CBPS (version 0.1)

CBPS: 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.

Usage

CBPS(formula, data, na.action, ATT = 1, iterations = 1000, 
	       standardize = TRUE, method = "over", twostep = TRUE, ...)
	  CBPS.fit(treat, X, ATT, method, iterations, 
			   standardize, twostep, ...)

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

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 fin

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).

treat

A vector of treatment assignments. Binary or multi-valued treatments should be factors. Continuous treatments should be numeric.

X

A covariate matrix.

...

Other parameters to be passed through to optim()

Value

• fitted.values
  The fitted propensity score
• deviance
  Minus twice the log-likelihood of the CBPS fit
• weights
  The optimal weights. Let $\pi_i = f(T_i | X_i)$. For binary ATE, these are given by $\frac{T_i}{\pi_i} + \frac{(1 - T_i)}{(1 - \pi_i)}$. For binary ATT, these are given by $\frac{n}{n_t} * T_i + \frac{n}{n_t} * \frac{1 - T_i}{1 - \pi_i}$. For multi_valued treatments, these are given by $\sum_{j=0}^{J-1} T_{i,j} / \pi_{i,j}$. For continuous treatments, these are given by $\frac{f(T_i)}{f(T_i | X_i)}$. 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.
• 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, evaluated numerically from optim().

Details

Fits covariate balancing propensity scores.

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. ``Parametric and Nonparametric Covariate Balancing Propensity Score for General Treatment Regimes.'' Unpublished Manuscript. http://imai.princeton.edu/research/files/CBGPS.pdf

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)
## 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 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, 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
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(mean(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"))