Description Usage Arguments Value Author(s) References See Also Examples
CBPS
estimates propensity scores such that both covariate balance and
prediction of treatment assignment are maximized. The method, therefore,
avoids an iterative process between model fitting and balance checking and
implements both simultaneously. For cross-sectional data, the method can
take continuous treatments and treatments with a control (baseline)
condition and either 1, 2, or 3 distinct treatment conditions.
Fits covariate balancing propensity scores.
### @aliases CBPS CBPS.fit print.CBPS
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formula |
An object of class |
data |
An optional data frame, list or environment (or object coercible
by as.data.frame to a data frame) containing the variables in the model. If
not found in data, the variables are taken from |
na.action |
A function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. |
ATT |
Default is 1, which finds the average treatment effect on the treated interpreting the second level of the treatment factor as the treatment. Set to 2 to find the ATT interpreting the first level of the treatment factor as the treatment. Set to 0 to find the average treatment effect. For non-binary treatments, only the ATE is available. |
iterations |
An optional parameter for the maximum number of iterations for the optimization. Default is 1000. |
standardize |
Default is |
method |
Choose "over" to fit an over-identified model that combines the propensity score and covariate balancing conditions; choose "exact" to fit a model that only contains the covariate balancing conditions. |
twostep |
Default is |
sample.weights |
Survey sampling weights for the observations, if applicable. When left NULL, defaults to a sampling weight of 1 for each observation. |
baseline.formula |
Used only to fit iCBPS (see Fan et al). Currently only works with binary treatments. A formula specifying the balancing covariates in the baseline outcome model, i.e., E(Y(0)|X). |
diff.formula |
Used only to fit iCBPS (see Fan et al). Currently only works with binary treatments. A formula specifying the balancing covariates in the difference between the treatment and baseline outcome model, i.e., E(Y(1)-Y(0)|X). |
... |
Other parameters to be passed through to |
fitted.values |
The fitted propensity score |
linear.predictor |
X * beta |
deviance |
Minus twice the log-likelihood of the CBPS fit |
weights |
The optimal weights. Let π_i =
f(T_i | X_i). For binary ATE, these are given by T_i/π_i + (1 - T_i)/(1 - π_i). For
binary ATT, these are given by n/n_t * (T_i - π_i)/(1 - π_i). For multi_valued treatments,
these are given by ∑_{j=0}^{J-1} T_i,j / π_i,j. For continuous treatments,
these are given by f(T_i) / f(T_i | X_i)
. These expressions for weights are all before standardization (i.e. with
standardize= |
y |
The treatment vector used |
x |
The covariate matrix |
model |
The model frame |
converged |
Convergence value. Returned from the call to
|
call |
The matched call |
formula |
The formula supplied |
data |
The data argument |
coefficients |
A named vector of coefficients |
sigmasq |
The sigma-squared value, for continuous treatments only |
J |
The J-statistic at convergence |
mle.J |
The J-statistic for the parameters from maximum likelihood estimation |
var |
The covariance matrix for the coefficients. |
Ttilde |
For internal use only. |
Xtilde |
For internal use only. |
beta.tilde |
For internal use only. |
simgasq.tilde |
For internal use only. |
Christian Fong, Marc Ratkovic, Kosuke Imai, and Xiaolin Yang; The CBPS function is based on the code for version 2.15.0 of the glm function implemented in the stats package, originally written by Simon Davies. This documentation is likewise modeled on the documentation for glm and borrows its language where the arguments and values are the same.
Imai, Kosuke and Marc Ratkovic. 2014. “Covariate Balancing
Propensity Score.” Journal of the Royal Statistical Society, Series B
(Statistical Methodology).
http://imai.princeton.edu/research/CBPS.html
Fong, Christian, Chad
Hazlett, and Kosuke Imai. 2018. “Covariate Balancing Propensity Score
for a Continuous Treatment.” The Annals of Applied Statistics.
http://imai.princeton.edu/research/files/CBGPS.pdf
Fan, Jianqing and Imai, Kosuke and Liu, Han and Ning, Yang and Yang,
Xiaolin. “Improving Covariate Balancing Propensity Score: A Doubly Robust
and Efficient Approach.” Unpublished Manuscript.
http://imai.princeton.edu/research/CBPStheory.html
summary.CBPS
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### Example: propensity score matching
###
##Load the LaLonde data
data(LaLonde)
## Estimate CBPS
fit <- CBPS(treat ~ age + educ + re75 + re74 +
I(re75==0) + I(re74==0),
data = LaLonde, ATT = TRUE)
summary(fit)
## Not run:
## matching via MatchIt: one to one nearest neighbor with replacement
library(MatchIt)
m.out <- matchit(treat ~ fitted(fit), method = "nearest",
data = LaLonde, replace = TRUE)
### Example: propensity score weighting
###
## Simulation from Kang and Shafer (2007).
set.seed(123456)
n <- 500
X <- mvrnorm(n, mu = rep(0, 4), Sigma = diag(4))
prop <- 1 / (1 + exp(X[,1] - 0.5 * X[,2] +
0.25*X[,3] + 0.1 * X[,4]))
treat <- rbinom(n, 1, prop)
y <- 210 + 27.4*X[,1] + 13.7*X[,2] + 13.7*X[,3] + 13.7*X[,4] + rnorm(n)
##Estimate CBPS with a misspecified model
X.mis <- cbind(exp(X[,1]/2), X[,2]*(1+exp(X[,1]))^(-1)+10,
(X[,1]*X[,3]/25+.6)^3, (X[,2]+X[,4]+20)^2)
fit1 <- CBPS(treat ~ X.mis, ATT = 0)
summary(fit1)
## Horwitz-Thompson estimate
mean(treat*y/fit1$fitted.values)
## Inverse propensity score weighting
sum(treat*y/fit1$fitted.values)/sum(treat/fit1$fitted.values)
rm(list=c("y","X","prop","treat","n","X.mis","fit1"))
### Example: Continuous Treatment as in Fong, Hazlett,
### and Imai (2018). See
### https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/AIF4PI
### for a real data example.
set.seed(123456)
n <- 1000
X <- mvrnorm(n, mu = rep(0,2), Sigma = diag(2))
beta <- rnorm(ncol(X)+1, sd = 1)
treat <- cbind(1,X)%*%beta + rnorm(n, sd = 5)
treat.effect <- 1
effect.beta <- rnorm(ncol(X))
y <- rbinom(n, 1, (1 + exp(-treat.effect*treat -
X%*%effect.beta))^-1)
fit2 <- CBPS(treat ~ X)
summary(fit2)
summary(glm(y ~ treat + X, weights = fit2$weights,
family = "quasibinomial"))
rm(list=c("n", "X", "beta", "treat", "treat.effect",
"effect.beta", "y", "fit2"))
### Simulation example: Improved CBPS (or iCBPS) from Fan et al
set.seed(123456)
n <- 500
X <- mvrnorm(n, mu = rep(0, 4), Sigma = diag(4))
prop <- 1 / (1 + exp(X[,1] - 0.5 * X[,2] + 0.25*X[,3] + 0.1 * X[,4]))
treat <- rbinom(n, 1, prop)
y1 <- 210 + 27.4*X[,1] + 13.7*X[,2] + 13.7*X[,3] + 13.7*X[,4] + rnorm(n)
y0 <- 210 + 13.7*X[,2] + 13.7*X[,3] + 13.7*X[,4] + rnorm(n)
##Estimate iCBPS with a misspecificied model
X.mis <- cbind(exp(X[,1]/2), X[,2]*(1+exp(X[,1]))^(-1)+10,
(X[,1]*X[,3]/25+.6)^3, (X[,2]+X[,4]+20)^2)
fit1 <- CBPS(treat ~ X.mis, baseline.formula=~X.mis[,2:4],
diff.formula=~X.mis[,1], ATT = FALSE)
summary(fit1)
## End(Not run)
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