Check Post-Weighting Balance for (A)IPW Estimators Using Generalized Additive Models

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Description

This function calculates weighted means of covariates where weights in inverse propensity weights and then examines the differences in the weighted means across treated and control units as a diagnostic for covariate balance.

Usage

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balance.IPW(pscore.formula, pscore.family,
             treatment.var, outcome.var, data = NULL, 
             divby0.action = c("fail", "truncate", "discard"), 
             divby0.tol = 1e-08, nboot = 501, 
             suppress.warnings = TRUE, ...)

Arguments

pscore.formula

A formula expression for the propensity score model. See the documentation of gam for details.

pscore.family

A description of the error distribution and link function to be used for the propensity score model. See the documentation of gam for details.

treatment.var

A character variable giving the name of the binary treatment variable in data. If treatment.var is a numeric variable, it is assumed that control corresponds to sort(unique(treatment.values))[1] and treatment corresponds to sort(unique(treatment.values))[2]. If treatment.var is a factor, it is assumed that control corresponds to levels(treatment.values)[1] and treatment corresponds to levels(treatment.values)[2].

outcome.var

A character variable giving the name of the outcome variable in data.

data

A non-optional data frame containing the variables in the propensity score model along with all covariates that one wishes to assess balance for. data cannot contain any missing values.

divby0.action

A character variable describing what action to take when some estimated propensity scores are less than divby0.tol or greater than 1 - \code{divby0.tol}. Options include: fail (abort the call to estimate.ATE), truncate (set all estimated propensity scores less than divby0.tol equal to divby0.tol and all estimated propensity scores greater than 1 - \code{divby0.tol} equal to 1 - \code{divby0.tol}), and discard (discard units that have estimate propensity scores less than divby0.tol or greater than 1 - \code{divby0.tol}). Note that discarding units will change the estimand.

divby0.tol

A scalar in [0,0.5) giving the tolerance level for extreme propensity scores. Defaults to 1e-8. See divby0.action for details.

nboot

Number of bootrap replications used for calculating bootstrap standard errors. If nboot is less than or equal to 0 then bootstrap standard errors are not calculated. Defaults to 501.

suppress.warnings

Logical value indicating whether warnings from the gam fitting procedures should be suppressed from printing to the screen. Defaults to TRUE.

...

Further arguments to be passed.

Details

This function provides diagnostic information that allows a user to judge whether the inverse propensity weights generated from a particular generalized additive model specification result in covariate balance across treated and control groups. The function is intended to be used before the estimate.ATE function in order to find a specification for the propensity score model that results in sufficient covariate balance.

The weighted mean differences between all variables in the dataset passed to balance.IPW are reported along with a z-statistics for these weighted differences. Univariate mean covariate balance is decreasing in the absolute value of the z-statistics (z-statistics closer to 0 imply better univariate mean balance).

Printing the output from balance.IPW will result in a table with k-2 rows (one for each variable other than the treatment and outcome variables) and 6 columns. The columns are (from left to right) the observed mean of the covariate among the treated units, the observed mean of the covariate among the control units, the weighted mean of the covariate among the treated units, the weighted mean of the covariate among the control units, the weighted mean difference, and the z-statistic for the difference.

It is often useful to include interactions and powers of the covariates in the dataset so that balance can be checked for these quantities as well.

Means, mean differences, and z-statistics are only reported for numeric covariates.

Value

An object of class balance with the following attributes:

obs.mean.control

The observed mean of each of the covariates within the control units.

obs.mean.treated

The observed mean of each of the covariates within the treated units.

weighted.mean.control

The weighted mean of each of the covariates within the control units.

weighted.mean.treated

The weighted mean of each of the covariates within the treated units.

weighted.diff.SE

The bootstrap standard errors for the differences betwen weighted.mean.treated and weighted.mean.control.

Author(s)

Adam Glynn, Harvard University

Kevin Quinn, UC Berkeley

References

Adam N. Glynn and Kevin M. Quinn. 2010. "An Introduction to the Augmented Inverse Propensity Weighted Estimator." Political Analysis.

See Also

gam, estimate.ATE

Examples

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## Not run: 
set.seed(1234)
## number of units in sample
n <- 2000


## measured potential confounders
z1 <- rnorm(n)
z2 <- rnorm(n)
z3 <- rnorm(n)
z4 <- rnorm(n)

## treatment assignment
prob.treated <-	pnorm(-0.5 + 0.75*z2)
x <- rbinom(n, 1, prob.treated)

## potential outcomes
y0 <- z4 + rnorm(n)
y1 <- z1 + z2 + z3 + cos(z3*2) + rnorm(n)

## observed outcomes
y <- y0
y[x==1] <- y1[x==1] 	     	


## put everything in a data frame
examp.data <- data.frame(z1, z2, z3, z4, x, y)

## augment data with interactions and powers of covariates
examp.data$z1z1 <- examp.data$z1^2
examp.data$z2z2 <- examp.data$z2^2
examp.data$z3z3 <- examp.data$z3^2
examp.data$z4z4 <- examp.data$z4^2

examp.data$z1z2 <- examp.data$z1 * examp.data$z2
examp.data$z1z3 <- examp.data$z1 * examp.data$z3
examp.data$z1z4 <- examp.data$z1 * examp.data$z4

examp.data$z2z3 <- examp.data$z2 * examp.data$z3
examp.data$z2z4 <- examp.data$z2 * examp.data$z4

examp.data$z3z4 <- examp.data$z3 * examp.data$z4



## check balance of a propensity score model that is not sufficient to
## control confounding bias

bal.1 <- balance.IPW(pscore.formula=x~s(z3)+s(z4),
                     pscore.family=binomial(probit),
                     treatment.var="x",
                     outcome.var="y",
                     data=examp.data,
                     nboot=250)

print(bal.1) ## some big z-statistics here indicating balance not so great


## try again
bal.2 <- balance.IPW(pscore.formula=x~z1+z2+z3+z4,
                     pscore.family=binomial(probit),
                     treatment.var="x",
                     outcome.var="y",
                     data=examp.data,
                     nboot=250)

print(bal.2) ## balance looks much better-- 
             ##    only 1 out of 14 zs > 2.0 in absval


## End(Not run)

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