method_optweight: Stable Balancing Weights

In WeightIt: Weighting for Covariate Balance in Observational Studies

Stable Balancing Weights

Description

This page explains the details of estimating stable balancing weights (also known as optimization-based weights) by setting method = "optweight" in the call to weightit(). This method can be used with binary, multi-category, and continuous treatments.

In general, this method relies on estimating weights by solving a quadratic programming problem subject to approximate or exact balance constraints. This method relies on \pkgfunoptweightoptweight.fit from the optweight package.

Because \pkgfunoptweightoptweight offers finer control and uses the same syntax as weightit(), it is recommended that optweight() be used instead of weightit() with method = "optweight".

Binary Treatments

For binary treatments, this method estimates the weights using \pkgfunoptweightoptweight.fit. The following estimands are allowed: ATE, ATT, and ATC. The weights are taken from the output of the optweight.fit fit object.

Multi-Category Treatments

For multi-category treatments, this method estimates the weights using \pkgfunoptweightoptweight.fit. The following estimands are allowed: ATE and ATT. The weights are taken from the output of the optweight.fit fit object.

Continuous Treatments

For continuous treatments, this method estimates the weights using \pkgfunoptweightoptweight.fit. The weights are taken from the output of the optweight.fit fit object.

Longitudinal Treatments

For longitudinal treatments, the weights are the product of the weights estimated at each time point. This method is not guaranteed to yield exact balance at each time point. NOTE: the use of stable balancing weights with longitudinal treatments has not been validated and should not be done!

Sampling Weights

Sampling weights are supported through s.weights in all scenarios, but only for versions of optweight greater than or equal to 1.0.0.

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

Stable balancing weights are weights that solve a constrained optimization problem, where the constraints correspond to covariate balance and the loss function is the variance (or other norm) of the weights. These weights maximize the effective sample size of the weighted sample subject to user-supplied balance constraints. An advantage of this method over entropy balancing is the ability to allow approximate, rather than exact, balance through the tols argument, which can increase precision even for slight relaxations of the constraints.

The function of the weights that is optimized can be changed using the norm argument. The default norm = "l2", minimizes the variance of the weights (i.e., maximizes the ESS). norm = "entropy" minimizes the negative entropy of the weights and is equivalent to entropy balancing, though in this implementation, inexact balance is allowed. norm = "log" minimizes the sum of the negative logs of the weights and is equivalent to nonparametric covariate balancing propensity score weighting (npCBPS). See \pkgfunoptweightoptweight.fit for the other allowed options to norm and other arguments.

plot() can be used on the output of weightit() with method = "optweight" to display the dual variables; see Examples and plot.weightit() for more details.

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 optweight.fit() can be passed through weightit() or weightitMSM(), with the following exception:

• targets cannot be used and is ignored.

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

Additional Outputs

info

A list with one entry:

duals

A data frame of dual variables for each balance constraint.

obj

When include.obj = TRUE, the output of the call to \pkgfunoptweightoptweight.fit.

Note

The specification of tols differs between weightit() and optweight(). In weightit(), one tolerance value should be included per level of each factor variable, whereas in optweight(), all levels of a factor are given the same tolerance, and only one value needs to be supplied for a factor variable. Because of the potential for confusion and ambiguity, it is recommended to only supply one value for tols in weightit() that applies to all variables. For finer control, use optweight() directly.

Seriously, just use \pkgfunoptweightoptweight. The syntax is almost identical and it's compatible with cobalt, too.

References

Binary treatments

Wang, Y., & Zubizarreta, J. R. (2020). Minimal dispersion approximately balancing weights: Asymptotic properties and practical considerations. Biometrika, 107(1), 93–105. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2015.1023805")}

Multi-Category Treatments

de los Angeles Resa, M., & Zubizarreta, J. R. (2020). Direct and Stable Weight Adjustment in Non-Experimental Studies With Multivalued Treatments: Analysis of the Effect of an Earthquake on Post-Traumatic Stress. Journal of the Royal Statistical Society Series A: Statistics in Society, 183(4), 1387–1410. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/rssa.12561")}

Continuous treatments

Greifer, N. (2020). Estimating Balancing Weights for Continuous Treatments Using Constrained Optimization. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.17615/DYSS-B342")}

See Also

weightit(), weightitMSM()

\pkgfun

optweightoptweight.fit for the fitting function.

method_entropy for entropy balancing, which is a special case of stable balancing weights.

method_npcbps for npCBPS weighting, which is also a special case of stable balancing weights.

Examples

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

#Balancing covariates between treatment groups (binary)
(W1 <- weightit(treat ~ age + educ + race +
                  nodegree + re74, data = lalonde,
                method = "optweight", estimand = "ATT",
                tols = 0))

summary(W1)

cobalt::bal.tab(W1)

plot(W1)

#Balancing covariates with respect to race (multi-category)
(W2 <- weightit(race ~ age + educ + married +
                  nodegree + re74, data = lalonde,
                method = "optweight", estimand = "ATE",
                tols = .01))

summary(W2)

cobalt::bal.tab(W2)

plot(W2)

#Balancing covariates with respect to re75 (continuous)
(W3 <- weightit(re75 ~ age + educ + race +
                  nodegree + re74, data = lalonde,
                method = "optweight", tols = .02))

summary(W3)

cobalt::bal.tab(W3)

plot(W3)

WeightIt documentation built on Nov. 5, 2025, 5:28 p.m.