"Improved Familiar" CR/ECL vs Caster level formula

[Tetujin]

I atempting to find the basic formula to figure out which other creatures I can use for improved familiar. At first I tried straight one half caster level = CR of creature, but there were a lot of inconsistancies, but there were a few that matched up, which leads me to believe that it is the ECL of the creature, but I simply not any good at that. Just a thought: I expect the rules to be similar to animal companions....but I dont know the rules for that either, so...I'm still stuck.