`method_ebcw.Rd`

This page explains the details of estimating weights using empirical balancing calibration weighting (EBCW) by setting `method = "ebcw"`

in the call to `weightit()`

. This method can be used with binary and multinomial treatments.

In general, this method relies on estimating weights by minimizing a function of the weights subject to exact moment balancing constraints. This method relies on `ATE::ATE()`

from the ATE package.

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

with `ATT = TRUE`

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

fit object. When the ATE is requested, `ATE()`

is run twice, once for each treatment group.

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

with `ATT = TRUE`

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

fit objects. When the ATE is requested, `ATE()`

is run once for each treatment group. When the ATT is requested, `ATE()`

is run once for each non-focal (i.e., control) group.

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 EBCW with longitudinal treatments has not 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 `ATE()`

can be passed through `weightit()`

, with the following exceptions:

`ATT`

is ignored because the estimand is passed using `estimand`

.

All arguments take on the defaults of those in `ATE`

.

`obj`

When

`include.obj = TRUE`

, the empirical balancing calibration model fit. For binary treatments with`estimand = "ATT"`

, the output of the call to`ATE::ATE()`

. For binary treatments with`estimand = "ATE"`

and multinomial treatments, a list of outputs of calls to`ATE::ATE()`

.

Chan, K. C. G., Yam, S. C. P., & Zhang, Z. (2016). Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 78(3), 673–700. doi:10.1111/rssb.12129

```
if (FALSE) { # requireNamespace("ATE", quietly = TRUE)
library("cobalt")
data("lalonde", package = "cobalt")
#Balancing covariates between treatment groups (binary)
(W1 <- weightit(treat ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "ebcw", estimand = "ATT"))
summary(W1)
bal.tab(W1)
#Balancing covariates with respect to race (multinomial)
(W2 <- weightit(race ~ age + educ + married +
nodegree + re74, data = lalonde,
method = "ebcw", estimand = "ATE"))
summary(W2)
bal.tab(W2)
}
```