Stable Balancing Weights for Generalization

Estimates stable balancing weights to generalize a sample characterized by supplied covariates to a given target population. The target means are specified with targets and the maximum distance between each weighted covariate mean. 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,
  norm = "l2",
  min.w = 1e-08,
  verbose = FALSE,
  ...
)

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

Arguments

formula: a formula with nothing on the left hand side and the covariates to be targeted on the right hand side. Interactions and functions of covariates are allowed. Can be omitted, in which case all variables in data are assumed targeted. If data is NULL and formula is a data.frame, data will be replaced with formula.
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 process_tols(). Default is 0 for all covariates.
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. For factor variables, a target value must be specified for each level of the factor, and these values must add up to 1. Can also be the output of a call to process_targets().
s.weights: a vector of sampling weights. For optweight(), 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 optweight(), 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 optweight(), additional arguments passed to optweight.fit(), including options that are passed to the settings function corresponding to solver.
covs: a numeric matrix of covariates to be targeted.
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 optweight.svy(), 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 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 optweight.svy.fit(), an optweight.svy.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

optweight.svy() is the primary user-facing function for estimating stable balancing weights for generalization to a target population. The optimization is performed by the lower-level function optweight.svy.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 optweight.svy(). Little processing of inputs is performed by optweight.svy.fit(), as this is normally handled by optweight.svy().

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.

Target constraints are applied to the product of the estimated weights and the sampling weights. In addition, sum of the product of the estimated weights and the sampling weights is constrained to be equal to the sum of the product of the base weights and sampling weights.

See optweight() for information on norm, solver, and convergence failure.

References

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