This page explains the details of estimating optimization-based weights (also known as stable balancing weights) by setting method = "optweight" in the call to weightit() or weightitMSM(). 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 optweightoptweight from the optweight package.
Because optweight() offers finer control and uses the same syntax as weightit(), it is recommended that optweightoptweight be used instead of weightit() with method = "optweight".
Binary Treatments
For binary treatments, this method estimates the weights using optweightoptweight. The following estimands are allowed: ATE, ATT, and ATC. The weights are taken from the output of the optweight fit object.
Multi-Category Treatments
For multi-category treatments, this method estimates the weights using optweightoptweight. The following estimands are allowed: ATE and ATT. The weights are taken from the output of the optweight fit object.
Continuous Treatments
For binary treatments, this method estimates the weights using optweightoptweight. The weights are taken from the output of the optweight fit object.
Longitudinal Treatments
For longitudinal treatments, optweight() estimates weights that simultaneously satisfy balance constraints at all time points, so only one model is fit to obtain the weights. Using method = "optweight" in weightitMSM() causes is.MSM.method to be set to TRUE by default. Setting it to FALSE will run one model for each time point and multiply the weights together, a method that is not recommended. NOTE: neither use of optimization-based weights with longitudinal treatments has been validated!
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
NAand 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 resultingweightitobject will be the original covariates with theNAs.
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.
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.
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 optweightoptweight. The syntax is almost identical and it's compatible with cobalt, too.
Additional Arguments
moments and int are accepted. See weightit() for details.
quantileA 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 ofx1in each treatment group will be balanced in the weighted sample. Can also be a single number (e.g.,.5) or an unnamed list of length 1 (e.g.,list(c(.25, .5, .75))) to request the same quantile(s) for all continuous covariates, or a named vector (e.g.,c(x1 = .5, x2 = .75)to request one quantile for each covariate. Only allowed with binary and multi-category treatments.
All arguments to optweight() can be passed through weightit() or weightitMSM(), with the following exception:
targetscannot be used and is ignored.
All arguments take on the defaults of those in optweight().
Additional Outputs
infoA list with one entry:
dualsA data frame of dual variables for each balance constraint.
objWhen
include.obj = TRUE, the output of the call to optweightoptweight.
References
Binary treatments
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
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), n/a(n/a). doi:10.1111/rssa.12561
Continuous treatments
Greifer, N. (2020). Estimating Balancing Weights for Continuous Treatments Using Constrained Optimization. doi:10.17615/DYSS-B342
Examples
data("lalonde", package = "cobalt")
#Balancing covariates between treatment groups (binary)
(W1 <- weightit(treat ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "optweight", estimand = "ATT",
tols = 0))
#> A weightit object
#> - method: "optweight" (stable balancing weights)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: 2-category
#> - estimand: ATT (focal: 1)
#> - covariates: age, educ, married, nodegree, re74
summary(W1)
#> Summary of weights
#>
#> - Weight ranges:
#>
#> Min Max
#> treated 1 || 1.0000
#> control 0 |---------------------------| 3.0426
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 5 4 3 2 1
#> treated 1 1 1 1 1
#> 411 589 269 409 296
#> control 2.5261 2.5415 2.6434 2.7396 3.0426
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> treated 0.000 0.000 0.000 0
#> control 0.788 0.697 0.393 83
#>
#> - Effective Sample Sizes:
#>
#> Control Treated
#> Unweighted 429. 185
#> Weighted 264.88 185
cobalt::bal.tab(W1)
#> Balance Measures
#> Type Diff.Adj
#> age Contin. -0
#> educ Contin. -0
#> married Binary -0
#> nodegree Binary 0
#> re74 Contin. -0
#>
#> Effective sample sizes
#> Control Treated
#> Unadjusted 429. 185
#> Adjusted 264.88 185
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))
#> A weightit object
#> - method: "optweight" (stable balancing weights)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: 3-category (black, hispan, white)
#> - estimand: ATE
#> - covariates: age, educ, married, nodegree, re74
summary(W2)
#> Summary of weights
#>
#> - Weight ranges:
#>
#> Min Max
#> black 0.4429 |-----------------------| 3.5741
#> hispan 0.0000 |-------------------| 2.5848
#> white 0.2574 |---------| 1.6593
#>
#> - Units with the 5 most extreme weights by group:
#>
#> 184 190 485 181 182
#> black 2.3351 2.3723 2.5586 2.8367 3.5741
#> 392 345 269 564 371
#> hispan 2.0459 2.0984 2.1887 2.1982 2.5848
#> 68 589 324 599 531
#> white 1.5706 1.5706 1.5725 1.5968 1.6593
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> black 0.550 0.443 0.130 0
#> hispan 0.566 0.449 0.176 2
#> white 0.353 0.295 0.065 0
#>
#> - Effective Sample Sizes:
#>
#> black hispan white
#> Unweighted 243. 72. 299.
#> Weighted 186.76 54.7 266.01
cobalt::bal.tab(W2)
#> Balance summary across all treatment pairs
#> Type Max.Diff.Adj
#> age Contin. 0.01
#> educ Contin. 0.01
#> married Binary 0.01
#> nodegree Binary 0.01
#> re74 Contin. 0.01
#>
#> Effective sample sizes
#> black hispan white
#> Unadjusted 243. 72. 299.
#> Adjusted 186.76 54.7 266.01
plot(W2)
#Balancing covariates with respect to re75 (continuous)