In the current US presidential election, both candidates have stated that the United States was more respected on the global stage during their presidency, and less respected during their opponents time in office.
The article linked and others I've found rely on polling of people in other countries of how they view US as "doing the right thing."
But the candidates' argument is more along the lines of negotiating power and respect on the world stage. How do you measure a country's true political power / respect on the world stage?
https://apnews.com/article/biden-trump-pew-poll-confidence-us-democracy-election-1c547bee39eb7ee926e1d5b1f38c9987