3  Additional Options

3.1 Controlling Exact/Approximate Balancing

Users can manually control which group of covariates to be exactly balanced and which group to be approximately balanced (via regularization) by using the group.exact argument. It takes in a binary vector with length equal to the number of covariate groups, with 1 indicating exact balance on that group and 0 indicating approximate balance. Appropriate penalties are then searched through cross-validation. When using this option, please make that the length of vector supplied equals the number of groups.

For example, we can ask hbal() to achieve exact balance on the linear terms and two-way interactions and approximate balance for the rest:

out <- hbal(Treat = 'D', X = c('X1', 'X2'),  Y = 'Y', data = dat, 
            expand.degree = 3, cv = TRUE, group.exact = c(1, 1, 0, 0, 0))
#> Crossvalidation...
summary(out)
#> Call:
#>  hbal(data = dat, Treat = "D", X = c("X1", "X2"), Y = "Y", expand.degree = 3, 
#>     cv = TRUE, group.exact = c(1, 1, 0, 0, 0))
#> 
#>  Treated Controls 
#>      256     1244 
#>  Co/Tr Ratio = 4.86 
#> 
#>  Groups
#>                #Terms Penalty
#> linear              2     0.0
#> two-way             1     0.0
#> squared             2     0.0
#> squared*linear      2     0.0
#> cubic               2     4.7
#> 
#>  Balance Table
#>          Tr.Mean Co.Mean W.Co.Mean Std.Diff.(O) Std.Diff.(W)
#> X1          0.35   -0.11      0.35         0.46         0.00
#> X2          0.42   -0.07      0.42         0.49         0.00
#> X1.X2       0.24   -0.10      0.24         0.32         0.00
#> X1.X1       1.01    1.01      1.01         0.00         0.00
#> X2.X2       0.99    0.99      0.99         0.00         0.00
#> X1.X1.X2    0.32   -0.01      0.32         0.18         0.00
#> X1.X2.X2    0.32   -0.17      0.32         0.29         0.00
#> X1.X1.X1    0.93   -0.25      1.02         0.30        -0.02
#> X2.X2.X2    1.16   -0.23      0.95         0.40         0.06

3.2 User-Supplied Penalties

If researchers have prior knowledge about covariates and would like to supply specific penalties for each group of covariates, we can do so by passing a vector of penalties to the group.alpha argument. For example, we can manually set penalties to be 0 for the the linear terms and two-way interactions and 100 for other groups:

out <- hbal(Treat = 'D', X = c('X1', 'X2', 'X3'),  Y = 'Y', data = dat, 
            expand.degree = 3, group.alpha = c(0, 0, 100, 100, 100, 100))
summary(out)
#> Call:
#>  hbal(data = dat, Treat = "D", X = c("X1", "X2", "X3"), Y = "Y", 
#>     expand.degree = 3, group.alpha = c(0, 0, 100, 100, 100, 100))
#> 
#>  Treated Controls 
#>      256     1244 
#>  Co/Tr Ratio = 4.86 
#> 
#>  Groups
#>                #Terms Penalty
#> linear              3       0
#> two-way             3       0
#> squared             2     100
#> three-way           1     100
#> squared*linear      4     100
#> cubic               2     100
#> 
#>  Balance Table
#>          Tr.Mean Co.Mean W.Co.Mean Std.Diff.(O) Std.Diff.(W)
#> X1          0.35   -0.11      0.35         0.46         0.00
#> X2          0.42   -0.07      0.42         0.49         0.00
#> X3          0.52    0.51      0.52         0.02         0.00
#> X1.X2       0.24   -0.10      0.24         0.32         0.00
#> X1.X3       0.07   -0.02      0.07         0.12         0.00
#> X2.X3       0.21   -0.01      0.21         0.33         0.00
#> X1.X1       1.01    1.01      1.18         0.00        -0.12
#> X2.X2       0.99    0.99      1.06         0.00        -0.06
#> X1.X2.X3    0.13    0.00      0.14         0.18        -0.02
#> X1.X1.X2    0.32   -0.01      0.52         0.18        -0.11
#> X1.X2.X2    0.32   -0.17      0.37         0.29        -0.03
#> X1.X1.X3    0.55    0.52      0.58         0.03        -0.03
#> X2.X2.X3    0.50    0.47      0.55         0.02        -0.06
#> X1.X1.X1    0.93   -0.25      1.06         0.30        -0.03
#> X2.X2.X2    1.16   -0.23      1.03         0.40         0.04

3.3 Controlling Serial Expansion

Sometimes we may not want to perform serial expansion on all covariates but instead expand on a select set of covariates, we can do so by using the X.expand argument to specify the covariates we want to expand on. For example, we can expand only on X1:

out <- hbal(Treat = 'D', X = c('X1', 'X2', 'X3'),  Y = 'Y', data = dat, 
            expand.degree = 3, X.expand = c('X1', 'X2'))
summary(out)
#> Call:
#>  hbal(data = dat, Treat = "D", X = c("X1", "X2", "X3"), Y = "Y", 
#>     X.expand = c("X1", "X2"), expand.degree = 3)
#> 
#>  Treated Controls 
#>      256     1244 
#>  Co/Tr Ratio = 4.86 
#> 
#>  Groups
#>                #Terms Penalty
#> linear              3       0
#> two-way             1       0
#> squared             2       0
#> squared*linear      2       0
#> cubic               2       0
#> 
#>  Balance Table
#>          Tr.Mean Co.Mean W.Co.Mean Std.Diff.(O) Std.Diff.(W)
#> X1          0.35   -0.11      0.35         0.46            0
#> X2          0.42   -0.07      0.42         0.49            0
#> X3          0.52    0.51      0.52         0.02            0
#> X1.X2       0.24   -0.10      0.24         0.32            0
#> X1.X1       1.01    1.01      1.01         0.00            0
#> X2.X2       0.99    0.99      0.99         0.00            0
#> X1.X1.X2    0.32   -0.01      0.32         0.18            0
#> X1.X2.X2    0.32   -0.17      0.32         0.29            0
#> X1.X1.X1    0.93   -0.25      0.93         0.30            0
#> X2.X2.X2    1.16   -0.23      1.16         0.40            0

3.4 Selecting Covariates

Performing serial expansion on many covariates can result in a prohibitive number of covariates that need to be balanced on. In such cases, users many want to reduce the number of covariates by using the double selection method by Belloni et al. (2014). This screens the expanded covariates and only keeps those that are predictive for the treatment assignment or the outcome. Users can enable double selection by setting ds = TRUE. In the following case, almost all the higher-order terms except X1*X2 and X2*X3 are screened out by the double selection procedure.

out <- hbal(Treat = 'D', X = c('X1', 'X2', 'X3'),  Y = 'Y', data = dat, 
            expand.degree = 3, ds = TRUE) 
summary(out)
#> Call:
#>  hbal(data = dat, Treat = "D", X = c("X1", "X2", "X3"), Y = "Y", 
#>     expand.degree = 3, ds = TRUE)
#> 
#>  Treated Controls 
#>      256     1244 
#>  Co/Tr Ratio = 4.86 
#> 
#>  Groups
#>         #Terms Penalty
#> linear       2       0
#> two-way      2       0
#> 
#>  Balance Table
#>       Tr.Mean Co.Mean W.Co.Mean Std.Diff.(O) Std.Diff.(W)
#> X1       0.35   -0.11      0.35         0.46            0
#> X2       0.42   -0.07      0.41         0.49            0
#> X1.X2    0.24   -0.10      0.24         0.32            0
#> X2.X3    0.21   -0.01      0.21         0.33            0
att(out)

3.5 Keeping/Excluding Covariates

If there are covariates that users would like to keep in the balancing conditions regardless of whether they are selected in double selection, we can use the X.keep argument to specify the covariates to keep. On the other hand, if a priori we know some combinations of the covariates are nonsensical, we can exclude them explicitly by using the exclude argument. For example, we can exclude any interaction that involves X1 and X2:

out <- hbal(Treat = 'D', X = c('X1', 'X2', 'X3'),  Y = 'Y', data = dat, 
            expand.degree = 3, exclude = list(c('X1', 'X2')))
summary(out) # X1.X2 and X1.X1.X2 removed from balancing scheme
#> Call:
#>  hbal(data = dat, Treat = "D", X = c("X1", "X2", "X3"), Y = "Y", 
#>     expand.degree = 3, exclude = list(c("X1", "X2")))
#> 
#>  Treated Controls 
#>      256     1244 
#>  Co/Tr Ratio = 4.86 
#> 
#>  Groups
#>                #Terms Penalty
#> linear              3       0
#> two-way             2       0
#> squared             2       0
#> squared*linear      2       0
#> cubic               2       0
#> 
#>  Balance Table
#>          Tr.Mean Co.Mean W.Co.Mean Std.Diff.(O) Std.Diff.(W)
#> X1          0.35   -0.11      0.35         0.46            0
#> X2          0.42   -0.07      0.42         0.49            0
#> X3          0.52    0.51      0.52         0.02            0
#> X1.X3       0.07   -0.02      0.07         0.12            0
#> X2.X3       0.21   -0.01      0.21         0.33            0
#> X1.X1       1.01    1.01      1.01         0.00            0
#> X2.X2       0.99    0.99      0.99         0.00            0
#> X1.X1.X3    0.55    0.52      0.55         0.03            0
#> X2.X2.X3    0.50    0.47      0.50         0.02            0
#> X1.X1.X1    0.93   -0.25      0.93         0.30            0
#> X2.X2.X2    1.16   -0.23      1.16         0.40            0
att(out) 

Athey, Susan, Guido W Imbens, and Stefan Wager. 2018. “Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80 (4): 597–623.

Belloni, Alexandre, Victor Chernozhukov, and Christian Hansen. 2014. “Inference on Treatment Effects After Selection Among High-Dimensional Controls.” The Review of Economic Studies 81 (2): 608–50.

Ben-Michael, Eli, Avi Feller, David A Hirshberg, and José R Zubizarreta. 2021. “The Balancing Act in Causal Inference.” arXiv Preprint arXiv:2110.14831.

Black, Ryan C, and Ryan J Owens. 2016. “Courting the President: How Circuit Court Judges Alter Their Behavior for Promotion to the Supreme Court.” American Journal of Political Science 60 (1): 30–43.

Bruns-Smith, David, Oliver Dukes, Avi Feller, and Elizabeth L Ogburn. 2023. “Augmented Balancing Weights as Linear Regression.” arXiv Preprint arXiv:2304.14545.

Dehejia, Rajeev H, and Sadek Wahba. 1999. “Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs.” Journal of the American Statistical Association 94 (448): 1053–62.

Golub, Gene H, Michael Heath, and Grace Wahba. 1979. “Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter.” Technometrics 21 (2): 215–23.

Hainmueller, Jens. 2012. “Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies.” Political Analysis 20 (1): 25–46.

LaLonde, Robert J. 1986. “Evaluating the Econometric Evaluations of Training Programs with Experimental Data.” The American Economic Review, 604–20.

Lin, Winston. 2013. “Agnostic Notes on Regression Adjustments to Experimental Data: Reexamining Freedman’s Critique.” The Annals of Applied Statistics 7 (1): 295–318.

Xu, Yiqing, and Eddie Yang. 2022. “Hierarchically Regularized Entropy Balancing.” Political Analysis forthcoming.