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Output Values

The output from the summary() command includes the following elements, when applicable:

• The original assignment model call.
• sum.all: a data frame that contains variable names and interactions down the row names, and summary statistics on all observations in each of the columns. The columns in sum.all contain:
  • means of all covariates $X$ for treated and control units, where Means Treated $= \mu_{X\vert T=1} = \frac{1}{n_1} \sum_{T=1} X_i$ and Means Control $= \mu_{X\vert T=0} = \frac{1}{n_0} \sum_{T=0} X_i$ ,
  • standard deviation in the control group for all covariates $X$ , where applicable,
    $$\quad s_{x\vert T=0} = \sqrt{\frac{\sum_{i \in \{i: T_i=0\}} (X_i - \mu_{X\vert T=0})^2}{n_0-1} }.$$

  • balance statistics of the original data (before matching), which compare treated and control covariate distributions. If standardize = FALSE, balance measures will be presented on the original scale. Specifically, mean differences (Mean Diff.) as well as the median, mean, and maximum value of differences in empirical quantile functions for each covariate will be given (eQQ Med, eQQ Mean, and eQQ Max, respectively). If standardize = TRUE, the balance measures will be standardized. Standardized mean differences (Std. Mean Diff.), defined as $\frac{\mu_{X\vert T=1} - \mu_{X\vert T=0}}{s_{x\vert T=1}}$ , as well as the median, mean, and maximum value of differences in empirical cumulative distribution functions for each covariate will be given (eCDF Med, eCDF Mean, and eCDF Max, respectively).

• sum.matched: a data frame which contains variable names down the row names, and summary statistics on only the matched observations in each of the columns. Specifically, the columns in sum.matched contain the following elements:
  • weighted means for matched treatment units and matched control units of all covariates $X$ and their interactions, where Means Treated $= \mu_{wX\vert T=1} = \frac{1}{n_1} \sum_{T=1} w_iX_i$ and Means Control $=\mu_{wX\vert T=0} = \frac{1}{n_0} \sum_{T=0} w_iX_i$ ,
  • weighted standard deviations in the matched control group for all covariates $X$ , where applicable, where SD $= s_{wX} = \sqrt{\frac{1}{n} \sum_{i} (w_iX_i - \overline{X}^*)^2}$ , where $\overline{X}^*$ is the weighted mean of $X$ in the matched control group, and
  • balance statistics of the matched data (after matching), which compare treated and control covariate distributions. If standardize = FALSE, balance measures will be presented on the original scale. Specifically, mean differences (Mean Diff.) as well as the median, mean, and maximum value of differences in empirical quantile functions for each covariate will be given (eQQ Med, eQQ Mean, and eQQ Max, respectively). If standardize = TRUE, the balance measures will be standardized. Standardized mean differences (Std. Mean Diff.), defined as $\frac{\mu_{wX\vert T=1} - \mu_{wX\vert T=0}}{s_{x\vert T=1}}$ , as well as the median, mean, and maximum value of differences in empirical cumulative distribution functions for each covariate will be given (eCDF Med, eCDF Mean, and eCDF Max, respectively).
  where $w$ represents the vector of weights.

• reduction: the percent reduction in the difference in means achieved in each of the balance measures in sum.all and sum.matched, defined as $100(\vert a\vert-\vert b\vert)/\vert a\vert$ , where $a$ was the value of the balance measure before matching and $b$ is the value of the balance measure after matching.

• nn: the sample sizes in the full and matched samples and the number of discarded units, by treatment and control.

• q.table: an array that contains the same information as sum.matched by subclass.

• qn: the sample sizes in the full and matched samples and the number of discarded units, by subclass and by treatment and control.
• match.matrix: the same object is contained in the output of matchit().