I was looking at a paper (link here) by Blackwell et al. (2010) on CEM in Stata.
In one example using an example data set, the authors ran CEM using the matching covariates such as age, education, black, nodegree, and re74.
For the imbalance measure for each covariate (univariate imbalance), all the measures became below 0.1 (where 0 means fully balanced and 1 means not at all balanced).
But why Multivariate L1 distance, which takes account for all the imbalance measures at a time, is relatively so high (nearly 0.51)?
I read the definition of how Multivariate L1 distance is caculated.
Is the above reason due to the fact that Multivariate L1 distance is calculated based on absolute difference of frequencies over all the matching covairates between treatment and control group?
In other words, does Multivariate L1 distance can be high because the range of the values for each matching covariate can differ from each other (e.g. age ranges 17-55 whereas black and nodegree have binary values) so that calculating absolute difference for all naturally generates higher Multivariate L1 distance?
I am really interested in to understand this and I could not find a good explanation for this on the internet.
If I am wrong, I am happy to hear someone's comment on this.
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