Fitting Function for Optweight for Survey Weights

optweight.svy.fit performs the optimization (via osqp; Anderson, 2018) for optweight.svy and should, in most coses, not be used directly. No processing of inputs is performed, so they must be given exactly as described below.

Usage

optweight.svy.fit(covs,
                  tols = 0,
                  targets,
                  s.weights = NULL,
                  norm = "l2",
                  std.binary = FALSE,
                  std.cont = TRUE,
                  min.w = 1E-8,
                  verbose = FALSE,
                  ...)

Arguments

covs: A matrix of covariates to be targeted. Should must be numeric but does not have to be full rank.
tols: A vector of target balance tolerance values.
targets: A vector of target populaton 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 covairate is equal to its unweighted mean (i.e., so that its orginal mean is its target mean), its original mean must be supplied as a target.
s.weights: A vector of sampling weights. Optimization occurs on the product of the sampling weights and the estimated weights.
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 mean of the weights; the L2 norm minimizes the variance of the weights; the L\(\infty\) norm minimizes the largest weight. 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.
min.w: A single numeric value between 0 and 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 magntiude 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.
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.
...: Options that are passed to osqpSettings for use in the par arguments of solve_osqp.

Value

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. See Zubizarreta (2015) for interpretation of these values.
info: The info component of the output of solve_osqp, which contains information on the performance of the optimization at termination.

Details

optweight.svy.fit transforms the inputs into the required inputs for solve_osqp, which are (sparse) matrices and vectors, and then supplies the outputs (the weights, duals variables, and convergence information) back to optweight.svy. No processing of inputs is performed, as this is normally handled by optweight.svy.

Author

Noah Greifer

References

Anderson, E. (2018). osqp: Quadratic Programming Solver using the 'OSQP' Library. R package version 0.1.0. https://CRAN.R-project.org/package=osqp

Wang, Y., & Zubizarreta, J. R. (2017). Approximate Balancing Weights: Characterizations from a Shrinkage Estimation Perspective. ArXiv:1705.00998 [Math, Stat]. Retrieved from http://arxiv.org/abs/1705.00998

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")

covs <- splitfactor(lalonde[c("age", "educ", "race",
                  "married", "nodegree")],
                  drop.first = FALSE)

targets <- c(23, 9, .3, .3, .4, .2, .5)

tols <- rep(0, 7)

ows.fit <- optweight.svy.fit(covs,
                             tols = tols,
                             targets = targets,
                             norm = "l2")

#Unweighted means
apply(covs, 2, mean)
#>         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
apply(covs, 2, weighted.mean, w = ows.fit$w)
#>         age        educ  race_black race_hispan  race_white     married 
#>  27.3631922  10.2687296   0.3957655   0.1172638   0.4869707   0.4153094 
#>    nodegree 
#>   0.6302932