[R] mixed model testing

[Irene Mantzouni]

Is there a formal way to prove the need of a mixed model, apart from e.g. comparing the intervals estimated by lmList fit? 
For example, should I compare (with AIC ML?) a model with seperately (unpooled) estimated fixed slopes (i.e.using an index for each group) with a model that treats this parameter as a random effect (both models treat the remaining parameters as random)?
 
Thank you!