Estimate Targeting Weights Using Optimization

Estimate targeting weights for covariates specified in formula. The target means are specified with targets and the maximum distance between each weighted covariate mean and the corresponding target mean is specified by tols. See Zubizarreta (2015) for details of the properties of the weights and the methods used to fit them.

Usage

optweight.svy(
  formula,
  data = NULL,
  tols = 0,
  targets = NULL,
  s.weights = NULL,
  b.weights = NULL,
  verbose = FALSE,
  ...
)

Arguments

formula

A formula with nothing on the left hand side and the covariates to be targeted on the right hand side. See glm() for more details. Interactions and functions of covariates are allowed.

data

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

tols

A vector of target balance tolerance values for each covariate. The resulting weighted covariate means will be no further away from the targets than the specified values. If only one value is supplied, it will be applied to all covariates. Can also be the output of a call to check_tols().

targets

A vector of target population mean values for each covariate. The resulting weights will yield sample means within tols units of the target values for each covariate. 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. To ensure the weighted mean for a covariate is equal to its unweighted mean (i.e., so that its original mean is its target mean), its original mean must be supplied as a target.

s.weights

A vector of sampling weights or the name of a variable in data that contains sampling weights. Optimization occurs on the product of the sampling weights and the estimated weights.

b.weights

A vector of base weights or the name of a variable in data that contains base weights. If supplied, the desired norm of the distance between the estimated weights and the base weights is minimized.

verbose

Whether information on the optimization problem solution should be printed. This information contains how many iterations it took to estimate the weights and whether the solution is optimal.

...

Arguments passed on to optweight.svy.fit

norm: A string containing the name of the norm corresponding to the objective function to minimize. The options are "l1" for the L1 norm, "l2" for the L2 norm (the default), and "linf" for the L\(\infty\) norm. The L1 norm minimizes the average absolute distance between each weight and the base weights; the L2 norm minimizes the average squared distance between each weight and the base weights; the L\(\infty\) norm minimizes the largest absolute distance between each weight and the base weights. The L2 norm has a direct correspondence with the effective sample size, making it ideal if this is your criterion of interest.
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.
min.w: A single numeric 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. Doing so will likely (slightly) increase the variance of the resulting weights depending on the magnitude of the minimum. The default is 1e-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 to estimate treatment effects.

Value

An optweight.svy object with the following elements:

weights: The estimated weights, one for each unit.
covs: The covariates used in the fitting. Only includes the raw covariates, which may have been altered in the fitting process.
s.weights: The provided sampling weights.
call: The function call.
tols: The tolerance values for each covariate.
duals: A data.frame containing the dual variables for each covariate. See Details for interpretation of these values.
info: The info component of the output of osqp::solve_osqp(), which contains information on the performance of the optimization at termination.

Details

The optimization is performed by the lower-level function optweight.svy.fit() using osqp::solve_osqp() in the osqp package, which provides a straightforward interface to specifying the constraints and objective function for quadratic optimization problems and uses a fast and flexible solving algorithm.

Weights are estimated so that the standardized differences between the weighted covariate means and the corresponding targets are within the given tolerance thresholds (unless std.binary or std.cont are FALSE, in which case unstandardized mean differences are considered for binary and continuous variables, respectively). For a covariate \(x\) with specified tolerance \(\delta\), the weighted mean will be within \(\delta\) of the target. If standardized tolerance values are requested, the standardization factor is the standard deviation of the covariate in the whole sample. The standardization factor is always unweighted.

See the optweight() help page for information on interpreting dual variables and solving convergence failure.

References

Stellato, B., Banjac, G., Goulart, P., Boyd, S., & Bansal, V. (2024). osqp: Quadratic Programming Solver using the 'OSQP' Library R package version 0.6.3.3. doi:10.32614/CRAN.package.osqp

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

Examples

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

cov.formula <- ~ age + educ + race + married +
                      nodegree

targets <- check_targets(cov.formula, data = lalonde,
                        targets = c(23, 9, .3, .3, .4,
                                    .2, .5))

tols <- check_tols(cov.formula, data = lalonde,
                   tols = 0)

ows <- optweight.svy(cov.formula,
                     data = lalonde,
                     tols = tols,
                     targets = targets)
ows
#> An optweight.svy object
#>  - number of obs.: 614
#>  - sampling weights: none
#>  - covariates: age, educ, race, married, nodegree

#Unweighted means
col_w_mean(ows$covs)
#>         age        educ  race_black race_hispan  race_white     married 
#>  27.3631922  10.2687296   0.3957655   0.1172638   0.4869707   0.4153094 
#>    nodegree 
#>   0.6302932 

#Weighted means; same as targets
col_w_mean(ows$covs, w = ows$weights)
#>         age        educ  race_black race_hispan  race_white     married 
#>        23.0         9.0         0.3         0.3         0.4         0.2 
#>    nodegree 
#>         0.5