Compute Balance and Summary Statistics for Covariates

These functions quickly compute balance statistics for the given covariates. These functions are used in bal.tab(), but they are available for use in programming without having to call bal.tab() to get them.

• col_w_mean() computes the (weighted) means for a set of covariates and weights and is essentially a weighted version of colMeans().

• col_w_sd() computes the (weighted) standard deviations for a set of covariates and weights.

• col_w_smd() computes the (weighted) (absolute) (standardized) difference in means for a set of covariates, a binary treatment, and weights.

• col_w_vr() computes the (weighted) variance ratio for a set of covariates, a binary treatment, and weights.

• col_w_ks() computes the (weighted) Kolmogorov-Smirnov (KS) statistic for a set of covariates, a binary treatment, and weights.

• col_w_ovl() computes the complement of the (weighted) overlapping coefficient compliment for a set of covariates, a binary treatment, and weights (based on Franklin et al, 2014).

• col_w_cov() and col_w_corr() compute the (weighted) (absolute) treatment-covariate covariance or correlation for a set of covariates, a continuous treatment, and weights.

Usage

col_w_mean(
  mat,
  weights = NULL,
  s.weights = NULL,
  subset = NULL,
  na.rm = TRUE,
  ...
)

col_w_sd(
  mat,
  weights = NULL,
  s.weights = NULL,
  bin.vars,
  subset = NULL,
  na.rm = TRUE,
  ...
)

col_w_smd(
  mat,
  treat,
  weights = NULL,
  std = TRUE,
  s.d.denom = "pooled",
  abs = FALSE,
  s.weights = NULL,
  bin.vars,
  subset = NULL,
  weighted.weights = weights,
  na.rm = TRUE,
  ...
)

col_w_vr(
  mat,
  treat,
  weights = NULL,
  abs = FALSE,
  s.weights = NULL,
  bin.vars,
  subset = NULL,
  na.rm = TRUE,
  ...
)

col_w_ks(
  mat,
  treat,
  weights = NULL,
  s.weights = NULL,
  bin.vars,
  subset = NULL,
  na.rm = TRUE,
  ...
)

col_w_ovl(
  mat,
  treat,
  weights = NULL,
  s.weights = NULL,
  bin.vars,
  integrate = FALSE,
  subset = NULL,
  na.rm = TRUE,
  ...
)

col_w_cov(
  mat,
  treat,
  weights = NULL,
  type = "pearson",
  std = FALSE,
  s.d.denom = "all",
  abs = FALSE,
  s.weights = NULL,
  bin.vars,
  subset = NULL,
  weighted.weights = weights,
  na.rm = TRUE,
  ...
)

col_w_corr(
  mat,
  treat,
  weights = NULL,
  type = "pearson",
  s.d.denom = "all",
  abs = FALSE,
  s.weights = NULL,
  bin.vars,
  subset = NULL,
  weighted.weights = weights,
  na.rm = TRUE,
  ...
)

Arguments

mat

a numeric matrix or a data frame containing the covariates for which the statistic is to be computed. If a data frame, splitfactor() with drop.first = "if2" will be called if any character or factor variables are present. This can slow down the function, so it's generally best to supply a numeric matrix. If a numeric vector is supplied, it will be converted to a 1-column matrix first.

weights

numeric; an optional set of weights used to compute the weighted statistics. If sampling weights are supplied through s.weights, the weights should not incorporate these weights, as weights and s.weights will be multiplied together prior to computing the weighted statistics.

s.weights

numeric; an optional set of sampling weights used to compute the weighted statistics. If weights are supplied through weights, weights and s.weights will be multiplied together prior to computing the weighted statistics. Some functions use s.weights in a particular way; for others, supplying weights and s.weights is equivalent to supplying their product to either weights or s.weights. See Details.

subset

a logical vector with length equal to the number of rows of mat used to subset the data. See Details for notes on its use with col_w_smd(), col_w_cov(), and col_w_corr().

na.rm

logical; whether NAs should be ignored or not. If FALSE, any variable with any NAs will have its corresponding statistic returned as NA. If TRUE, any variable with any NAs will have its corresponding statistic computed as if the missing value were not there.

...

for all functions, additional arguments supplied to splitfactor() when mat is a data.frame. data, var.name, drop.first, and drop.level are ignored; drop.first is automatically set to "if2". For col_w_ovl() and col_w_ent(), other arguments passed to density() besides x and weights. Note that the default value for bw when unspecified is "nrd" rather than the default in density(), which is "nrd0".

bin.vars

a vector used to denote whether each variable is binary or not. Can be a logical vector with length equal to the number of columns of mat or a vector of numeric indices or character names of the binary variables. If missing (the default), the function will figure out which covariates are binary or not, which can increase computation time. If NULL, it will be assumed no variables are binary. All functions other than col_w_mean() treat binary variables different from continuous variables. If a factor or character variable is in mat, all the dummies created will automatically be marked as binary, but it should still receive an entry when bin.vars is supplied as logical.

treat

a vector of treatment status for each individual. For col_w_smd(), col_w_vr(), col_w_ks(), and col_w_ovl(), treat should have exactly two unique values. For col_w_cov() and col_w_corr(), treat should be a many-valued numeric vector.

std

logical; for col_w_smd(), whether the computed mean differences for each variable should be standardized; for col_w_cov(), whether treatment-covariate correlations should be computed (TRUE) rather than covariances (FALSE). Can be either length 1, whereby all variables will be standardized or not, or length equal to the number of columns of mat, whereby only variables with a value of TRUE will be standardized. See Details.

s.d.denom

for col_w_smd() and col_w_cov() when std is TRUE for some variables, and for col_w_corr(), how the standardization factor should be computed. For col_w_smd() (i.e., when computing standardized mean differences), allowable options include

• "treated" - uses the standard deviation of the variable in the treated group

• "control" - uses the standard deviation of the variable in the control group

• "pooled" - uses the square root of the average of the variances of the variable in the treated and control groups

• "all" - uses the standard deviation of the variable in the full sample

• "weighted" - uses the standard deviation of the variable in the full sample weighted by weighted.weights

• "hedges" - uses the small-sample corrected version of Hedge's G described in the WWC Procedures Handbook (see References)

• the name of one of the treatment values - uses the standard deviation of the variable in that treatment group.

For col_w_cov() and col_w_corr(), only "all" and "weighted" are allowed. Abbreviations allowed. This can also be supplied as a numeric vector of standard deviations with length equal to the number of columns of mat; the values will be used as the standardization factors.

abs

logical; for col_w_smd(), col_w_cov(), and col_w_corr(), whether the returned statistics should be in absolute value (TRUE) or not. For col_w_vr(), whether the ratio should always include the larger variance in the numerator, so that the ratio is always greater than or equal to 1. Default is FALSE.

weighted.weights

for col_w_smd(), col_w_cov(), and col_w_corr(), when std = TRUE and s.d.denom = "weighted", a vector of weights to be applied to the computation of the denominator standard deviation. If not specified, will use the argument to weights. When s.d.denom is not "weighted", this is ignored. The main purpose of this is to allow weights to be NULL while weighting the denominator standard deviations for assessing balance in the unweighted sample but using the standard deviations of the weighted sample.

integrate

logical; for col_w_ovl(), whether to use integrate() to calculate the area of overlap or the distance between the densities, respectively. If FALSE, a midpoint Riemann sum with 1000 partitions will be used instead. The Riemann sum is a little slower and very slightly imprecise (unnoticibly in most contexts), but the integral can fail sometimes and thus is less stable. The default is to use the Riemann sum.

type

for col_w_cov() and col_w_corr(), the type of covariance/correlation to be computed. Allowable options include "pearson" and "spearman". When "spearman" is requested, the covariates and treatment are first turned into ranks using rank() with na.last = "keep".

Value

A vector of balance statistics, one for each variable in mat. If mat has column names, the output will be named as well.

Details

col_w_mean() computes column weighted means for a matrix of variables. It is similar to colMeans() but (optionally) incorporates weights. weights and s.weights are multiplied together prior to being used, and there is no distinction between them. This could be used to compute the weighted means of each covariate in the general population to examine the degree to which a weighting method has left the weighted samples resembling the original population.

col_w_sd() computes column weighted standard deviations for a matrix of variables. weights and s.weights are multiplied together prior to being used, and there is no distinction between them. The variance of binary variables is computed as \(p(1-p)\), where \(p\) is the (weighted) proportion of 1s, while the variance of continuous variables is computed using the standard formula; the standard deviation is the square root of this variance.

col_w_smd() computes the mean difference for each covariate between treatment groups defined by treat. These mean differences can optionally be weighted, standardized, and/or in absolute value. The standardization factor is computed using the unweighted standard deviation or variance when s.weights are absent, and is computed using the s.weights-weighted standard deviation or variance when s.weights are present, except when s.d.denom = "weighted", in which case the product of weighted.weights and s.weights (if present) are used to weight the standardization factor. The standardization factor is computed using the whole sample even when subset is used. Note that unlike bal.tab(), col_w_smd() requires the user to specify whether each individual variable should be standardized using std rather than relying on continuous or binary. The weighted mean difference is computed using the product of weights and s.weights, if specified. The variance of binary variables is computed as \(p(1-p)\), where \(p\) is the (weighted) proportion of 1s, while the variance of continuous variables is computed using the standard formula.

col_w_vr() computes the variance ratio for each covariate between treatment groups defined by treat. When abs = TRUE, pmax(out, 1/out) is applied to the output so that the ratio is always greater than or equal to 1. For binary variables, the variance is computed as \(p(1-p)\), where \(p\) is the (weighted) proportion of 1s, while the variance of continuous variables is computed using the standard formula. Note that in bal.tab(), variance ratios are not computed for binary variables, while here, they are (but likely should not be interpreted). weights and s.weights are multiplied together prior to being used, and there is no distinction between them. Because of how the weighted variance is computed, exactly balanced groups may have variance ratios that differ slightly from 1.

col_w_ks() computes the KS statistic for each covariate using the method implemented in twang. The KS statistics can optionally be weighted. For binary variables, the KS statistic is just the difference in proportions. weights and s.weights are multiplied together prior to being used, and there is no distinction between them.

col_w_ovl() computes the complement of the overlapping coefficient as described by Franklin et al. (2014). It does so by computing the density of the covariate in the treated and control groups, then finding the area where those density overlap, and subtracting that number from 1, yielding a value between 0 and 1 where 1 indicates complete imbalance, and 0 indicates perfect balance. density() is used to model the density in each group. The bandwidth of the covariate in the smaller treatment group is used for both groups. The area of overlap can be computed using integrate, which quickly and accurately computes the integral, or using a midpoint Riemann sum with 1000 partitions, which approximates the area more slowly. A reason to prefer the Riemann sum is that integrate can fail for unknown reasons, though Riemann sums will fail with some extreme distributions. When either method fails, the resulting value will be NA. For binary variables, the complement of the overlapping coefficient is just the difference in proportions. weights and s.weights are multiplied together prior to being used, and there is no distinction between them. The weights are used to compute the weighted density by supplying them to the weights argument of density.

col_w_cov() computes the covariance between a continuous treatment and the covariates to assess balance for continuous treatments as recommended in Austin (2019). These covariance can optionally be weighted or in absolute value or can be requested as correlations (i.e., standardized covariances). The correlations are computed as the covariance between the treatment and covariate divided by a standardization factor, which is equal to the square root of the product of the variance of treatment and the variance of the covariate. The standardization factor is computed using the unweighted variances when s.weights are absent, and is computed using the sampling weighted variances when s.weights are present, except when s.d.denom = "weighted", in which case the product of weighted.weights and s.weights (if present) are used to weight the standardization factor. For this reason, the computed correlation can be greater than 1 or less than -1. The standardization factor is always computed using the whole sample even when subset is used. The covariance is computed using the product of weights and s.weights, if specified. The variance of binary variables is computed as \(p(1-p)\), where \(p\) is the (weighted) proportion of 1s, while the variance of continuous variables is computed using the standard formula.

col_w_corr() is a wrapper for col_w_cov with std set to TRUE.

References

Austin, P. C. (2019). Assessing covariate balance when using the generalized propensity score with quantitative or continuous exposures. Statistical Methods in Medical Research, 28(5), 1365–1377. doi:10.1177/0962280218756159

Franklin, J. M., Rassen, J. A., Ackermann, D., Bartels, D. B., & Schneeweiss, S. (2014). Metrics for covariate balance in cohort studies of causal effects. Statistics in Medicine, 33(10), 1685–1699. doi:10.1002/sim.6058

What Works Clearinghouse. (2020). WWC Procedures Handbook (Version 4.1). Retrieved from https://ies.ed.gov/ncee/wwc/Handbooks

See also

• bal.tab()

• bal.compute()

• balance-statistics

Examples

data("lalonde", package = "cobalt")

treat <- lalonde$treat
covs <- subset(lalonde, select = -c(treat, re78))
covs0 <- splitfactor(covs, drop.first = "if2")
bin.vars <- c(FALSE, FALSE, TRUE, TRUE, TRUE,
              TRUE, TRUE, FALSE, FALSE)
W <- WeightIt::weightit(treat ~ covs, method = "glm", 
                        estimand = "ATE")
weights <- W$weights

round(data.frame(
    m0 = col_w_mean(covs0, weights = weights, subset = treat == 0),
    sd0 = col_w_sd(covs0, weights = weights,
                   bin.vars = bin.vars, subset = treat == 0),
    m1 = col_w_mean(covs0, weights = weights, subset = treat == 1),
    sd1 = col_w_sd(covs0, weights = weights,
                   bin.vars = bin.vars, subset = treat == 1),
    smd = col_w_smd(covs0, treat = treat, weights = weights,
                    std = TRUE, bin.vars = bin.vars),
    vr = col_w_vr(covs0, treat = treat, weights = weights,
                  bin.vars = bin.vars),
    ks = col_w_ks(covs0, treat = treat, weights = weights,
                  bin.vars = bin.vars),
    row.names = colnames(covs0)
), 4)
#>                    m0       sd0        m1       sd1     smd     vr     ks
#> age           27.1000   10.8071   25.5663    6.5640 -0.1676 0.3689 0.1912
#> educ          10.2863    2.7430   10.6064    2.0631  0.1296 0.5657 0.0768
#> race_black     0.3979    0.4895    0.4478    0.4973  0.1302 1.0322 0.0499
#> race_hispan    0.1170    0.3215    0.1217    0.3269  0.0156 1.0344 0.0047
#> race_white     0.4851    0.4998    0.4305    0.4951 -0.1378 0.9815 0.0546
#> married        0.4089    0.4916    0.3146    0.4643 -0.2102 0.8920 0.0944
#> nodegree       0.6250    0.4841    0.5702    0.4950 -0.1157 1.0456 0.0547
#> re74        4552.7364 6339.3397 2932.1845 5743.4197 -0.2740 0.8208 0.3121
#> re75        2172.0386 3161.2645 1658.0651 3091.1829 -0.1579 0.9562 0.1526

# Compare to bal.tab():
bal.tab(covs, treat = treat, weights = weights,
        disp = c("m", "sd"), stats = c("m", "v", "ks"),
        estimand = "ATE", method = "weighting",
        binary = "std")
#> Balance Measures
#>                Type   M.0.Adj  SD.0.Adj   M.1.Adj  SD.1.Adj Diff.Adj
#> age         Contin.   27.1000   10.8071   25.5663    6.5640  -0.1676
#> educ        Contin.   10.2863    2.7430   10.6064    2.0631   0.1296
#> race_black   Binary    0.3979    0.4895    0.4478    0.4973   0.1302
#> race_hispan  Binary    0.1170    0.3215    0.1217    0.3269   0.0156
#> race_white   Binary    0.4851    0.4998    0.4305    0.4951  -0.1378
#> married      Binary    0.4089    0.4916    0.3146    0.4643  -0.2102
#> nodegree     Binary    0.6250    0.4841    0.5702    0.4950  -0.1157
#> re74        Contin. 4552.7364 6339.3397 2932.1845 5743.4197  -0.2740
#> re75        Contin. 2172.0386 3161.2645 1658.0651 3091.1829  -0.1579
#>             V.Ratio.Adj KS.Adj
#> age              0.3689 0.1912
#> educ             0.5657 0.0768
#> race_black            . 0.0499
#> race_hispan           . 0.0047
#> race_white            . 0.0546
#> married               . 0.0944
#> nodegree              . 0.0547
#> re74             0.8208 0.3121
#> re75             0.9562 0.1526
#> 
#> Effective sample sizes
#>            Control Treated
#> Unadjusted  429.    185.  
#> Adjusted    329.01   58.33