I continue to give thought to the concept of literary influences. If I were studying an author and trying to understand what elements came together to help form his literary identity, I suspect it would be a life's work, with many undefined areas and several unsatisfactory answers. Also, ultimately, I suspect it doesn't really matter. Consider how little is known about Shakespeare, for instance, yet the author continues to be a presence in literature.
I think when an author claims someone as being a literary influence, one needs to take that with a grain of salt. Perhaps it's more of a tribute to that author than a true declaration. I believe that an author is the sum of many parts. Family influences, teachers, friends, and life changing experiences probably weigh more heavily on a writer's process of creativity than having read another author's creations.
Here is another suggestion. Perhaps the idea of a literary influence, besides being a form of tribute, is a marketing ruse. If I'm a publisher and I'm doing a second or third run of a Carver title, why not add "Another anthology from one of the most influential short story writers of the last two decades."? Why not?