balance.IPW: Check Post-Weighting Balance for (A)IPW Estimators Using... In CausalGAM: Estimation of Causal Effects with Generalized Additive Models

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

 ```1 2 3 4 5``` ```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)

Kevin Quinn, University of Michigan

References

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

`gam`, `estimate.ATE`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71``` ```## 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) ```