There is no easy way to determine the exact value of
capacitor to use. The manufactures often list a minimum
size to keep the regulator stable.
They have no idea of the frequency or amplitude of noise
their regulator might see in your application.
Although, if one follows the manufactures recommendation,
it is unlikely to see a regulator oscillate, but I've see it happen.
There are a lot of variables that one doesn't have access
to but one can figure that if there are large the current changes
on the output, one might want to use a larger capacitor
on the output.
The more noise on the input, one might want to add to the
input filter.
The choice of capacitor type should be considered as
well. Electrolytics tend to have poor high frequency response
so one often sees a 47 uf electrolytic paralleled with a .01
ceramic.
Dwight