Nonparametric Covariate Balancing Propensity Score Weighting

This page explains the details of estimating weights from nonparametric covariate balancing propensity scores by setting method = "npcbps" in the call to weightit() or weightitMSM(). This method can be used with binary, multi-category, and continuous treatments.

In general, this method relies on estimating weights by maximizing the empirical likelihood of the data subject to balance constraints. This method relies on CBPS::npCBPS() from the CBPS package.

Binary Treatments

For binary treatments, this method estimates the weights using CBPS::npCBPS(). The ATE is the only estimand allowed. The weights are taken from the output of the npCBPS fit object.

Multi-Category Treatments

For multi-category treatments, this method estimates the weights using CBPS::npCBPS(). The ATE is the only estimand allowed. The weights are taken from the output of the npCBPS fit object.

Continuous Treatments

For continuous treatments, this method estimates the weights using CBPS::npCBPS(). The weights are taken from the output of the npCBPS fit object.

Longitudinal Treatments

For longitudinal treatments, the weights are the product of the weights estimated at each time point. NOTE: the use of npCBPS with longitudinal treatments has not been validated!

Sampling Weights

Sampling weights are not supported with method = "npcbps".

Missing Data

In the presence of missing data, the following value(s) for missing are allowed:

"ind" (default): First, for each variable with missingness, a new missingness indicator variable is created which takes the value 1 if the original covariate is NA and 0 otherwise. The missingness indicators are added to the model formula as main effects. The missing values in the covariates are then replaced with the covariate medians (this value is arbitrary and does not affect estimation). The weight estimation then proceeds with this new formula and set of covariates. The covariates output in the resulting weightit object will be the original covariates with the NAs.

M-estimation

M-estimation is not supported.

Details

Nonparametric CBPS involves the specification of a constrained optimization problem over the weights. The constraints correspond to covariate balance, and the loss function is the empirical likelihood of the data given the weights. npCBPS is similar to entropy balancing and will generally produce similar results. Because the optimization problem of npCBPS is not convex it can be slow to converge or not converge at all, so approximate balance is allowed instead using the cor.prior argument, which controls the average deviation from zero correlation between the treatment and covariates allowed.

Additional Arguments

moments: integer; the highest power of each covariate to be balanced. For example, if moments = 3, each covariate, its square, and its cube will be balanced. Can also be a named vector with a value for each covariate (e.g., moments = c(x1 = 2, x2 = 4)). Values greater than 1 for categorical covariates are ignored. Default is 1 to balance covariate means.
int: logical; whether first-order interactions of the covariates are to be balanced. Default is FALSE.
quantile: a named list of quantiles (values between 0 and 1) for each continuous covariate, which are used to create additional variables that when balanced ensure balance on the corresponding quantile of the variable. For example, setting quantile = list(x1 = c(.25, .5. , .75)) ensures the 25th, 50th, and 75th percentiles of x1 in each treatment group will be balanced in the weighted sample. Can also be a single number (e.g., .5) or a vector (e.g., c(.25, .5, .75)) to request the same quantile(s) for all continuous covariates. Only allowed with binary and multi-category treatments.

All arguments to npCBPS() can be passed through weightit() or weightitMSM().

All arguments take on the defaults of those in npCBPS().

Additional Outputs

obj: When include.obj = TRUE, the nonparametric CB(G)PS model fit. The output of the call to CBPS::npCBPS().

References

Fong, C., Hazlett, C., & Imai, K. (2018). Covariate balancing propensity score for a continuous treatment: Application to the efficacy of political advertisements. The Annals of Applied Statistics, 12(1), 156–177. doi:10.1214/17-AOAS1101

Examples

# Examples take a long time to run
data("lalonde", package = "cobalt")
# \donttest{
  #Balancing covariates between treatment groups (binary)
  (W1 <- weightit(treat ~ age + educ + married +
                    nodegree + re74, data = lalonde,
                  method = "npcbps", estimand = "ATE"))
#> A weightit object
#>  - method: "npcbps" (non-parametric covariate balancing propensity score weighting)
#>  - number of obs.: 614
#>  - sampling weights: none
#>  - treatment: 2-category
#>  - estimand: ATE
#>  - covariates: age, educ, married, nodegree, re74

  summary(W1)
#>                   Summary of weights
#> 
#> - Weight ranges:
#> 
#>           Min                                 Max
#> treated 0.559 |---------------------------| 9.886
#> control 0.559 |---|                         2.129
#> 
#> - Units with the 5 most extreme weights by group:
#>                                       
#>            182   181   172    69    58
#>  treated 3.363 4.199 8.369  8.44 9.886
#>            410   226   224   111    84
#>  control 1.645 1.663 1.741 1.825 2.129
#> 
#> - Weight statistics:
#> 
#>         Coef of Var   MAD Entropy # Zeros
#> treated       1.143 0.512   0.302       0
#> control       0.269 0.230   0.035       0
#> 
#> - Effective Sample Sizes:
#> 
#>            Control Treated
#> Unweighted  429.    185.  
#> Weighted    400.19   80.48

  cobalt::bal.tab(W1)
#> Balance Measures
#>             Type Diff.Adj
#> age      Contin.   0.0295
#> educ     Contin.  -0.0135
#> married   Binary   0.0407
#> nodegree  Binary  -0.0121
#> re74     Contin.   0.0704
#> 
#> Effective sample sizes
#>            Control Treated
#> Unadjusted  429.    185.  
#> Adjusted    400.19   80.48

  #Balancing covariates with respect to race (multi-category)
  (W2 <- weightit(race ~ age + educ + married +
                    nodegree + re74, data = lalonde,
                  method = "npcbps", estimand = "ATE"))
#> A weightit object
#>  - method: "npcbps" (non-parametric covariate balancing propensity score weighting)
#>  - number of obs.: 614
#>  - sampling weights: none
#>  - treatment: 3-category (black, hispan, white)
#>  - estimand: ATE
#>  - covariates: age, educ, married, nodegree, re74

  summary(W2)
#>                   Summary of weights
#> 
#> - Weight ranges:
#> 
#>          Min                                 Max
#> black  0.642  |--------------------------| 9.367
#> hispan 0.285 |---------------|             5.525
#> white  0.468 |-----|                       2.515
#> 
#> - Units with the 5 most extreme weights by group:
#>                                      
#>           241   166   163   153   152
#>   black 2.537 2.728 3.089 4.505 9.367
#>            67    43    39    36    28
#>  hispan 2.006 2.232 3.075 4.275 5.525
#>           291   285   258   205     6
#>   white  1.95 1.971 2.017 2.134 2.515
#> 
#> - Weight statistics:
#> 
#>        Coef of Var   MAD Entropy # Zeros
#> black        0.753 0.413   0.160       0
#> hispan       0.820 0.462   0.220       0
#> white        0.414 0.331   0.079       0
#> 
#> - Effective Sample Sizes:
#> 
#>            black hispan  white
#> Unweighted 243.   72.   299.  
#> Weighted   155.3  43.31 255.36

  cobalt::bal.tab(W2)
#> Balance summary across all treatment pairs
#>             Type Max.Diff.Adj
#> age      Contin.       0.0310
#> educ     Contin.       0.0431
#> married   Binary       0.0225
#> nodegree  Binary       0.0158
#> re74     Contin.       0.0432
#> 
#> Effective sample sizes
#>            black hispan  white
#> Unadjusted 243.   72.   299.  
#> Adjusted   155.3  43.31 255.36
# }