If the trap doesn’t work, do you have any friends/neighbors nearby that might try coaxing her out? When our dog was a pup and escaped a few times he was very good at evading us but more than happy to approach strangers that he apparently thought were less apt to return him to incarceration.
When I was living in Chicago we might as well have had a cat door, because most of our menagerie would bolt outside at the slightest opportunity. They would generally hang around the house and come in when they were damn good and ready; they seldom responded to our attempts to entice or catch them. When I came home from work I would expect to find one or two of them either on the porch or running up the stairs with me; sometimes they would follow me in, sometimes not, and like as not when I opened the door one would dash out. It got to the point where after I came in I would announce who had come in and who had gone out, and then get a report on who was probably still outside.
In all the years only two cats went permanently missing. One was a friend’s that we had inherited when she died, who had never acclimated well to the change in residence; we figured she had gone off in search of her late owner. The other was part of one of the litters one of our cats had, who had always been less social than the others; I occasionally saw a cat that I was certain was her in the neighborhood but she would never come when I called her. She appeared healthy, so I assumed that she was getting handouts from someone.
Neither do small children. When they are young enough that they have not yet developed the capacity to be reasoned with, those who know better (their parents, teachers, etc.) have no choice but to “force” the child to do something he doesn’t want to do, because it really is for the child’s own good.
Cats never develop the capacity to be reasoned with. And so those of us who know better (and by that I mean humans) have no choice but to “force” them, sometimes, to do things that they’d rather not do, because it really is for the cat’s own good. As other posters have pointed out, the outdoors is very unsafe for cats, despite what you may think about their toughness; I’ve never met a cat yet tough enough to withstand a hit from a car.
Besides, even if the cat is perfectly safe under the shed, the OP does, in fact, own the cat and has every right to force it indoors, if that’s what the OP wants. As long as a cat is not being abused in some way, the owner has the right to dictate to it.
Good for you. Anyone can “have” an animal, it’s another thing entirely to be a responsible pet owner. In the same way that “having a kid” and “parenting” do not mean the same thing.
Well, we set out the cat trap last night, and caught a neighborhood tom. He was pretty pissed off when I let him out this morning, but he pees on our bushes, so maybe this will make him think twice before he comes back. 
Still no sign of Anna, but at least we know the trap works.
Which makes the odds of something bad happening before the cat comes back inside what? Do the math.
And good parents know that parenting works best when you can get the children to want to do what you want them to do. You miss the thrust of my post, and what is wrong with the OP’s attitude.
It makes the odds considerably higher than if the cat was in the house.
There’s a tom cat in the neighborhood and you wonder why Anna won’t come home? 
Exactly. Since I’m responsible for my pets’ health and safety, I like having a little control over it. That’s both emotionally and financially responsible, by the way, and I have no desire to incur either the emotional or the financial costs associated with outdoor cats.
Sure it does. Good parents also know that sometimes you’re gonna have to get shit done without their cooperation, because what they want is not always best for them, which is why kids need parents. No good parent has ever said “Junior, mommy will give you a cookie if you stop playing in traffic!” No, you go and GET him.
Cats aren’t for reasoning with, and there’s nothing wrong with the OP’s attitude.
just thought of something, while you are looking down and around don[t forget to look up, as on roof tops.
Darmah turned up missing one time for a couple days and I looked all over for her. Decided to look again one morning before work and I took a different route out of the neighborhood. For some reason i looked up at a house I was passing and there on their porch roof was my kitty. I had to get a ladder to get her down and the silly fought me and then once home tried to scramble back out of the house!
I think she climbed a tree (chased a bird or was chased by dogs) to the house roof, jumped down to the porch roof then got stuck there all night in the freezing cold.
I’ve read through this discussion and haven’t seen anyone asking if the OP’s cat is spayed. If she is not spayed, she may be pregnant when she comes back in.
Also I don’t see anyone asking if there have been changes in the OP’s home that might have prompted the cat to go out and stay out.
Just my 2 cents’ worth.
SMullen, she’s definitely spayed. Nothing’s changed at home; Anna’s always been interested in outside and lately she’s been batting at the windows like crazy when the leaves fall off the trees and birds fly by. I think she just wanted to see it all close up.
I’m hoping the cold and the rain (we have both today) will encourage her to come home.
Put a can of her favorite food out and sit down next to kind of ignoring it. It may take a bit of time but hunger wins.
Dunno about your Anna, but my cat knows the “ccrrrrrrkkksh” sound of one of those pull-tab cans being pulled open. Knows it well.
Might help to not open the can till you’re outside, on a quiet day.
(Ditto if you’ve been feeding kibble - shake the kibble bag outside.)
What about playing? Does she play? Can you walk by where she is and tempt her out with a dragged string?
The tom may be the reason she is not coming home, but not because she likes him. If he has been peeing in your yard, he may also be scaring her away. (his territory, and she isn’t breedable.)
CeeJayTee, I’m glad your little girl is spayed and that nothing has changed at home. I hope she comes back inside very soon.
There are some really yummy canned foods that you can try. I agree with the poster who recommended opening the can outside so that telltale whooshing sound is easy for your girl to hear. Ditto shaking a bag with kibble, if that’s what she likes.
I hate to suggest this, but I remember a very difficult cat glomming onto me like a magnet when I was cooking some (gasp) sausage. That smell really carries, too. And it wouldn’t be a waste of food if it brought your little girl in. You could give each of your cats a little taste, too. Don’t just give it to the errant girl, or she might get the idea that she gets sausage every time she runs out of the house.
Another thing you can try is if your girl has a very favorite person other than you, having that person call her.