Can't figure out how to physically change index order of selected elements

Can't figure out how to physically change index order of selected elements

I'm attempting to physically change the index order of the elements returned by a selector.  For example, I'm attempting to make it so when someone clicks on a button, it swaps the index position of the element above or below it (depending on which button they press).  I tried to assign it using something like
 
  1. $('.draggable :eq(2)').attr('index', 3)
 
But it didn't seem to work.  Is there a way to do it using jQuery, or do I have to change it within DOM itself?  Or is there another way to do it?