| Title: | Doubly Robust Distribution Balancing Weighting Estimation |
|---|---|
| Description: | Implements the doubly robust distribution balancing weighting proposed by Katsumata (2024) <doi:10.1017/psrm.2024.23>, which improves the augmented inverse probability weighting (AIPW) by estimating propensity scores with estimating equations suitable for the pre-specified parameter of interest (e.g., the average treatment effects or the average treatment effects on the treated) and estimating outcome models with the estimated inverse probability weights. It also implements the covariate balancing propensity score proposed by Imai and Ratkovic (2014) <doi:10.1111/rssb.12027> and the entropy balancing weighting proposed by Hainmueller (2012) <doi:10.1093/pan/mpr025>, both of which use covariate balancing conditions in propensity score estimation. The point estimate of the parameter of interest and its uncertainty as well as coefficients for propensity score estimation and outcome regression are produced using the M-estimation. The same functions can be used to estimate average outcomes in missing outcome cases. |
| Authors: | Hiroto Katsumata [aut, cre, cph]
|
| Maintainer: | Hiroto Katsumata <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.1.4 |
| Built: | 2025-02-16 05:30:54 UTC |
| Source: | https://github.com/hirotokatsumata/dbw |
dbw estimates a pre-specified parameter of interest (e.g.,
the average treatment effects (ATE) or the average treatment effects
on the treated (ATT)) with the augmented inverse probability weighting
(AIPW), where propensity scores are estimated using estimating
equations suitable for the parameter of interest and outcome models are
estimated using inverse probability weights. dbw can
also be used to estimate average outcomes (AO) in missing outcome cases.
dbw( formula_y, formula_ps, estimand = "ATE", method = "dbw", method_y = "wls", data, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95, tol = 1e-10, init_lambda = 0.01 )dbw( formula_y, formula_ps, estimand = "ATE", method = "dbw", method_y = "wls", data, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95, tol = 1e-10, init_lambda = 0.01 )
formula_y |
an object of class |
formula_ps |
an object of class |
estimand |
a character string specifying a parameter of interest. Choose
"ATT" for the average treatment effects on the treated estimation, "ATE"
for the average treatment effects estimation, "ATC" for the average
outcomes estimation in missing outcome cases. You can choose "ATEcombined"
for the combined estimation for the average treatment effects estimation
when using the covariate balancing weighting ( |
method |
a character string specifying a method for propensity score estimation. Choose "dbw" for the distribution balancing weighting, "cb" for the covariate balancing weighting, "eb" for the entropy balancing weighting, and "mle" for the logistic regression with the maximum likelihood estimation. |
method_y |
a character string specifying a method for potential outcome
prediction. Choose "wls" for the linear model, "logit" for the logistic
regression, "gam" for the generalized additive model for the continuous
outcome, and "gambinom" for the generalized additive model for the binary
outcome. Note that variance-covariance matrix is calculated only when
|
data |
a data frame (or one that can be coerced to that class) containing the outcomes and the variables in the model. |
normalize |
a logical parameter indicating whether to normalize the estimated
weights to sum up to one for each treatment group for |
vcov |
a logical parameter indicating whether to estimate the variance. Default is TRUE. |
lambda |
a parameter taking 0 or larger specifying the degree of the
L2-regularization for propensity score estimation. |
weights |
an optional vector of ‘prior weights’ (e.g. sampling weights) to be used in the fitting process. Should be NULL or a numeric vector. |
clevel |
confidence levels. Default is 0.95. |
tol |
a tolerance parameter for |
init_lambda |
a parameter for |
The treatment variable (or, response variable in missing outcome cases) must be binary and coded as 0 (for controlled or missing observations) or 1 (for treated or non-missing observations).
When the data frame has incomplete cases, which have NAs for either of
the treatment variable, the outcome variable, or explanatory variables
either for propensity score or outcome model estimation, dbw conducts
listwise deletion. Returned values (e.g., est_weights, ps, data)
do not contain values for these deleted cases.
For propensity score estimation, dbw can utilize the distribution
balancing weighting (method = "dbw"), covariate balancing weighting
(method = "cb"), entropy balancing weighting (method = "eb"), or
standard maximum likelihood estimation (method = "mle"). For the
covariate balancing weighting and entropy balancing weighting, dbw runs
much faster than the original functions (CBPS and ebalance)
by using loss-function-based algorithms, which also results in more
accurate covariate balance. For the ATT and ATC estimation, the distribution
balancing weighting, covariate balancing weighting, and entropy balancing
weighting are theoretically equivalent and dbw implements accordingly.
The parameter of interest is estimated by the AIPW estimator, where inverse
probability weights are standardized within each treatment group by being
devided by the size of the group after being calculated as
for the ATE estimation,
for the ATT estimation,
for the ATC estimation, and
for the missing outcome cases. The resulting inverse probability
weights sum to 1 for the distribution balancing weighting, covariate
balancing weighting, and entropy balancing weighting estimators without
regularization.
The variance-covariance matrix for the parameter of interest and ancillary parameters is calculated using the sandwich variance formula obtained in the M-estimation framework.
When using regularization for propensity score estimation (lambda > 0),
you should standardize the covariates for propensity score estimation
by std_comp before using dbw. See example below for more details.
For the ATE estimation, it is recommended to specify the estimand as
"ATE", but you may specify it as "ATEcombined" when using the
covariate balancing weighting. The former utilizes the separated propensity
score estimation whereas the latter utilizes the combined estimation, and
the former should produce smaller biases and variances. Note that the
former estimates two propensity scores for each observation by estimating
two propensity score functions with different estimating equations.
For the AO estimation, NA values for the outcome variable for missing cases (the response variable taking "0") are not deleted. For this processing, the outcome variable name must not contain spaces.
dbw returns an object of "dbw" class.
The function summary (i.e., summary.dbw) can be used to obtain or print a
summary of the results.
An object of class "dbw" is a list containing the following components:
est |
the point estimate of the parameter of interest. |
coef_ps |
a named vector of coefficients for propensity score estimation.
A list of two sets of coefficients for two sets of propensity scores
(one for estimating |
coef_y |
a named vector of coefficients for outcome model estimation.
A list of two sets of coefficients for two sets of outcome models
(one for estimating |
varcov |
the variance-covariance matrix of the coefficients and the parameter of interest. |
est_weights |
the estimated inverse probability weights. |
ps |
the estimated propensity scores. A list of two sets of the
estimated propensity scores (one for estimating |
predicted_y |
the predicted outcomes. A list of two sets of the
predicted outcomes (one for estimating |
converged |
logical. Were the propensity score estimation algorithms judged to have converged? |
effn |
the effective sample size for the parameter of interest estimation. |
effn_original |
the effective sample size with the initial weights. |
estimand |
the parameter of interest specified. |
method |
the method for propensity score estimation specified. |
method_y |
the method for outcome model estimation specified. |
response |
the treatment vector. The response (non-missingness) vector when the missing outcome cases. |
outcome |
the outcome vector. |
original_weights |
the weights initially supplied, a vector of 1s if none were. |
ci |
a matrix of the confidence intervals for the parameter of interest. |
formula_y |
the outcome model formula specified. |
formula_ps |
the propensity score model formula specified. |
call |
the matched call. |
data |
the data argument. |
normalize |
a logical argument indicating whether to normalize the
estimated weights for each treatment group for |
lambda |
the parameter specifying the degree of the L2-regularization. |
Hiroto Katsumata
Katsumata, Hiroto. 2024. "How Should We Estimate Inverse Probability Weights with Possibly Misspecified Propensity Score Models?" Political Science Research and Methods.
Imai, Kosuke and Marc Ratkovic. 2014. "Covariate Balancing Propensity Score." Journal of the Royal Statistical Society, Series B (Statistical Methodology) 76 (1): 243–63.
Hainmueller, Jens. 2012. "Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies." Political Analysis 20 (1): 25–46.
# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATE estimation # True ATE is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(stats::rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 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] + tau * treat + stats::rnorm(n = n, mean = 0, sd = 1) ybinom <- (y > 210) + 0 df0 <- data.frame(X, treat, y, ybinom) colnames(df0) <- c("x1", "x2", "x3", "x4", "treat", "y", "ybinom") # Variables for a misspecified model Xmis <- data.frame(x1mis = exp(X[, 1] / 2), x2mis = X[, 2] * (1 + exp(X[, 1]))^(-1) + 10, x3mis = (X[, 1] * X[, 3] / 25 + 0.6)^3, x4mis = (X[, 2] + X[, 4] + 20)^2) # Data frame and formulas for propensity score estimation df <- data.frame(df0, Xmis) formula_ps_c <- stats::as.formula(treat ~ x1 + x2 + x3 + x4) formula_ps_m <- stats::as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Formula for a misspecified outcome model formula_y <- stats::as.formula(y ~ x1mis + x2mis + x3mis + x4mis) # Correct propensity score model # Distribution balancing weighting with normalization and # without regularization fitdbwc <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) fitdbwc summary(fitdbwc) # Covariate balancing weighting function without regularization fitcbwc <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitcbwc) # Entropy balancing weighting function without regularization fitebwc <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "eb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitebwc) # Standard logistic regression fitmlec <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlec) # Distribution balancing weighting without normalization and # without regularization fitdbwcnn <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwcnn) # Misspecified propensity score model # Distribution balancing weighting with normalization and # without regularization fitdbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwm) # Covariate balancing weighting function without regularization fitcbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitcbwm) # Entropy balancing weighting function without regularization fitebwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "eb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitebwm) # Standard logistic regression fitmlem <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlem) # Distribution balancing weighting without normalization and # without regularization fitdbwmnn <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwmnn) # Distribution balancing weighting with normalization and # with regularization # Standardization res_std_comp <- std_comp(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method_y = "wls", data = df, std = TRUE, weights = NULL) # Estimation fitdbwmr <- dbw(formula_y = formula_y, formula_ps = res_std_comp$formula_ps, estimand = "ATE", method = "dbw", method_y = "wls", data = res_std_comp$data, normalize = TRUE, vcov = TRUE, lambda = 0.01, weights = res_std_comp$weights, clevel = 0.95) summary(fitdbwmr) # Covariate balancing weighting function with an estimating equation # for the original covariate balancing propensity score method fitcbwmcmb <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATEcombined", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitcbwmcmb) # Formula for a misspecified outcome model for the GAM library(mgcv) formula_y_gam <- stats::as.formula(y ~ s(x1mis) + s(x2mis) + s(x3mis)+ s(x4mis)) # Distribution balancing weighting with the GAM fitdbwmg <- dbw(formula_y = formula_y_gam, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "gam", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwmg) # Binary outcome case # Empirically correct ATE ybinom_t <- (y + (1 - treat) * 10 > 210) + 0 ybinom_c <- (y - treat * 10 > 210) + 0 ATEbinom <- mean(ybinom_t - ybinom_c) ATEbinom # Formula for a misspecified binary outcome model formula_y_bin <- stats::as.formula(ybinom ~ x1mis + x2mis + x3mis + x4mis) # Distribution balancing weighting for the binary outcome fitdbwmbin <- dbw(formula_y = formula_y_bin, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "logit", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwmbin) # Standard logistic regression with the Horvitz-Thompson estimator fitmlem_ht <- dbw(formula_y = y ~ 0, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlem_ht) # Standard logistic regression with the Hajek estimator fitmlem_hj <- dbw(formula_y = y ~ 1, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlem_hj)# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATE estimation # True ATE is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(stats::rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 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] + tau * treat + stats::rnorm(n = n, mean = 0, sd = 1) ybinom <- (y > 210) + 0 df0 <- data.frame(X, treat, y, ybinom) colnames(df0) <- c("x1", "x2", "x3", "x4", "treat", "y", "ybinom") # Variables for a misspecified model Xmis <- data.frame(x1mis = exp(X[, 1] / 2), x2mis = X[, 2] * (1 + exp(X[, 1]))^(-1) + 10, x3mis = (X[, 1] * X[, 3] / 25 + 0.6)^3, x4mis = (X[, 2] + X[, 4] + 20)^2) # Data frame and formulas for propensity score estimation df <- data.frame(df0, Xmis) formula_ps_c <- stats::as.formula(treat ~ x1 + x2 + x3 + x4) formula_ps_m <- stats::as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Formula for a misspecified outcome model formula_y <- stats::as.formula(y ~ x1mis + x2mis + x3mis + x4mis) # Correct propensity score model # Distribution balancing weighting with normalization and # without regularization fitdbwc <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) fitdbwc summary(fitdbwc) # Covariate balancing weighting function without regularization fitcbwc <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitcbwc) # Entropy balancing weighting function without regularization fitebwc <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "eb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitebwc) # Standard logistic regression fitmlec <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlec) # Distribution balancing weighting without normalization and # without regularization fitdbwcnn <- dbw(formula_y = formula_y, formula_ps = formula_ps_c, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwcnn) # Misspecified propensity score model # Distribution balancing weighting with normalization and # without regularization fitdbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwm) # Covariate balancing weighting function without regularization fitcbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitcbwm) # Entropy balancing weighting function without regularization fitebwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "eb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitebwm) # Standard logistic regression fitmlem <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlem) # Distribution balancing weighting without normalization and # without regularization fitdbwmnn <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwmnn) # Distribution balancing weighting with normalization and # with regularization # Standardization res_std_comp <- std_comp(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method_y = "wls", data = df, std = TRUE, weights = NULL) # Estimation fitdbwmr <- dbw(formula_y = formula_y, formula_ps = res_std_comp$formula_ps, estimand = "ATE", method = "dbw", method_y = "wls", data = res_std_comp$data, normalize = TRUE, vcov = TRUE, lambda = 0.01, weights = res_std_comp$weights, clevel = 0.95) summary(fitdbwmr) # Covariate balancing weighting function with an estimating equation # for the original covariate balancing propensity score method fitcbwmcmb <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATEcombined", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitcbwmcmb) # Formula for a misspecified outcome model for the GAM library(mgcv) formula_y_gam <- stats::as.formula(y ~ s(x1mis) + s(x2mis) + s(x3mis)+ s(x4mis)) # Distribution balancing weighting with the GAM fitdbwmg <- dbw(formula_y = formula_y_gam, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "gam", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwmg) # Binary outcome case # Empirically correct ATE ybinom_t <- (y + (1 - treat) * 10 > 210) + 0 ybinom_c <- (y - treat * 10 > 210) + 0 ATEbinom <- mean(ybinom_t - ybinom_c) ATEbinom # Formula for a misspecified binary outcome model formula_y_bin <- stats::as.formula(ybinom ~ x1mis + x2mis + x3mis + x4mis) # Distribution balancing weighting for the binary outcome fitdbwmbin <- dbw(formula_y = formula_y_bin, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "logit", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitdbwmbin) # Standard logistic regression with the Horvitz-Thompson estimator fitmlem_ht <- dbw(formula_y = y ~ 0, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlem_ht) # Standard logistic regression with the Hajek estimator fitmlem_hj <- dbw(formula_y = y ~ 1, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) summary(fitmlem_hj)
Summarizes and plots covariate balance between treatment and control groups before and after the distribution balancing weighting.
## S3 method for class 'dbw' plot( x, addcov = NULL, standardize = TRUE, plot = TRUE, absolute = TRUE, threshold = 0, sort = TRUE, ... )## S3 method for class 'dbw' plot( x, addcov = NULL, standardize = TRUE, plot = TRUE, absolute = TRUE, threshold = 0, sort = TRUE, ... )
x |
an object of class “dbw”, usually, a result of a call to |
addcov |
a one-sided formula specifying additional covariates whose balance is checked. Covariates containing NAs are automatically dropped. |
standardize |
a logical value indicating whether weighted mean differences are standardized or not. |
plot |
a logical value indicating whether a covariate balance plot is displayed. |
absolute |
a logical value indicating whether the absolute values of differences in weighted means are used in the covariate balance plot. |
threshold |
an optional numeric vector used as threshold markers in the covariate balance plot. |
sort |
a logical value indicating whether covariates in the covariate balance plot are sorted by the values of differences in the weighted means before the distribution balancing weighting. |
... |
other graphical parameters (see |
Estimated weights are normalized to sum to one. Position of the legend is
determined internally. Set absolute = TRUE and sort = TRUE for choosing
a better location automatically.
A matrix whose rows are the covariates and columns are the
differences in the (un)standardized weighted mean between the treatment and
control groups before (diff.un) and after (diff.adj) the
distribution balancing weighting. The standardized weighted mean is the
weighted mean divided by the standard deviation of the covariate for the
target population (the treatment group for the average treatment effects on
the treated estimation, the control group for the average treatment effects
on the controlled estimation and the whole population for the other
quantity of interest). The differences in the categorical variables are not
standardized.
Hiroto Katsumata
# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATE estimation # True ATE is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(stats::rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 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] + tau * treat + stats::rnorm(n = n, mean = 0, sd = 1) ybinom <- (y > 210) + 0 df0 <- data.frame(X, treat, y, ybinom) colnames(df0) <- c("x1", "x2", "x3", "x4", "treat", "y", "ybinom") # Variables for a misspecified model Xmis <- data.frame(x1mis = exp(X[, 1] / 2), x2mis = X[, 2] * (1 + exp(X[, 1]))^(-1) + 10, x3mis = (X[, 1] * X[, 3] / 25 + 0.6)^3, x4mis = (X[, 2] + X[, 4] + 20)^2) # Data frame and formulas for propensity score estimation df <- data.frame(df0, Xmis) formula_ps_c <- stats::as.formula(treat ~ x1 + x2 + x3 + x4) formula_ps_m <- stats::as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Formula for a misspecified outcome model formula_y <- stats::as.formula(y ~ x1mis + x2mis + x3mis + x4mis) # Set plot margins oldpar <- par(no.readonly = TRUE) # Just for adjusting plot margins par(mar = c(5.1, 5.1, 4.1, 2.1)) # Just for adjusting plot margins # Misspecified propensity score model # Distribution balancing weighting without regularization fitdbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) # Non-absolute values plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, absolute = FALSE, threshold = c(0.1, 0.2)) # No sorting plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2), sort = FALSE) # Covariate balancing weighting function without regularization fitcbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitcbwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) # Entropy balancing weighting function without regularization fitebwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "eb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitebwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) # Standard logistic regression fitmlem <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitmlem, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) par(oldpar) # Display the covariate balance matrix cb <- plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, plot = FALSE) cb# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATE estimation # True ATE is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(stats::rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 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] + tau * treat + stats::rnorm(n = n, mean = 0, sd = 1) ybinom <- (y > 210) + 0 df0 <- data.frame(X, treat, y, ybinom) colnames(df0) <- c("x1", "x2", "x3", "x4", "treat", "y", "ybinom") # Variables for a misspecified model Xmis <- data.frame(x1mis = exp(X[, 1] / 2), x2mis = X[, 2] * (1 + exp(X[, 1]))^(-1) + 10, x3mis = (X[, 1] * X[, 3] / 25 + 0.6)^3, x4mis = (X[, 2] + X[, 4] + 20)^2) # Data frame and formulas for propensity score estimation df <- data.frame(df0, Xmis) formula_ps_c <- stats::as.formula(treat ~ x1 + x2 + x3 + x4) formula_ps_m <- stats::as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Formula for a misspecified outcome model formula_y <- stats::as.formula(y ~ x1mis + x2mis + x3mis + x4mis) # Set plot margins oldpar <- par(no.readonly = TRUE) # Just for adjusting plot margins par(mar = c(5.1, 5.1, 4.1, 2.1)) # Just for adjusting plot margins # Misspecified propensity score model # Distribution balancing weighting without regularization fitdbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "dbw", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) # Non-absolute values plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, absolute = FALSE, threshold = c(0.1, 0.2)) # No sorting plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2), sort = FALSE) # Covariate balancing weighting function without regularization fitcbwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "cb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitcbwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) # Entropy balancing weighting function without regularization fitebwm <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "eb", method_y = "wls", data = df, normalize = TRUE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitebwm, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) # Standard logistic regression fitmlem <- dbw(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method = "mle", method_y = "wls", data = df, normalize = FALSE, vcov = TRUE, lambda = 0, weights = NULL, clevel = 0.95) plot(fitmlem, addcov = ~ x1 + x2 + x3 + x4, threshold = c(0.1, 0.2)) par(oldpar) # Display the covariate balance matrix cb <- plot(fitdbwm, addcov = ~ x1 + x2 + x3 + x4, plot = FALSE) cb
Prints a fitted dbw object.
## S3 method for class 'dbw' print(x, ...)## S3 method for class 'dbw' print(x, ...)
x |
an object of class “dbw”, usually, a result of a call to |
... |
additional arguments to be passed to print. |
No retrun value, called for side effects.
Hiroto Katsumata
Standardizes covariates for propensity score estimation before the
distribution balancing weighting dbw with the regularization.
std_comp( formula_y, formula_ps, estimand = "ATE", method_y = "wls", data, std = TRUE, weights = NULL )std_comp( formula_y, formula_ps, estimand = "ATE", method_y = "wls", data, std = TRUE, weights = NULL )
formula_y |
an object of class |
formula_ps |
an object of class |
estimand |
a character string specifying a parameter of interest. Choose
"ATT" for the average treatment effects on the treated estimation, "ATE"
for the average treatment effects estimation, "ATC" for the average
outcomes estimation in missing outcome cases. You can choose "ATEcombined"
for the combined estimation for the average treatment effects estimation
when using the covariate balancing weighting ( |
method_y |
a character string specifying a method for potential outcome prediction. Choose "wls" for the linear model, "logit" for the logistic regression, "gam" for the generalized additive model for the continuous outcome, and "gambinom" for the generalized additive model for the binary outcome. |
data |
a data frame (or one that can be coerced to that class) containing the outcomes and the variables in the model. |
std |
a logical parameter indicating whether to standardize the covariates for propensity score estimation. |
weights |
an optional vector of ‘prior weights’ (e.g. sampling weights) to be used in the fitting process. Should be NULL or a numeric vector. |
std_comp first extracts complete cases for both propensity score estimation
and outcome model estimation. Then it standardizes covariates for propensity
score estimation by takeing the provided weights into account. The returned
data frame is the "design matrix", which contains a set of dummy variables
(depending on the contrasts) for factors and similarly expanded interaction
terms.
For the AO estimation, NA values for the outcome variable for missing cases (the response variable taking "0") are not deleted. For this processing, the outcome variable name must not contain spaces.
data |
the complete-case data frame containing the outcome variable, the response (treatment) variable, and the standardized covariates for propensity score estimation. |
weights |
the initially-supplied weights for the complete cases, a vector of 1s if none were. |
formula_ps |
the automatically-created formula for propensity score estimation, which includes expanded factors and interactions. |
mean_x |
the weighted mean of each covariates. |
sd_x |
the weighted standard deviation of each covariates. |
Hiroto Katsumata
# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATE estimation # True ATE is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(stats::rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 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] + tau * treat + stats::rnorm(n = n, mean = 0, sd = 1) ybinom <- (y > 210) + 0 df0 <- data.frame(X, treat, y, ybinom) colnames(df0) <- c("x1", "x2", "x3", "x4", "treat", "y", "ybinom") # Variables for a misspecified model Xmis <- data.frame(x1mis = exp(X[, 1] / 2), x2mis = X[, 2] * (1 + exp(X[, 1]))^(-1) + 10, x3mis = (X[, 1] * X[, 3] / 25 + 0.6)^3, x4mis = (X[, 2] + X[, 4] + 20)^2) # Data frame and formulas for propensity score estimation df <- data.frame(df0, Xmis) formula_ps_c <- stats::as.formula(treat ~ x1 + x2 + x3 + x4) formula_ps_m <- stats::as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Formula for a misspecified outcome model formula_y <- stats::as.formula(y ~ x1mis + x2mis + x3mis + x4mis) # Distribution balancing weighting with regularization # Standardization res_std_comp <- std_comp(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method_y = "wls", data = df, std = TRUE, weights = NULL) fitdbwmr <- dbw(formula_y = formula_y, formula_ps = res_std_comp$formula_ps, estimand = "ATE", method = "dbw", method_y = "wls", data = res_std_comp$data, vcov = TRUE, lambda = 0.01, weights = res_std_comp$weights, clevel = 0.95) summary(fitdbwmr)# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATE estimation # True ATE is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(stats::rnorm(n * 4, mean = 0, sd = 1), nrow = n, ncol = 4) prop <- 1 / (1 + exp(X[, 1] - 0.5 * X[, 2] + 0.25 * X[, 3] + 0.1 * X[, 4])) treat <- rbinom(n, 1, prop) y <- 210 + 27.4 * X[, 1] + 13.7 * X[, 2] + 13.7 * X[, 3] + 13.7 * X[, 4] + tau * treat + stats::rnorm(n = n, mean = 0, sd = 1) ybinom <- (y > 210) + 0 df0 <- data.frame(X, treat, y, ybinom) colnames(df0) <- c("x1", "x2", "x3", "x4", "treat", "y", "ybinom") # Variables for a misspecified model Xmis <- data.frame(x1mis = exp(X[, 1] / 2), x2mis = X[, 2] * (1 + exp(X[, 1]))^(-1) + 10, x3mis = (X[, 1] * X[, 3] / 25 + 0.6)^3, x4mis = (X[, 2] + X[, 4] + 20)^2) # Data frame and formulas for propensity score estimation df <- data.frame(df0, Xmis) formula_ps_c <- stats::as.formula(treat ~ x1 + x2 + x3 + x4) formula_ps_m <- stats::as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Formula for a misspecified outcome model formula_y <- stats::as.formula(y ~ x1mis + x2mis + x3mis + x4mis) # Distribution balancing weighting with regularization # Standardization res_std_comp <- std_comp(formula_y = formula_y, formula_ps = formula_ps_m, estimand = "ATE", method_y = "wls", data = df, std = TRUE, weights = NULL) fitdbwmr <- dbw(formula_y = formula_y, formula_ps = res_std_comp$formula_ps, estimand = "ATE", method = "dbw", method_y = "wls", data = res_std_comp$data, vcov = TRUE, lambda = 0.01, weights = res_std_comp$weights, clevel = 0.95) summary(fitdbwmr)
Prints a summary of a fitted dbw object.
## S3 method for class 'dbw' summary(object, ...)## S3 method for class 'dbw' summary(object, ...)
object |
an object of class “dbw”, usually, a result of a call to |
... |
additional arguments to be passed to summary. |
Prints a summary of a dbw object, in a format similar to glm.
call |
the matched call. |
est |
the point estimate of the parameter of interest. |
coefficients |
a table including coefficients, standard errors, z-values, and two-sided p-values. |
effn |
the effective sample size for the parameter of interest estimation. |
Hiroto Katsumata
# For examples see example(dbw)# For examples see example(dbw)