Balance for Categorical Covariate: Random Strata as part of a PSA

Function provides a measure of the balance achieved between control and treatment groups for a categorical covariate from user defined strata. This statistic is compared to the same measure for randomly permuted strata.

bal.cs.psa(
  categorical,
  treatment = NULL,
  strata = NULL,
  B = 1000,
  eps = 0.02,
  main = NULL,
  ...
)

Arguments

categorical: Categorical covariate that is being balanced within strata in a PSA. If categorical has three columns, then the second and third are assumed to be the treatment and strata respectively. Missing values are not allowed. May be factor or numeric.
treatment: Binary variable of same length as categorical; generally 0 for 'control,' 1 for 'treatment.'
strata: Integer variable; a vector of same length as categorical indicating the derived strata from estimated propensity scores.
B: Numeric; number of randomly generated iterations of the balance measure are created for the comparison distribution.
eps: Numeric; ensures that weighting is reasonable for small categories.
main: Title passed to histogram.
...: Other graphical parameters passed to histogram.

Value

In addition to the histogram, a list with the following components is returned:

balance.orig: Balance measure of user defined strata.
rank.orig: Rank of original balance measure in comparison with the B randomly generated values.

Details

This function measures the balance achieved across K strata for a categorical covariate with J categories. If \(p_{ijk}\) is the proportion of cases in stratum k, category j, and treatment i, then the statistic is the sum over all K, J of \( |\sqrt{p_{0jk} + \epsilon} - \sqrt{p_{1jk} + \epsilon } | \). A permutation distribution is generated by randomly assigning cases to strata, thus generating B permuted stratifications and the associated B permutation statistics. The permutation stratifications are generated under a fixed marginals model to retain comparability with the original stratification. A histogram of the permutation statistics is produced with the original statistic referenced as a red dot.

Author

James E. Helmreich James.Helmreich@Marist.edu

Robert M. Pruzek RMPruzek@yahoo.com

Examples

#Everything random
categorical<-sample(4,1000,replace=TRUE)
treatment<-sample(c(0,1),1000,replace=TRUE)
strata<-sample(5,1000,replace=TRUE)
bal.cs.psa(categorical,treatment,strata)

#> $balance.orig
#> [1] 0.8724279
#> 
#> $rank.orig
#> [1] 105
#> 

#Perfect balance on 80%, random on last 20%
categorical<-rep(sample(5,1000,replace=TRUE),2)
treatment<-c(rep(0,1000),rep(1,1000))
strat<-sample(6,1200,replace=TRUE)
strat<-c(strat[1:1000],strat[1:800],strat[1001:1200])
bal.cs.psa(categorical,treatment,strat,B=200)

#> $balance.orig
#> [1] 0.3864591
#> 
#> $rank.orig
#> [1] 1
#>