I'm trying to piece together some of the bits and pieces from this thread with regard to collar ties. Jim cited a study suggesting that a collar tie is only effective in preventing spread at the rafter base if the tie is within a foot of the base. The conclusion being that any collar tie position higher in the triangle only serves to prevent sagging of the rafter under load (with the force on the tie being compression).
Later in the thread, Mike says that collar ties are unnecessary with a supportive ridge.
So, taking both points into account, am I to conclude that the only reason I see so many roof structures with collar ties higher up in the triangle is because the rafters are undersized for the load?