Package 'sbw'

Estimate causal contrasts and population means

Description

Function for estimating causal contrasts and population means using the output from sbw.

Usage

estimate(object, out = NULL, digits = 6, ...)

Arguments

object	an object from function sbw.
out	outcome, a vector of strings with the names of the outcome variables. The default is the out argument from the object.
digits	a scalar with the number of significant digits used to display the estimates. The default is 6.
...	ignored arguments.

Value

An estimate for the estimand of interest. The standard error is calculated by robust sandwich variance estimator.

Examples

# Please see the examples in the function sbw below.

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The Lalonde data set

Description

Data set from the National Supported Work Demonstration (Lalonde 1986, Dehejia and Wahba 1999). This data set is publicly available at https://users.nber.org/~rdehejia/data/.nswdata2.html.

Usage

data(lalonde)

Format

A data frame with 614 observations, corresponding to 185 treated and 429 control subjects, and 10 variables. The treatment assignment indicator is the first variable of the data frame; the next eight columns are the covariates; the last column is the outcome:

treatment

the treatment assignment indicator (1 if treated, 0 otherwise)

age

a covariate, measured in years

education

a covariate, measured in years

black

a covariate indicating race (1 if black, 0 otherwise)

hispanic

a covariate indicating race (1 if Hispanic, 0 otherwise)

married

a covariate indicating marital status (1 if married, 0 otherwise)

nodegree

a covariate indicating high school diploma (1 if no degree, 0 otherwise)

re74

a covariate, real earnings in 1974

re75

a covariate, real earnings in 1975

re78

the outcome, real earnings in 1978

Source

https://users.nber.org/~rdehejia/data/.nswdata2.html

References

Dehejia, R., and Wahba, S. (1999), "Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs," Journal of the American Statistical Association, 94, 1053-1062.

Lalonde, R. (1986), "Evaluating the Econometric Evaluations of Training Programs," American Economic Review, 76, 604-620.

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Stable balancing weights for causal contrasts and population means.

Description

Function for finding stable weights (that is, weights of minimum variance) that approximately balance the empirical distribution of the observed covariates.

Usage

sbw(
  dat,
  ind = NULL,
  out = NULL,
  bal = list(bal_cov, bal_alg = TRUE, bal_tol, bal_std = "group", bal_gri = c(1e-04,
    0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1), bal_sam = 1000),
  wei = list(wei_sum = TRUE, wei_pos = TRUE),
  sol = list(sol_nam = "quadprog", sol_dis = FALSE),
  par = list(par_est = "att", par_tar = NULL),
  mes = TRUE
)

Arguments

dat	data, a data frame with a treatment assignment or missingness indicator, covariates, and possibly outcomes (which are optional).
ind	treatment assignment or missingness indicator, a string with the name of the binary treatment or missingness indicator, equal to 1 if treated (missing) and 0 otherwise. When par$par_est = "aux", ind is omitted.
out	outcome, a vector of strings with the names of the outcome variables. The default is NULL.
bal	balance requirements, a list with the requirements for covariate balance with the form list(bal_cov, bal_alg, bal_tol, bal_std, bal_gri, bal_sam), where: bal_cov balance covariates, a vector of strings with the names of the covariates in dat to be balanced. In simple applications, the balance covariates in bal_cov will be the column names of dat (without including the treatment or outcome variables) for the original covariates in the data set. The covariates need to be either continuous or binary. Categorical covariates need to be transformed into dummies. In more complex applications, the covariates in dat can be transformations of the original covariates in order to balance higher order single or multidimensional moments, or other basis functions. If the transformations of the covariates are indicators of the quantiles of the empirical distribution of a covariate, then balancing all these indicators will tend to balance the entire marginal distribution of the covariate. bal_alg balance algorithm, a logical that indicates whether the tuning algorithm in Wang and Zubizarreta (2020) is to be used for automatically selecting the degree of approximate covariates balance. The default is TRUE. See the argument bal_gri below for the candidate values for the degree of approximate covariate balance. bal_tol balance tolerances, a scalar or vector of scalars that define the tolerances or maximum differences in means after weighting for the covariates (or transformations thereof) defined in bal_cov. Note that if bal_tol is a vector, then its length has to be equal to the length of bal_cov. Otherwise, the first element in bal_tol will be taken as the balance tolerance for all the constraints in bal_cov. bal_std balance tolerances in standard deviations, a string that represent how the tolerances are adjusted. If bal_std = "group", the tolerances are proportional to the standard deviations in the group/groups to be weighted. If bal_std = "target", the tolerances are proportional to the standard deviations in the target group. If bal_std = "manual", the tolerances equal to bal_tol. The default is "group". bal_gri grid of values for the tuning algorithm bal_alg, a vector of candidate values for the degree of approximate covariate balance. The default is c(0.0001, 0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1). The computational time is roughly proportional to the number of grid values. bal_sam number of replicates to be used in bal_alg, an integer specifying the number of bootstrap sample replicates to be used to select the degree of approximate covariate balance. See Wang and Zubizarreta (2020) for details. The default is 1000.
wei	weighting constraints, a list with all the weighting constraints with the form list(wei_sum, wei_pos), where: wei_sum sum of weights, a logical variable indicating whether the weights are constrained to sum up to one, or whether their sum is unconstrained. The default is TRUE for the sum of weights equal to one. Note that if wei_sum = TRUE, then wei_pos = TRUE. wei_pos positive or zero (non-negative) weights, a logical variable indicating whether the weights are constrained to be non-negative, or whether they are unconstrained. The default is TRUE for non-negative weights. Again, note that if wei_sum = TRUE, then wei_pos = TRUE.
sol	solver, a list that specifies the solver option with the form list(sol_nam, sol_dis, sol_pog), where: sol_nam solver name, a string equal to either "cplex", "gurobi", "mosek", "osqp", "pogs", or "quadprog". CPLEX, Gurobi and MOSEK are commercial solvers, but free for academic users. POGS and QUADPROG are free for all. In our experience, POGS is the fastest solver option and able to handle larger datasets, but it can be difficult to install for non-Mac users and more difficult to calibrate. MOSEK is more stable than POGS and faster. The default option is sol_nam = "quadprog". sol_dis solver display, a logical variable indicating whether the output is to be displayed or not. The default is FALSE. This option is specific to "cplex", "gurobi", "mosek", "pogs", and "osqp". sol_pog solver options specific to "pogs", with the following default parameters: sol_pog = list(sol_pog_max_iter = 100000, sol_pog_rel_tol = 1e-4, sol_pog_abs_tol = 1e-4, sol_pog_gap_stp = TRUE, sol_pog_adp_rho = TRUE). See the POGS manual for details.
par	parameter of interest, a list describing the parameter of interest or estimand with the form list(par_est, par_tar), where: par_est estimand. For causal inference, a string equal to: "att" (Average Treatment effect on the Treated), "atc" (Average Treatment effect on the Controls), "ate" (Average Treatment Effect), "cate" (Conditional Average Treatment Effect). For estimation with incomplete outcome data, a string equal to: "pop" (General population means) or "aux" (Means for a population specified by the user). The default is "att". par_tar target, a string, or a vector of scalars. It specifies the targeted population for inference in terms of the observed covariates when par_est = "cate", "pop" or "aux". Please see the examples.
mes	a logical variable indicating whether the messages are printed.

Value

A list with the following elements:

dat_weights, a data frame with the optimal weights dat_weights$sbw_weights;

ind, an argument provided by the user;

out, an argument provided by the user;

bal, an argument provided by the user;

wei, an argument provided by the user;

sol, an argument provided by the user;

par, an argument provided by the user;

effective_sample_size, effective sample size/sizes for the weighted group/groups;

objective_value, value/values of the objective function/functions at the optimum;

status, status of the solution. If the optimal weights are found, status = optimal; otherwise, the solution may be not optimal or not exist, in which case an error will be returned with details specific to the solver used. For the solver "quadprog", the status code is missing, therefore, status = NA;

time, time elapsed to find the optimal solution;

shadow_price, dual variables or shadow prices of the covariate balance constraints;

balance_parameters, details of the balance parameters;

cstat, covariate balance statistic used in Wang and Zubizarreta (2020). A magnitude to be minimized to select the degree of approximate balance in bal$bal_gri.

Source

https://www.ibm.com/products/ilog-cplex-optimization-studio

https://www.gurobi.com/products/gurobi-optimizer/

https://www.mosek.com/products/mosek/

http://foges.github.io/pogs/stp/r

References

Chattopadhyay, A., Hase, C. H., and Zubizarreta, J. R. (2020), "Balancing Versus Modeling Approaches to Weighting in Practice," Statistics in Medicine, 39, 3227-3254.

Kang, J. D. Y., and Schafer, J. L. (2007), "Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data," Statistical Science, 22, 523-539.

Stuart, E. A. Matching methods for causal inference: a review and a look forward. Statistical Science 2010; 25(1): 1-21.

Wang, Y., and Zubizarreta, J. R. (2020), "Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations," Biometrika, 107, 93-105.

Zubizarreta, J. R. (2015), "Stable Weights that Balance Covariates for Estimation with Incomplete Outcome Data," Journal of the American Statistical Association, 110, 910-922.

Examples

# Simulate data
kangschafer = function(n_obs) {
 # Z are the true covariates
 # t is the indicator for the respondents (treated)
 # y is the outcome
 # X are the observed covariates
 # Returns Z, t y and X sorted in decreasing order by t
 Z = MASS::mvrnorm(n_obs, mu=rep(0, 4), Sigma=diag(4))
 p = 1/(1+exp(Z[, 1]-.5*Z[, 2]+.25*Z[, 3]+.1*Z[, 4]))
 t = rbinom(n_obs, 1, p)
 Zt = cbind(Z, p, t)
 Zt = Zt[order(t), ]
 Z = Zt[, 1:4]
 p = Zt[, 5]
 t = Zt[, 6]
 y = 210+27.4*Z[, 1]+13.7*Z[, 2]+13.7*Z[, 3]+13.7*Z[, 4]+rnorm(n_obs)
 X = cbind(exp(Z[, 1]/2), (Z[, 2]/(1+exp(Z[, 1])))+10, (Z[, 1]*Z[, 3]/
25+.6)^3, (Z[, 2]+Z[, 4]+20)^2)
 return(list(Z=Z, p=p, t=t, y=y, X=X))
}
set.seed(1234)
n_obs = 200
aux = kangschafer(n_obs)
Z = aux$Z
p = aux$p
t = aux$t
y = aux$y
X = aux$X

# Generate data frame
t_ind = t
bal_cov = X
data_frame = as.data.frame(cbind(t_ind, bal_cov, y))
names(data_frame) = c("t_ind", "X1", "X2", "X3", "X4", "Y")

# Define treatment indicator and 
t_ind = "t_ind"
# moment covariates
bal = list()
bal$bal_cov = c("X1", "X2", "X3", "X4")

# Set tolerances
bal$bal_tol = 0.02
bal$bal_std = "group"

# Solve for the Average Treatment Effect on the Treated, ATT (default)
bal$bal_alg = FALSE
sbwatt_object = sbw(dat = data_frame, ind = t_ind, out = "Y", bal = bal)

# # Solve for a Conditional Average Treatment Effect, CATE
# sbwcate_object = sbw(dat = data_frame, ind = t_ind, out = "Y", bal = bal, 
# sol = list(sol_nam = "quadprog"), par = list(par_est = "cate", par_tar = "X1 > 1 & X3 <= 0.22"))

# # Solve for the population mean, POP
# tar = colMeans(bal_cov)
# names(tar) = bal$bal_cov
# sbwpop_object = sbw(dat = data_frame, ind = t_ind, out = "Y", bal = bal, 
# sol = list(sol_nam = "quadprog"), par = list(par_est = "pop"))

# # Solve for a target population mean, AUX
# sbwaux_object = sbw(dat = data_frame, bal = bal, 
# sol = list(sol_nam = "quadprog"), par = list(par_est = "aux", par_tar = tar*1.05))

# # Solve for the ATT using the tuning algorithm
# bal$bal_alg = TRUE
# bal$bal_sam = 1000
# sbwatttun_object = sbw(dat = data_frame, ind = t_ind, out = "Y", bal = bal, 
# sol = list(sol_nam = "quadprog"), par = list(par_est = "att", par_tar = NULL))

# Check
summarize(sbwatt_object)
# summarize(sbwcate_object)
# summarize(sbwpop_object)
# summarize(sbwaux_object)
# summarize(sbwatttun_object)

# Estimate
estimate(sbwatt_object)
# estimate(sbwcate_object)
# estimate(sbwpop_object)
# estimate(sbwatttun_object)

# Visualize
visualize(sbwatt_object)
# visualize(sbwcate_object)
# visualize(sbwpop_object)
# visualize(sbwaux_object)
# visualize(sbwatttun_object)

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Summarize output from sbw

Description

Function for summarizing the output from sbw.

Usage

summarize(object, digits = 6, ...)

Arguments

object	an object from the class sbwcau or sbwpop obtained after using sbw.
digits	The number of significant digits that will be displayed. The default is 6.
...	ignored arguments.

Value

A list with the following elements:

variance, variance of the weights

coefficient_variation, coefficient of variation of the weights

effective_sample_size, effective sample size

balance_table, mean/TASDM balance tables for samples before/after weighting

shadow_price, dual tables or shadow prices for the balanced groups

Examples

# Please see the examples in the function sbw above.

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Visualize output from sbw

Description

Function for visualizing the output from sbw.

Usage

visualize(object, plot_cov, ask = TRUE, ...)

Arguments

object	an object from function sbw.
plot_cov	names of covariates for which balance is to be displayed. If NULL, all of the covariates will be displayed.
ask	logical. If TRUE (and the R session is interactive) the user is asked for input, before a new figure is drawn.
...	ignored arguments.

Value

No return value. The figures will be shown in the Plots window.

Examples

# Please see the examples in the function sbw above.

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