Determining licensing in CaGel by means of substitution test
More of a comment than a real answer but I'm not able to comment on here just yet. It seems to me this test works relatively well if you bear in mind that in:
She stayed in her bedroom
You can't drop in her bedroom without changing the meaning of the verb, whereas in
She disappeared in her bedroom
you can.
In the second sentence in her bedroom just adds detail about the circumstances of the disappearing, whereas in the first it is integral to the meaning of the verb.
If you change the second sentence to she disappeared into her bedroom, you make the last bit a complement again, but now the meaning of disappeared is different - almost opposite, if you consider that if someone is said to have disappeared, it usually means we don't know where to find them.
In answer to your comments Hannah:
I haven't got the book you mention, but the way I understand the substitution test is that if the result is not grammatical in the original sense of the verb, that counts as a failure. Therefore, if the new sentence is not obviously ungrammatical, the omission test is used to check whether the verb is being used in a different sense - but if it is, that means that the substitution has changed the meaning, and hence that the substitution test is failed.
Maybe the omission test is more of an intuition pump than anything else, and maybe we have different intuitions about the meaning of stayed, but to me, it has the sense of we're having Jack and Caitlin to stay when used by itself. If you use it with something that's obviously an adjunct, you seem to end up with this sense - if you said she stayed a long time, I would take that to mean that she didn't leave the party until late, or stayed with friends or at a hotel - somewhere away from home - for a long time. There is an idea of being hosted or put up that's not there in she stayed in her bedroom.