psweight() is a Mata class that computes inverse-probability weighting (IPW) weights for average treatment effect, average treatment effect on the treated, and average treatment effect on the untreated estimators for observational data. IPW estimators use estimated probability weights to correct for the missing data on the potential outcomes. Probabilities of treatment--propensity scores--are computed for each observation with one of variety of methods, including logistic regression (traditional IPW), covariate-balancing propensity scores (CBPS), penalized covariate-balancing propensity scores (PCBPS), prognostic score-balancing propensity scores, and other methods. It also constructs balance tables and assesses the distribution of the IPW weights.

psweight.ado is a Stata command that offers Stata users easy access to the class. However, the class offers more flexibility and can conduct some analyses unavailable with the Stata command.

psweight::solve() and psweight subcmd solve for propensity score model coefficients, propensity scores, and IPW weights as follows:

The first step involves computing coefficients for the propensity score model, b. The propensity score model takes the form of a logit regression model. Specifically, the propensity score for each row in the data is defined as

     p = invlogit(X * b')

where X is the vector of matching variables (tmvarlist) for the respective row.

You specify a subcmd to control how the vector b is computed in the internal numerical optimization problem. As discussed in Kranker, Blue, and Vollmer Forrow (2019), we can set up optimization problems to solve for the b that produces the best fit in the propensity score model, the b that produces the best balance on matching variables, the b that produces the best balance on prognostic scores, or something else. The subcmd also determines how the term "best balance" is defined in the previous sentence. That is, for a given subcmd, we can generically define b as the vector that solves the problem:

     b = argmin L(X,T,W)

where L(X,T,W) is a "loss function" that corresponds to the specified subcmd (e.g., logit regression or CBPS), given the data (X,T) and a vector of weights (W). (The weights are computed using the propensity scores, as we describe below. The propensity scores are calculated using b, the data, and the formula given above.) The available subcmds are listed in the documentation and include logit regression and CBPS (Imai and Ratkovic 2014).

In Kranker, Blue, and Vollmer Forrow (2019), we proposed adding a "penalty" to the loss function that lets you effectively prespecify the variance (or higher-order moments) of the IPW weight distribution. By constraining the distribution of the weights, you can choose among alternative sets of matching weights, some of which produce better balance and others of which yield higher statistical power. The penalized method solves for b in:

     b = argmin L(X,T,W) + f(W)

where f(W) is a smooth, flexible function that increases as the vector of observation weights (W) becomes more variable. The penalty options control the functional form of f(W); see details below.

Once the b is estimated, we can compute propensity scores (p) for each observation with the formula given above and the observation's matching variables (tmvarlist). The propensity scores are returned in a variable named _pscore.

Once propensity scores are computed for each observation, we can compute IPW "matching weights" for each observation. The formulas for the IPW weights depend on whether you request weights for estimating the average treatment effect (ate), the average treatment effect on the treated (atet), or the average treatment effect on the untreated (ateu).

Next, the weights are normalized to have mean equal to 1 in each group, and returned in the variable named _weight_mtch.

Finally, the final weights (a variable named _weight) are set equal to: _weight = W :* _weight_mtch, where W are the sample weights.

Keith Kranker

The code for implementing the CBPS method is based on work by Fong et al. (2018), namely the CBPS package for R. I also reviewed the Stata CBPS implementation by Filip Premik.

• Kranker, Keith, Laura Blue, and Lauren Vollmer Forrow. “Improving Effect Estimates by Limiting the Variability in Inverse Propensity Score Weights.” The American Statistician, Volume 75, 2021, Issue 3, pp 276-87. https://doi.org/10.1080/00031305.2020.1737229.

or

• Kranker, Keith. "psweight: IPW- and CBPS-type propensity score reweighting, with various extensions," Statistical Software Components S458657, Boston College Department of Economics, 2019. Available at https://ideas.repec.org/c/boc/bocode/s458657.html.

Source code is available at https://github.com/kkranker/psweight. Please report issues at https://github.com/kkranker/psweight/issues.

To install official releases from SSC, type this from your Stata command line:

. net describe psweight, from(http://fmwww.bc.edu/RePEc/bocode/p)

To install the latest version from Github, type this from your Stata command line:

. net from https://raw.githubusercontent.com/kkranker/psweight/master/

• Fong, C., M. Ratkovic, K. Imai, C. Hazlett, X. Yang, and S. Peng. 2018. CBPS: Covariate Balancing Propensity Score, Package for the Rprogramming langauage, The Comprehensive R Archive Network.Available at: https://CRAN.R-project.org/package=CBPS

• Imai, K. and M. Ratkovic. 2014. "Covariate Balancing Propensity Score."Journal of the Royal Statistical Society: Series B (StatisticalMethodology), 76(1): 243–263, doi:10.1111/rssb.12027.

• Kranker, Keith, Laura Blue, and Lauren Vollmer Forrow. “Improving Effect Estimates by Limiting the Variability in Inverse Propensity Score Weights.” The American Statistician, Volume 75, 2021, Issue 3, pp 276-87. https://doi.org/10.1080/00031305.2020.1737229.