Optimization-Based Weighting
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() from the optweight package.
Because optweight() offers finer control and uses the same syntax as weightit(), it is recommended that optweight() be used instead of weightit with method = "optweight".
For binary treatments, this method estimates the weights using 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(). 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(). 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!
Sampling weights are supported through s.weights in all scenarios.
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 NAs.
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.
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().
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 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(). The syntax is almost identical and it's compatible with cobalt, too.
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))
summary(W1)
bal.tab(W1)
#Balancing covariates with respect to race (multinomial)
(W2 <- weightit(race ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "optweight", estimand = "ATE",
tols = .01))
summary(W2)
bal.tab(W2)
#Balancing covariates with respect to re75 (continuous)
(W3 <- weightit(re75 ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "optweight", tols = .05))
summary(W3)
bal.tab(W3)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.