Evaluates L1 distance between multidimensional histograms
L1.meas(group, data, drop=NULL, breaks = NULL, weights, grouping = NULL)An object of class L1.meas which is a list with the following fields
The numerical value of the L1 measure
A list of cutpoints used to calculate the L1 measure
The numerical value of the Local Common Support proportion
the group variable
the data
a vector of variable names in the data frame to ignore
a list of vectors of cutpoints; if not specified, automatic choice will be made
weights
named list, each element of which is a list of groupings for a single categorical variable. See Details.
Stefano Iacus, Gary King, and Giuseppe Porro
This function calculates the L1 distance on the k-dimensional histogram in order to measure the level of imbalance in a matching solution.
If breaks is not specified, the Scott automated bin calculation
is used (which coarsens less than Sturges, which used in
cem). Please refer to cem help page. In
this case, breaks are used to calculate the L1 measure.
When choosing breaks for L1, a very fine coarsening (many cut
points) produces values of L1 close to 1. A very mild coarsening (very
fex cutpoints), is not able to discriminate, i.e. L1 close to 0
(particularly true when the number of observations is small with respect
to the number of continuous variables).
The grouping option is a list where each element is itself a
list. For example, suppose for variable quest1 you have the
following possible levels "no answer", NA, "negative", "neutral",
"positive" and you want to collect ("no answer", NA, "neutral")
into a single group, then the grouping argument should contain
list(quest1=list(c("no answer", NA, "neutral"))). Or if you have
a discrete variable elements with values 1:10 and you want
to collect it into groups ``1:3,NA'', ``4'',
``5:9'', ``10'' you specify in grouping the
following list list(elements=list(c(1:3,NA), 5:9)). Values not
defined in the grouping are left as they are. If cutpoints
and groupings are defined for the same variable, the
groupings take precedence and the corresponding cutpoints are set
to NULL.
The L1.profile function
shows how to compare matching solutions for any level of (i.e., without
regard to) coarsening.
This code also calculate the Local Common Support (LCS) measure, which is the proportion of non empty k-dimensional cells of the histogram which contain at least one observation per group.
Iacus, King, Porro (2011) tools:::Rd_expr_doi("10.1198/jasa.2011.tm09599")
Iacus, King, Porro (2012) tools:::Rd_expr_doi("10.1093/pan/mpr013")
Iacus, King, Porro (2019) tools:::Rd_expr_doi("10.1017/pan.2018.29")
data(LL)
set.seed(123)
L1.meas(LL$treated,LL, drop=c("treated","re78"))
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