CBPS {CBPS}R Documentation

Covariate Balancing Propensity Score (CBPS) Estimation

Description

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

Usage

CBPS(formula, data, na.action, ATT = 1, iterations = 1000,
  standardize = TRUE, method = "over", twostep = TRUE,
  sample.weights = NULL, baseline.formula = NULL,
  diff.formula = NULL, ...)

Arguments

formula

An object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

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 environment(formula), typically the environment from which CBPS is called.

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 TRUE, which normalizes weights to sum to 1 within each treatment group. For continuous treatments, normalizes weights to sum up to 1 for the entire sample. Set to FALSE to return Horvitz-Thompson weights.

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 TRUE for a two-step estimator, which will run substantially faster than continuous-updating. Set to FALSE to use the continuous-updating estimator described by Imai and Ratkovic (2014).

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 optim().

Value

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=FALSE). Standardization will make weights sum to 1 within each treatment group. For continuous treatment, standardization will make all weights sum to 1. If sampling weights are used, the weight for each observation is multiplied by the survey sampling weight.

y

The treatment vector used

x

The covariate matrix

model

The model frame

converged

Convergence value. Returned from the call to optim().

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.

Author(s)

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.

References

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

See Also

summary.CBPS

Examples


###
### 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)


[Package CBPS version 0.22 Index]