the way the analog stick works is by resistance, if it detects a resistance in one of it's 2 axis, then it will move, this can happen a couple of ways.
The silicon connector between the mother board and the analog daughter board may not be making proper connection.
The resistive traces on the analog board may be damaged.
These are the two main reasons "ghost analog" can happen, but most times replacing the silicon connector will alleviate the situation, the soft mod way of fixing this is to use joysens.prx, but the results are iffy...
P.S. Just remembered this was in the PSP Slim section, so since there isn't a silicon present in the slim, ensure the connection between the mother board and the analog daughter board are properly seated. If that doesn't help, then you can still try the joysens.prx