Propensity Scores

Computing Propensity Scores

Propensity scores are probabilities that range from 0 to 1, where scores above .5 predict being in one condition (i.e., the treatment group) and those below .5 predict being in the other condition (i.e., the comparison group). Traditionally, propensity scores are computed using a logistic regression; however, more recently, other methods have been used, such as classification trees, bagging, and boosted modeling.

Logistic regression is the most common method for computing propensity scores. In this method, a set of known covariates is used in a logistic regression to predict the condition of assignment (treatment or control), and the propensity scores are the resulting predicted probabilities for each unit. The model for this regression equation is typically based on variables that affect selection into either the treatment or the outcome, including interactions among the predictors. It is not necessary that all predictors be statistically significant at p < .05 to be included in the model.

Classification and regression trees predict categorical outcomes (often dichotomous) from predictor variables through a sequence of hierarchical, binary splits. Each split is determined by the predicted probability that a unit will select into conditions based on a single predictor. With each dichotomous split, two branches result, and the splitting process continues for each new predictor until a certain number of nodes is obtained or all significant predictor variables are used. The result is a binary tree with terminal nodes (branches) representing groups of units that have the same predicted condition, although each node may have reached the same condition using different predictors. The predicted outcomes are propensity scores. A disadvantage of classification and regression trees is that their results are not very robust. The modeled trees are highly variable, and splits often change with minor variations in the data. One way to increase the stability of trees is to use bagging.

Bagging (bootstrap aggregation) averages results of many classification trees that are based on a series [Page 794] of bootstrap samples. In this case, random samples (with replacement) are drawn from the observed data set and additional observations are simulated to mimic the observed distributions. A new classification tree is computed for each simulated data set. Bootstrapped trees are aggregated to form aggregated trees, resulting in a more stable prediction model.

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