His residence is not established. Probably he does not have a fixed residence, and lives invisibly among the people, interacting with them. It is also possible that he may have selected a far away place for his domicile. In some hadith-reports it is stated that the twelfth Imam comes to Mecca during the pilgrimage season and participates in the hajj rituals. He sees and knows the people, whereas people do not see him. Shi'is believe that the Imam disappeared in the city of Samarra, in that cellar which is ascribed to him and is a place of visitation (ziyarat).
It is here, they say, that the Hidden Imam lives, and he will reappear also from this spot. If he is there in that cellar why cannot he be seen? Who brings food and drink for him? Why does he not go out from there? One of the Arab poets has composed a poem about this subject. He says: Has not the time come for the cellar to bring out what you, out of your conjecture, believe to be a human being? Shame on you, for creating a third fictitious being, other than a legendary bird and a ghost.
This ascription is nothing more than a falsehood which has been circulated out of obstinacy. The Shi'is do not maintain such a belief. There is absolutely no report that says that the twelfth Imam lives in the cellar and will rise from there. No Shi'i scholar has mentioned such a thing. On the contrary, many hadith-reports narrate that he lives among the people and associates with them.
Sadir Sayrafi has related a tradition from Imam Sadiq (peace be upon him) which says: That which makes the condition of the Master of the Command (i.e., the twelfth Imam) resemble Joseph is that in spite of being mature and wise, and in spite of having associated with him before, Joseph's brothers could not recognize him when they came to him [in Egypt] until he introduced himself to them. Moreover, in spite of the fact that the distance that existed between Joseph and Jacob was no more than eighteen days, Jacob had no information about him.
Then why are these people denying that God can do a similar thing for His Proof, the Master of the Command? He too can interact with people, walk around their market place, sit on their carpets and still they would not recognize him! He would continue to do that until God permits him to introduce himself.