| Title: | Navigated Weighting for the Inverse Probability Weighting |
|---|---|
| Description: | Implements the navigated weighting (NAWT) proposed by Katsumata (2020) <arXiv:2005.10998>, which improves the inverse probability weighting by utilizing estimating equations suitable for a specific pre-specified parameter of interest (e.g., the average treatment effects or the average treatment effects on the treated) in propensity score estimation. It includes the covariate balancing propensity score proposed by Imai and Ratkovic (2014) <doi:10.1111/rssb.12027>, which uses covariate balancing conditions in propensity score estimation. The point estimate of the parameter of interest as well as coefficients for propensity score estimation and their uncertainty 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] |
| Maintainer: | Hiroto Katsumata <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.4 |
| Built: | 2025-03-08 02:44:48 UTC |
| Source: | https://github.com/hirotokatsumata/nawtilus |
Summarizes and plots covariate balance between treatment and control groups before and after the navigated weighting.
cbcheck( object, addcov = NULL, standardize = TRUE, plot = TRUE, absolute = TRUE, threshold = 0, sort = TRUE )cbcheck( object, addcov = NULL, standardize = TRUE, plot = TRUE, absolute = TRUE, threshold = 0, sort = TRUE )
object |
an object of class “nawt”, 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 navigated weighting. |
Position of the legend is determined internally.
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
navigated 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 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) # ATT estimation # True ATT is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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, 1 - prop) y <- 210 + 27.4 * X[, 1] + 13.7 * X[, 2] + 13.7 * X[, 3] + 13.7 * X[, 4] + tau * treat + rnorm(n) df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") # 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 a misspecified formula for propensity score estimation df <- data.frame(df, Xmis) formula_m <- as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Misspecified propensity score model # Power weighting function with alpha = 2 fits2m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) cbcheck(fits2m, addcov = ~ x1 + x2 + x3 + x4) # Covariate balancing weighting function fitcbm <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "cb", data = df) cbcheck(fitcbm, addcov = ~ x1 + x2 + x3 + x4) # Standard logistic regression fits0m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 0) cbcheck(fits0m, addcov = ~ x1 + x2 + x3 + x4) # Display the covariate balance matrix cb <- cbcheck(fits2m, addcov = ~ x1 + x2 + x3 + x4, plot = FALSE) cb# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATT estimation # True ATT is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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, 1 - prop) y <- 210 + 27.4 * X[, 1] + 13.7 * X[, 2] + 13.7 * X[, 3] + 13.7 * X[, 4] + tau * treat + rnorm(n) df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") # 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 a misspecified formula for propensity score estimation df <- data.frame(df, Xmis) formula_m <- as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Misspecified propensity score model # Power weighting function with alpha = 2 fits2m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) cbcheck(fits2m, addcov = ~ x1 + x2 + x3 + x4) # Covariate balancing weighting function fitcbm <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "cb", data = df) cbcheck(fitcbm, addcov = ~ x1 + x2 + x3 + x4) # Standard logistic regression fits0m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 0) cbcheck(fits0m, addcov = ~ x1 + x2 + x3 + x4) # Display the covariate balance matrix cb <- cbcheck(fits2m, addcov = ~ x1 + x2 + x3 + x4, plot = FALSE) cb
Data from the National Supported Work Demonstration Program and the Panel Study for Income Dynamics. A benchmark data set, which is extensively analyzed by LaLonde (1986), Dehejia and Wahba (1999), and Imai and Ratkovic (2014).
LaLondeLaLonde
A data frame with 3212 observations and 12 variables.
an indicator for whether the observed unit was in the experimental subset
an indicator for whether the individual received the treatment
age in years
schooling in years
an indicator for black
an indicator for Hispanic
an indicator for marriage status, one for married
an indicator for no high school degree
reported earnings in 1974
reported earnings in 1975
reported earnings in 1978
an indicator for whether the 1974 earnings variable is missing
Data not missing 1974 earnings are the Dehejia-Wahba subsample of the LaLonde data. Missing values for 1974 earnings set to zero. 1974 and 1975 earnings are pre-treatment. 1978 earnings is taken as the outcome variable.
This version of the data is from LaLonde data in CBPS package.
Dehejia, Rajeev H., and Sadek Wahba. 1999. "Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs." Journal of the American Statistical Association 94 (448): 1053–62.
Imai, Kosuke and Marc Ratkovic. 2014. "Covariate Balancing Propensity Score." Journal of the Royal Statistical Society, Series B (Statistical Methodology) 76 (1): 243–63.
LaLonde, Robert J. 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data." American Economic Review 76 (4): 604–20.
nawt 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 inverse probability weighting where propensity scores
are estimated using estimating equations suitable for the parameter of
interest. It includes the covariate balancing propensity score proposed by
Imai and Ratkovic (2014), which uses covariate balancing conditions in
propensity score estimation. nawt can also be used to estimate average
outcomes in missing outcome cases.
nawt( formula, outcome, estimand = "ATT", method = "score", data, weights = NULL, alpha = 2, twostep = TRUE, boot = FALSE, B = 2000, clevel = 0.95, message = TRUE )nawt( formula, outcome, estimand = "ATT", method = "score", data, weights = NULL, alpha = 2, twostep = TRUE, boot = FALSE, B = 2000, clevel = 0.95, message = TRUE )
formula |
an object of class |
outcome |
a character string specifying the name of outcome values
in |
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. |
method |
a character string specifying a type of weighting functions in
propensity score estimation ( |
data |
a data frame (or one that can be coerced to that class) containing the outcomes and the variables in the model. |
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. |
alpha |
a positive value for an exponent in a power weighting function
( |
twostep |
a logical value indicating whether to use a two-step estimator
when |
boot |
a logical value indicating whether to use a non-parametric
bootstrapping method to estimate the variance-covariance matrix and
confidence intervals for parameters. Default is |
B |
the number of bootstrap replicates. Default is 2,000. |
clevel |
confidence level. Default is 0.95. |
message |
a logical value indicating whether messages are shown or not. |
The treatment variable (or, missingness variable in missing outcome cases) must be binary and coded as 0 (for controlled or non-missing observations) or 1 (for treated or missing observations).
When the data frame has incomplete cases, which have NAs for either of
the treatment variable, explanatory variables for propensity score
estimation, or the outcome variable, nawt conducts listwise deletion.
Returned values (e.g., weights, ps, data) do not contain
values for these deleted cases.
The parameter of interest is estimated by the Hajek estimator, where inverse
probability weights are standardized to sum to 1 within each treatment group
after being calculated as for the
ATE estimation, for the ATT estimation,
for the ATC estimation, and
for the missing outcome cases.
For the ATE estimation, it is recommended to specify the estimand as
"ATE" but you may specify it as "ATEcombined". The former utilizes
the separated 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.
When a two-step estimator is used in nawt with method = "both",
scratio () is calculated in the first step. scratio is a
ratio of accuracy in propensity score estimation in the NAWT with a power
weighting function with a specified alpha to that with a covariate balancing
weighting function. It determines the mixture weight in the second step, like
the weighting matrix in the two-step over-identified GMM estimation, where
weighted estimating equations of those with the power weighting function and
the covariate balancing function is used. This mixture weight is proportional
to the scratio (e.g., ,
in the ATT estimation).
Since the NAWT utilizes weighted estimating equations in propensity score
estimation, it may sometimes become unstable especially when only a few
observations have extremely large weights in propensity score estimation.
nawt generates a warning when the effective sample size for propensity
score estimation is smaller than a quarter of the effective sample size with
the initial weights. In that case, carefully look at the estimated
coefficients to check whether the estimation fails or not and cbcheck
will be helpful.
nawt returns an object of class inheriting from "nawt".
The function summary (i.e., summary.nawt) can be used to obtain or print a
summary of the results.
An object of class "nawt" is a list containing the following components:
est |
the point estimate of the parameter of interest. |
weights |
the estimated inverse probability weights. |
ps |
the estimated propensity scores. A matrix of two sets of the
estimated propensity scores is returned when |
coefficients |
a named vector of coefficients. A matrix of two sets of
coefficients for two sets of propensity scores is returned when
|
varcov |
the variance-covariance matrix of the coefficients and parameter of interest. |
converged |
logical. Was the algorithm judged to have converged? |
naive_weights |
the estimated inverse probability weights with the standard logistic regression for the propensity score estimation. |
naive_coef |
a named vector of coefficients with the standard logistic regression for the propensity score estimation. |
scratio |
an optimal ratio of the covariate balancing weighting function
to the power weighting function in taking the weighted average weights for
the weighted score conditions when |
estimand |
the parameter of interest specified. |
method |
the method specified. |
outcome |
the outcome vector. |
alpha |
alpha specified. |
names.x |
names of the explanatory variables in propensity score estimation. |
prior.weights |
the weights initially supplied, a vector of 1s if none were. |
treat |
the treatment vector. The missingness vector when the missing outcome cases. |
ci |
a matrix of the confidence intervals for the parameter of interest. |
omega |
a vector of weights for the weighted score conditions ( |
effN_ps |
the effective sample size for the propensity score estimation.
A vector of length two for two propensity score estimation is returned when
|
effN_est |
the effective sample size for the parameter of interest estimation. |
effN_original |
the effective sample size with the initial weights. |
formula |
formula specified. |
call |
the matched call. |
data |
the data argument. |
Hiroto Katsumata
Imai, Kosuke and Marc Ratkovic. 2014. "Covariate Balancing Propensity Score." Journal of the Royal Statistical Society, Series B (Statistical Methodology) 76 (1): 243–63.
Christian Fong, Marc Ratkovic and Kosuke Imai (2019). CBPS: Covariate Balancing Propensity Score. R package version 0.21. https://CRAN.R-project.org/package=CBPS
Katsumata, Hiroto. 2020. "Navigated Weighting to Improve Inverse Probability Weighting for Missing Data Problems and Causal Inference." arXiv preprint arXiv:2005.10998.
# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATT estimation # True ATT is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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 + rnorm(n) df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") # 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(df, Xmis) formula_c <- as.formula(treat ~ x1 + x2 + x3 + x4) formula_m <- as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Correct propensity score model # Power weighting function with alpha = 2 fits2c <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) summary(fits2c) # Covariate balancing weighting function fitcbc <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "cb", data = df) summary(fitcbc) # Standard logistic regression fits0c <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 0) summary(fits0c) # Misspecified propensity score model # Power weighting function with alpha = 2 fits2m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) summary(fits2m) # Covariate balancing weighting function fitcbm <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "cb", data = df) summary(fitcbm) # Standard logistic regression fits0m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 0) summary(fits0m) # Empirical example # Load the LaLonde data data(LaLonde) formula_l <- as.formula("exper ~ age + I(age^2) + educ + I(educ^2) + black + hisp + married + nodegr + I(re75 / 1000) + I(re75 == 0) + I(re74 / 1000)") # Experimental benchmark mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - mean(subset(LaLonde, exper == 1 & treat == 0)$re78) # Power weighting function with alpha = 2 fits2l <- nawt(formula = formula_l, estimand = "ATT", method = "score", outcome = "re78", data = LaLonde, alpha = 2) mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - with(LaLonde, sum((1 - exper) * re78 * fits2l$weights) / sum((1 - exper) * fits2l$weights)) # Covariate balancing weighting function fitcbl <- nawt(formula = formula_l, estimand = "ATT", method = "cb", outcome = "re78", data = LaLonde) mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - with(LaLonde, sum((1 - exper) * re78 * fitcbl$weights) / sum((1 - exper) * fitcbl$weights)) # Standard logistic regression fits0l <- nawt(formula = formula_l, estimand = "ATT", method = "score", outcome = "re78", data = LaLonde, alpha = 0) mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - with(LaLonde, sum((1 - exper) * re78 * fits0l$weights) / sum((1 - exper) * fits0l$weights))# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) # ATT estimation # True ATT is 10 tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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 + rnorm(n) df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") # 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(df, Xmis) formula_c <- as.formula(treat ~ x1 + x2 + x3 + x4) formula_m <- as.formula(treat ~ x1mis + x2mis + x3mis + x4mis) # Correct propensity score model # Power weighting function with alpha = 2 fits2c <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) summary(fits2c) # Covariate balancing weighting function fitcbc <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "cb", data = df) summary(fitcbc) # Standard logistic regression fits0c <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 0) summary(fits0c) # Misspecified propensity score model # Power weighting function with alpha = 2 fits2m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) summary(fits2m) # Covariate balancing weighting function fitcbm <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "cb", data = df) summary(fitcbm) # Standard logistic regression fits0m <- nawt(formula = formula_m, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 0) summary(fits0m) # Empirical example # Load the LaLonde data data(LaLonde) formula_l <- as.formula("exper ~ age + I(age^2) + educ + I(educ^2) + black + hisp + married + nodegr + I(re75 / 1000) + I(re75 == 0) + I(re74 / 1000)") # Experimental benchmark mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - mean(subset(LaLonde, exper == 1 & treat == 0)$re78) # Power weighting function with alpha = 2 fits2l <- nawt(formula = formula_l, estimand = "ATT", method = "score", outcome = "re78", data = LaLonde, alpha = 2) mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - with(LaLonde, sum((1 - exper) * re78 * fits2l$weights) / sum((1 - exper) * fits2l$weights)) # Covariate balancing weighting function fitcbl <- nawt(formula = formula_l, estimand = "ATT", method = "cb", outcome = "re78", data = LaLonde) mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - with(LaLonde, sum((1 - exper) * re78 * fitcbl$weights) / sum((1 - exper) * fitcbl$weights)) # Standard logistic regression fits0l <- nawt(formula = formula_l, estimand = "ATT", method = "score", outcome = "re78", data = LaLonde, alpha = 0) mean(subset(LaLonde, exper == 1 & treat == 1)$re78) - with(LaLonde, sum((1 - exper) * re78 * fits0l$weights) / sum((1 - exper) * fits0l$weights))
Plots weight of each observation in the score condition for
propensity score estimation and estimated propensity score distribution
in the navigated weighting.
plot_omega(object, relative = TRUE)plot_omega(object, relative = TRUE)
object |
an object of class “nawt”, usually, a result of a call to |
relative |
a logical value indicating whether or not relative weights standardized to have mean one are shown. |
The x-axis shows estimated propensity scores, and the y-axis shows weight of
each observation in propensity score estimation. When estimand = "ATE",
the navigated weighting estimates two propensity scores for each observation;
one for estimating the average of the potential outcomes with treatment and
the other for estimating the average of the potential outcomes without
treatment. Therefore, there are two weighting functions for estimating two
sets of propensity scores and two propensity score distributions. Points
rising to the right and a solid curve represent the weighting functions and
distribution of propensity scores for estimating the average of the potential
outcomes without treatment whereas points rising to the left and a dashed
curve represent the weighting functions and distribution of propensity scores
for estimating the average of the potential outcomes with treatment.
Position of the legend is determined internally.
No retrun value, called for side effects.
Hiroto Katsumata
# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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 + rnorm(n) # Data frame and formulas for propensity score estimation df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") formula_c <- as.formula(treat ~ x1 + x2 + x3 + x4) # Power weighting function with alpha = 2 # ATT estimation fitatt <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) plot_omega(fitatt) # ATE estimation fitate <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "score", data = df, alpha = 2) plot_omega(fitate) # Use method = "both" # Two-step estimation fitateb2s <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "both", data = df, alpha = 2, twostep = TRUE) plot_omega(fitateb2s) # Continuously-updating GMM estimation ## Not run: fitatebco <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "both", data = df, alpha = 2, twostep = FALSE) plot_omega(fitatebco) # error ## End(Not run)# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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 + rnorm(n) # Data frame and formulas for propensity score estimation df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") formula_c <- as.formula(treat ~ x1 + x2 + x3 + x4) # Power weighting function with alpha = 2 # ATT estimation fitatt <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) plot_omega(fitatt) # ATE estimation fitate <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "score", data = df, alpha = 2) plot_omega(fitate) # Use method = "both" # Two-step estimation fitateb2s <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "both", data = df, alpha = 2, twostep = TRUE) plot_omega(fitateb2s) # Continuously-updating GMM estimation ## Not run: fitatebco <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "both", data = df, alpha = 2, twostep = FALSE) plot_omega(fitatebco) # error ## End(Not run)
Plots a scattered plot comparing the resulting inverse probability weights estimated by the navigated weighting and the standard logistic regression.
## S3 method for class 'nawt' plot(x, ...)## S3 method for class 'nawt' plot(x, ...)
x |
an object of class “nawt”, usually, a result of a call to |
... |
additional arguments to be passed to plot. |
The x-axis shows the inverse probability weights estimated by estimating propensity scores with the standard logistic regression whereas the y-axis shows those with the navigated weighting. Excessively heavy weights on only a few observations in the navigated weighting may indicate the failure of the estimation.
Position of the legend is determined internally.
No retrun value, called for side effects.
Hiroto Katsumata
# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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 + rnorm(n) # Data frame and formulas for propensity score estimation df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") formula_c <- as.formula(treat ~ x1 + x2 + x3 + x4) # Power weighting function with alpha = 2 # ATT estimation fitatt <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) plot(fitatt) # ATE estimation fitate <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "score", data = df, alpha = 2) plot(fitate)# Simulation from Kang and Shafer (2007) and Imai and Ratkovic (2014) tau <- 10 set.seed(12345) n <- 1000 X <- matrix(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 + rnorm(n) # Data frame and formulas for propensity score estimation df <- data.frame(X, treat, y) colnames(df) <- c("x1", "x2", "x3", "x4", "treat", "y") formula_c <- as.formula(treat ~ x1 + x2 + x3 + x4) # Power weighting function with alpha = 2 # ATT estimation fitatt <- nawt(formula = formula_c, outcome = "y", estimand = "ATT", method = "score", data = df, alpha = 2) plot(fitatt) # ATE estimation fitate <- nawt(formula = formula_c, outcome = "y", estimand = "ATE", method = "score", data = df, alpha = 2) plot(fitate)
Prints a fitted nawt object.
## S3 method for class 'nawt' print(x, ...)## S3 method for class 'nawt' print(x, ...)
x |
an object of class “nawt”, usually, a result of a call to |
... |
additional arguments to be passed to print. |
No retrun value, called for side effects.
Hiroto Katsumata
Prints a summary of a fitted nawt object.
## S3 method for class 'nawt' summary(object, ...)## S3 method for class 'nawt' summary(object, ...)
object |
an object of class “nawt”, usually, a result of a call to |
... |
additional arguments to be passed to summary. |
Prints a summary of a nawt 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_ps |
the effective sample size for the propensity score estimation. |
effN_est |
the effective sample size for the parameter of interest estimation. |
Hiroto Katsumata
# For examples see example(nawt)# For examples see example(nawt)