Using bal.tab() with Multi-Category Treatments
When using bal.tab()
with multi-category treatments, the output will be different from the case with binary or continuous treatments, and there are some options that are common across all bal.tab()
methods. This page outlines the outputs and options in this case.
There are two main components of the output of bal.tab()
with multi-category treatments: the two-group treatment comparisons and the balance summary. The two-group treatment comparisons are standard binary treatment comparison either for pairs of groups (e.g., for treatments A, B, and C, "A vs. B", "A vs. C", and "B vs. C") or each group against all the groups (i.e., the entire sample).
The balance summary is, for each variable, the greatest imbalance across all two-group comparisons. So, for variable X1, if "A vs. B" had a standardized mean difference of 0.52, "A vs. C" had a standardized mean difference of .17, and "B vs. C" had a standardized mean difference of .35, the balance summary would have 0.52 for the value of the standardized mean difference for X1. The same goes for other variables and other measures of balance. If the greatest observed imbalance is tolerable, then all other imbalances for that variable will be tolerable too, so focusing on reducing the greatest imbalance is sufficient for reducing imbalance overall. (Note that when s.d.denom = "pooled"
, i.e., when the estimand is the ATE, the pooled standard deviation in the denominator will be the average of the standard deviations across all treatment groups, not just those used in the pairwise comparison.) The balance summary will not be computed if multiply imputed data are used.
There are four arguments for each bal.tab()
method that can handle multi-category treatments: pairwise
, focal
, which.treat
, and multi.summary
.
pairwise |
Whether to compute the two-group comparisons pairwise or not. If |
focal |
When one group is to be compared to multiple control groups in an ATT analysis, the group considered "treated" is the focal group. Only comparisons between other groups and the focal group are of interest. By specifying the name or index of the treatment condition considered focal, |
which.treat |
This is a display option that does not affect computation. When displaying the |
multi.summary |
If |
The output is a bal.tab.multi
object, which inherits from bal.tab
. It has the following elements:
Pair.Balance |
For each pair of treatment groups, a regular |
Balance.Across.Pairs |
The balance summary across two-group comparisons. This will include the greatest (i.e., maximum) absolute balance statistics(s) for each covariate across all comparisons computed. Thresholds can be requested for each balance measure as with binary treatments. |
Observations |
A table of sample sizes or effective sample sizes for each treatment group before and after adjustment. |
As with other methods, multiple weights can be specified, and values for all weights will appear in all tables.
Noah Greifer
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