). Full matching creates a series of matched sets, where each matched set contains at least one treated individual and at least one control individual (and each matched set may have manyfrom either group).” (Stuart 2010, 11)↩

  6. “Propensity scores can also be used directly as inverseweights in estimates of the ATE, known as inverse probability of treatment weighting” (Stuart 2010, 12)↩