In the Amulet of Samarkand, Underwood says that more powerful spirits can turn invisible then summons an invisible spirit. Underwood is weak though and likely can only summon up to a mid-level djinn based on his fight against Lovelace and his reaction to Nathaniel summoning Batimaeus. Batimaeus never turns invisible although Farqual and Jabor do apparently as they get hit by a truck just after Batimaeus' theft. Furthermore, the guards Lovelace creates after the raid can turn invisible yet appear to be weaker than Batimaeus.
High level spirits never seem to turn invisible, Uraziel and Ammit both travel visibly which seems odd, especially in Ammit's case as he often goes around stealthily.
With this in mind what are the restricting factor for invisibility? Is it power, intelligence or can all spirits do it?