an analogy that attributes human qualities to something not human
Do you know what an analogy means? Generally speaking it is an argument that you use in a discussion that is almost, but not quite, the same as the situation you discussing. You use this parallel argument to try to make the real argument understandable.
I think what you really want is metaphor. This is language is that directly compares seemingly unrelated subjects.(Wikipedia definition)
The man is a beast. Beast is a metaphor describing the man (he is not a beast but shows beast like characteristics)
More to the point of your request, this might be an example sentence.
The door to the room yawned before him.
Obviously a door cannot yawn like a human but you get the impression of a huge open door like that of a human mouth yawning.
we could also put forth personification or even prosopo(po)eia: The attribution of human characteristics to things. However, this is not truly an analogic mode.