Incorporates sampling weight in rank correlation

[shem shen]

Dear list,

I guess this is an old question on this forum, but so far I have not found any solutions yet. Briefly speaking, I want to incorporate weight into my calculation of tie-corrected rank correlation, but neither ktau or spearman supports sampling weight. I would like to propose a solution here and hear about your opinion (I am not sure if there is any literature supporting this approach, or if there is any flaw with this approach):

1. Use fracrank to calculate fractional ranks of both variables, as fracrank allows the use of weight;
2. Use the normal command corr to calculate the Pearson's correlation between the two fractional ranks and using weight.

sysuse auto,clear
fracrank price [aw=weight], gen(rank1 , replace)
fracrank mpg [aw=weight] , gen(rank2 , replace)
corr rank1 rank2 [aw=weight]
spearman price mpg //compare

fracrank is a user-written command provided by Philippe Van Kerm. It can be installed from within Stata by typing "ssc install sgini". Another package, somersd (by Roger Newson), calcualtes kendall's taua and allows weight, but taua does not correct for ties.

[Felix Bittmann]

I know this is an old post, but maybe this is helpful for other users as well. One solution to use spearman with sampling weights is generalized bootstrapping. An ado is available.
Ado: https://github.com/fbittmann/gbs
Working paper: https://doi.org/10.5281/zenodo.17581255

Let me know if this works for you.

[Mike Lacy]

Another possibility would be to take advantage of the fact that Spearman's rho is identical to the Pearson correlation coefficient computed on the ranks of the variables. -correlate- and -pwcorr- both accept weights. The -egen- function rank() calculates ranks with options for various treatments of ties.

[Leonardo Guizzetti]

There’s a deeper question of what does it even mean to have a weighted rank? Is this a sensible quantity to estimate? I have not seen good justifications on this topic, though they may exist (I haven’t looked much). If anyone has suggested reading, I’d like to learn more.