bal.tab methods use.
bal.tab(x, ...)"bal.tab". The use of cotinuous treatments, subclasses, and/or clusters will also cause the object to inherit other classes. The class "bal.tab" has its own print method (print.bal.tab), which formats the output nicely and in accordance with print-related options given in the call to bal.tab(). Each inherited class also has its own print method.
bal.tab() performs various calculations on the the data objects given, and some of these calculations are not transparent on the help pages of the individual methods. This page details the calculations that are used across bal.tab methods.With Binary Treatments
Prior to computation, all variables are checked for variable type, which allows users to differentiate balance statistic calculations based on type using the arguments to continuous and binary. First, if a given covariate is numeric and has only 2 levels, it is converted into a binary (0,1) variable. If 0 is a value in the original variable, it retains its value and the other value is converted to 1; otherwise, the lower value is converted to 0 and the other to 1. Next, if the covariate is not numeric or logical (i.e., is a character or factor variable), it will be split into new binary variables, named with the original variable and the value, seperated by an underscore. Otherwise, the covariate will be used as is and treated as a continuous variable.
The default balance statistic for mean differences for continuous variables is the standardized difference, which is the difference in the means divided by a measure of spread (i.e., a d-type effect size measure). This is the default because it puts the mean differences on the same scale for comparison with each other and with a given threshold. It can be helpful to see the raw mean differences if the analyst is familiar with the true significance of the mean difference irrespective of the spread of the variable in the sample. For binary variables, the default balance statistic is the raw difference in proportion. Although standardized differences can be computed, proportion differences for binary variables are already on the same scale, and computing the standardized difference can obscure the true difference in proprotion by dividing the difference in proportion by a number that is itself a function of the observed proportions. For example, if $XT = .2$ and $XC = .3$, the standardized difference in proportion would be different from that if $XT = .5$ and $XC = .6$, which seems counterintuitive and not a useful distinction. However, to remain in line with the methodological literature and for comparability with other balance assessment tools (e.g., MatchIt's summary()), the option to use standardized differences for binary variables remains.
Standardized differences are calculated as follows: the numerator is the mean of the treated group minus the mean of the control group, and the denominator is a measure of spread calculated in accordance with the argument to s.d.denom or the default of the specific method used. Common approaches in the literature include using the standard deviation of the treated group or using the "pooled" standard deviation (i.e., the square root of the mean of the group variances) in calculating standardized mean differences. The computed spread bal.tab() uses is always that of the full, unadjusted sample (i.e., before matching, weighting, or subclassification), as recommended by Stuart (2010) and institued in MatchIt, though some analysts and other packages use the spread of the sample in question (i.e., before or after adjustment). One reason to favor the use of the spead of the unadjusted sample is that it prevents the paradoxical situation of adjustment descreasing both the mean difference and the spread of the sample, yielding a larger standardized mean difference than that prior to adjusting even though the adjusted groups are now more similar.
Although the reported mean differences (standardized or otherwise) are presented as they are calculated, when m.threshold is specified, it is compared to the absolute mean difference for simplicty of reporting. bal.tab() takes the absolute value of the input to m.threshold as well before comparing.
Variance ratios are computed within-sample, with the larger of the two variances in the numerator, always yielding values greater than or equal to 1. Variance ratios are not calculated for binary variables since they are only a function of the group proportions and thus provide the same information as differences in proportion. bal.tab() takes the reciprocal of the input to v.threshold if it is less than 1.
When matching is used for conditioning, the presented sample sizes are calculated simply by summing the number of observations in each group with matching weights greater than 0. When weighting is used, an "effective sample size" is calculated for each group using the following formula: $(\sum w)^2 / \sum w^2$, as is used in twang. The effective sample size is "approximately the number of observations from a simple random sample that yields an estimate with sampling variation equal to the sampling variation obtained with the weighted comparison observations" (Ridgeway et al., 2016). The calculated number tends to underestimate the true effective sample size of the weighted samples.
When subclassification is used, the balance tables for each subclass stored in $Subclass.Balance use values calculated as described above. For the aggregate balance table stored in $Balance.Across.Subclass, the values of each statistic are computed as a weighted average of the statistic across subclasses, weighted by the proportion of units in each subclass, as is done in MatchIt.
With Continuous Treatments
When continuous treatment variables are considered, the balance statistic calculated is the Pearson correlation between the covariate and treatment. Currently only weighting is supported with continuous treatments; the calculated correlation after adjustment is weighted by the generated weights.
Quick
Calculations can take some time, especially when there are many variables, interactions, or clusters. One reason for this is that bal.tab() computes all values that it can, even if they are not requested by the user. For example, even if un = FALSE, which is the default, values for the unadjusted samples are still calculated. This can be useful if the output is to be further examined with print() or love.plot() or is to be used in some other way after the original call to bal.tab(). To avoid these extra calculations if they are not needed, users can set quick = TRUE, which will often quite dramatically speed up calculation and still display all statistics the user requests. For simple and quick model comparisons, it may be quite useful to do so, but for model reporting and graphical displays, it may be more useful to leave quick = FALSE, which is the default.
Stuart, E. A. (2010). Matching Methods for Causal Inference: A Review and a Look Forward. Statistical Science, 25(1), 1-21. http://doi.org/10.1214/09-STS313
bal.tab.matchit for the method for objects returned by MatchIt.
bal.tab.ps for the method for objects returned by twang.
bal.tab.Match for the method for objects returned by Matching.
bal.tab.CBPS for the method for objects returned by CBPS.
bal.tab.formula and bal.tab.data.frame for the methods for formula and data frame interfaces when the user has covariate values and weights (including matching weights) or subclasses or wants to evaluate balance on an unconditioned data set.