`method_optweight.Rd`

This page explains the details of estimating optimization-based weights 9also known as stable balancing weights) by setting `method = "optweight"`

in the call to `weightit()`

or `weightitMSM()`

. This method can be used with binary, multinomial, 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 `optweight::optweight()`

from the optweight package.

Because `optweight()`

offers finer control and uses the same syntax as `weightit()`

, it is recommended that `optweight::optweight()`

be used instead of `weightit`

with `method = "optweight"`

.

For binary treatments, this method estimates the weights using `optweight::optweight()`

. The following estimands are allowed: ATE, ATT, and ATC. The weights are taken from the output of the `optweight`

fit object.

For multinomial treatments, this method estimates the weights using `optweight::optweight()`

. The following estimands are allowed: ATE and ATT. The weights are taken from the output of the `optweight`

fit object.

For binary treatments, this method estimates the weights using `optweight::optweight()`

. The weights are taken from the output of the `optweight`

fit object.

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!

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 0s (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`NA`

s.

All arguments to `optweight()`

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()`

.

`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`optweight::optweight()`

.

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 `optweight::optweight()`

. The syntax is almost identical and it's compatible with cobalt, too.

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.

**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

**Multinomial 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

`optweight::optweight()`

for the fitting function

```
library("cobalt")
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" (targeted 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 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
bal.tab(W1)
#> Call
#> weightit(formula = treat ~ age + educ + married + nodegree +
#> re74, data = lalonde, method = "optweight", estimand = "ATT",
#> tols = 0)
#>
#> 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
#Balancing covariates with respect to race (multinomial)
(W2 <- weightit(race ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "optweight", estimand = "ATE",
tols = .01))
#> A weightit object
#> - method: "optweight" (targeted 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 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
bal.tab(W2)
#> Call
#> weightit(formula = race ~ age + educ + married + nodegree + re74,
#> data = lalonde, method = "optweight", estimand = "ATE", tols = 0.01)
#>
#> 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
#Balancing covariates with respect to re75 (continuous)
(W3 <- weightit(re75 ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "optweight", tols = .05))
#> A weightit object
#> - method: "optweight" (targeted stable balancing weights)
#> - number of obs.: 614
#> - sampling weights: none
#> - treatment: continuous
#> - covariates: age, educ, married, nodegree, re74
summary(W3)
#> Summary of weights
#>
#> - Weight ranges:
#>
#> Min Max
#> all 0 |---------------------------| 3.966
#>
#> - Units with 5 most extreme weights by group:
#>
#> 482 483 200 178 180
#> all 2.9566 3.0117 3.048 3.5934 3.966
#>
#> - Weight statistics:
#>
#> Coef of Var MAD Entropy # Zeros
#> all 0.574 0.445 0.173 34
#>
#> - Effective Sample Sizes:
#>
#> Total
#> Unweighted 614.
#> Weighted 462.02
bal.tab(W3)
#> Call
#> weightit(formula = re75 ~ age + educ + married + nodegree + re74,
#> data = lalonde, method = "optweight", tols = 0.05)
#>
#> Balance Measures
#> Type Corr.Adj
#> age Contin. -0.0087
#> educ Contin. -0.0106
#> married Binary 0.0499
#> nodegree Binary -0.0451
#> re74 Contin. 0.0499
#>
#> Effective sample sizes
#> Total
#> Unadjusted 614.
#> Adjusted 462.02
```