Coming up with ideas for a novel is different than coming up with them for short stories. Sure, the basic process is the same--ideas are all around us, and any can make a captivating story. Ideas for novels, however, need to be bigger. They need to be grand. That's not to say they necessarily need to be better than short story ideas (short story ideas can be just as good), but they need to be able to carry a story much further.
When I begin to choose which idea I want to use for my next novel project, I think through two things. First, is the idea enough to take me through 60,000 or so words if I'm writing a young adult novel (or 75,000 to 100,000 words if I'm tackling one tailored for adults)? Second, and possibly more important, is this an idea that I'm excited about and will still be excited about months down the road?
Let's look at that second question first. You will be working on this project for quite a while. The process usually takes me a minimum of six months (times will, of course, vary by author, but the entire process takes awhile). If the idea doesn't excite you at the beginning, chances are it will downright bore you before you even get halfway through your first draft. And that speaks nothing of the revision process, which, in my opinion, is the biggest part of writing a novel. If that original idea is not strong enough, you will probably rather tear your hear out than read through for revision again, and your story will no doubt suffer because of it.
Now back to the first point: picking an idea that is big enough for a novel-length work. At this point in the process, I don't write anything down. I take an idea that excites and intrigues me, and I think about things I can do with it. When I discover a neat thread that will make a good story, instead of jumping right into the process like I would with a short story, I continue expanding and dissecting the idea. Is there potential for great conflict? Is this a problem that will not have a simple solution (or if it does, will that simple solution be well guarded)? Is there enough potential emotion to fire up not only a protagonist, but an antagonist and various minor characters as well? Does this main idea lend itself to believable subplots? If I can answer yes to these questions, I know I have the makings of a novel, and I can take the first few baby steps in creating this story.
Next time I'll go through what those first steps are. Some people can dive right in once they have that initial workable idea, but I need to go through a bunch of pre-first draft exercises. Until then, keep writing and/or reading.