Stable Balancing Weights for Multivariate Treatments

Estimates stable balancing weights for the supplied multivariate (i.e., multiple) treatments and covariates. The degree of balance for each covariate is specified by tols.list. See Zubizarreta (2015) and Wang & Zubizarreta (2020) for details of the properties of the weights and the methods used to fit them.

Usage

optweightMV(
  formula.list,
  data = NULL,
  tols.list = list(0),
  estimand = "ATE",
  targets = NULL,
  s.weights = NULL,
  b.weights = NULL,
  norm = "l2",
  min.w = 1e-08,
  verbose = FALSE,
  ...
)

optweightMV.fit(
  covs.list,
  treat.list,
  tols.list = list(0),
  estimand = "ATE",
  targets = NULL,
  s.weights = NULL,
  b.weights = NULL,
  norm = "l2",
  std.binary = FALSE,
  std.cont = TRUE,
  min.w = 1e-08,
  verbose = FALSE,
  solver = NULL,
  ...
)

Arguments

formula.list

a list of formulas, each with a treatment variable on the left hand side and the covariates to be balanced on the right hand side.

data

an optional data set in the form of a data frame that contains the variables in formula.list.

tols.list

a list of vectors of balance tolerance values for each covariate for each treatment. The resulting weighted balance statistics will be at least as small as these values. If only one value is supplied, it will be applied to all covariates. See Details. Default is 0 for all covariates.

estimand

the desired estimand, which determines the target population. Only "ATE" or NULL are supported. estimand is ignored when targets is non-NULL. If both estimand and targets are NULL, no targeting will take place.

targets

an optional vector of target population mean values for each covariate. The resulting weights will yield sample means within tols/2 units of the target values for each covariate. If NULL or all NA, estimand will be used to determine targets. Otherwise, estimand is ignored. If any target values are NA, the corresponding variable will not be targeted and its weighted mean will be wherever the weights yield the smallest variance; this is only allowed if all treatments are binary or multi-category. Can also be the output of a call to process_targets(). See Details.

s.weights

a vector of sampling weights. For optweightMV(), can also be the name of a variable in data that contains sampling weights.

b.weights

a vector of base weights. If supplied, the desired norm of the distance between the estimated weights and the base weights is minimized. For optweightMV(), can also the name of a variable in data that contains base weights.

norm

character; a string containing the name of the norm corresponding to the objective function to minimize. Allowable options include "l1" for the L1 norm, "l2" for the L2 norm (the default), "linf" for the L\(\infty\) norm, "entropy" for the negative entropy, and "log" for the sum of the logs. See Details.

min.w

numeric; a single value less than 1 for the smallest allowable weight. Some analyses require nonzero weights for all units, so a small, nonzero minimum may be desirable. The default is 1e-8 (\(10^{-8}\)), which does not materially change the properties of the weights from a minimum of 0 but prevents warnings in some packages that use weights in model fitting. When norm is "entropy" or "log" and min.w <= 0, min.w will be set to the smallest nonzero value.

verbose

logical; whether information on the optimization problem solution should be printed. Default is FALSE.

...

for optweightMV(), additional arguments passed to optweightMV.fit(), including options that are passed to the settings function corresponding to solver.

covs.list

a list containing one numeric matrix of covariates to be balanced for each treatment.

treat.list

a list containing one vector of treatment statuses for each treatment.

std.binary, std.cont

logical; whether the tolerances are in standardized mean units (TRUE) or raw units (FALSE) for binary variables and continuous variables, respectively. The default is FALSE for std.binary because raw proportion differences make more sense than standardized mean difference for binary variables. These arguments are analogous to the binary and continuous arguments in bal.tab() in cobalt.

solver

string; the name of the optimization solver to use. Allowable options depend on norm. Default is to use whichever eligible solver is installed, if any, or the default solver for the corresponding norm. See Details for information.

Value

For optweightMV(), an optweightMV object with the following elements:

weights

The estimated weights, one for each unit.

treat.list

A list of the values of the treatment variables.

covs.list

A list of the covariates for each treatment used in the fitting. Only includes the raw covariates, which may have been altered in the fitting process.

s.weights

The provided sampling weights.

b.weights

The provided base weights.

call

The function call.

tols

A list of tolerance values for each covariate for each treatment.

duals

A list of data.frames containing the dual variables for each covariate for each treatment. See optweight() for interpretation of these values.

info

A list containing information about the performance of the optimization at termination.

norm

The norm used.

solver

The solver used.

For optweightMV.fit(), an optweightMV.fit object with the following elements:

w

The estimated weights, one for each unit.

duals

A data.frame containing the dual variables for each covariate.

info

A list containing information about the performance of the optimization at termination.

norm

The norm used.

solver

The solver used.

Details

optweightMV() is the primary user-facing function for estimating stable balancing weights for multivariate treatments. The optimization is performed by the lower-level function optweightMV.fit(), which transforms the inputs into the required inputs for the optimization functions and then supplies the outputs (the weights, dual variables, and convergence information) back to optweightMV(). Little processing of inputs is performed by optweightMV.fit(), as this is normally handled by optweightMV().

See optweight() for more information about balance tolerances (i.e., those specified in tols.list), targets, norm, solver, and convergence failure.

References

Chattopadhyay, A., Cohn, E. R., & Zubizarreta, J. R. (2024). One-Step Weighting to Generalize and Transport Treatment Effect Estimates to a Target Population. The American Statistician, 78(3), 280–289. doi:10.1080/00031305.2023.2267598

Källberg, D., & Waernbaum, I. (2023). Large Sample Properties of Entropy Balancing Estimators of Average Causal Effects. Econometrics and Statistics. doi:10.1016/j.ecosta.2023.11.004

Wang, Y., & Zubizarreta, J. R. (2020). Minimal dispersion approximately balancing weights: Asymptotic properties and practical considerations. Biometrika, 107(1), 93–105. doi:10.1093/biomet/asz050

Zubizarreta, J. R. (2015). Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data. Journal of the American Statistical Association, 110(511), 910–922. doi:10.1080/01621459.2015.1023805

See also

optweight() for more information on the optimization, specifications, and options.

Examples

library("cobalt")
data("lalonde", package = "cobalt")

# Balancing two treatments
(ow1 <- optweightMV(list(treat ~ age + educ + race + re74,
                         re75 ~ age + educ + race + re74),
                    data = lalonde))
#> A optweightMV object
#>  - number of obs.: 614
#>  - norm minimized: "l2"
#>  - sampling weights: present
#>  - base weights: present
#>  - number of treatments: 2
#>     treat: 2-category
#>     re75: continuous
#>  - covariates: 
#>     + for treat: age, educ, race, re74
#>     + for re75: age, educ, race, re74

summary(ow1)
#>                   Summary of weights
#> 
#>             Treatment 1            
#>  - - - - - - - - - - Treatment 1 - - - - - - - - - -
#> - Weight ranges:
#> 
#>         Min                                 Max
#> treated   0 |---------------------------| 8.786
#> control   0 |--------------------|        6.704
#> 
#> - Units with the 5 most extreme weights by group:
#>                                       
#>            179   166   162   124    23
#>  treated 5.682 5.913   6.4 6.819 8.786
#>            300    48    26    19    15
#>  control 3.854 3.955 3.991 5.418 6.704
#> 
#> 
#> - Weight statistics:
#> 
#>            L2    L1    L∞ Rel Ent # Zeros
#> treated 1.783 1.35  7.786   1.276       0
#> control 0.955 0.743 5.704   0.477       0
#> 
#> - Effective Sample Sizes:
#> 
#>            Control Treated
#> Unweighted  429.    185.  
#> Weighted    224.31   44.26
#>             Treatment 2            
#>  - - - - - - - - - - Treatment 2 - - - - - - - - - -
#> - Weight ranges:
#> 
#>     Min                                 Max
#> all   0 |---------------------------| 8.786
#> 
#> - Units with the 5 most extreme weights:
#>                                 
#>        200 179   166   124    23
#>  all 5.913 6.4 6.704 6.819 8.786
#> 
#> 
#> - Weight statistics:
#> 
#>        L2    L1    L∞ Rel Ent # Zeros
#> all 1.263 0.926 7.786   0.718       0
#> 
#> - Effective Sample Sizes:
#> 
#>             Total
#> Unweighted 614.  
#> Weighted   236.54

bal.tab(ow1)
#> Balance by Time Point
#> 
#>  - - - Time: 1 - - - 
#> Balance Measures
#>                Type Diff.Adj
#> age         Contin.       -0
#> educ        Contin.       -0
#> race_black   Binary       -0
#> race_hispan  Binary        0
#> race_white   Binary       -0
#> re74        Contin.       -0
#> 
#> Effective sample sizes
#>            Control Treated
#> Unadjusted  429.    185.  
#> Adjusted    224.31   44.26
#> 
#>  - - - Time: 2 - - - 
#> Balance Measures
#>                Type Corr.Adj Diff.Target.Adj
#> age         Contin.       -0               0
#> educ        Contin.       -0               0
#> race_black   Binary       -0               0
#> race_hispan  Binary       -0              -0
#> race_white   Binary       -0              -0
#> re74        Contin.       -0               0
#> 
#> Effective sample sizes
#>             Total
#> Unadjusted 614.  
#> Adjusted   236.54
#>  - - - - - - - - - - - 
#>