Toilets, Sinks, Showers, Tubs and Disposals - Strange toilet problem

I hope you can help as I've tried everything.
I recently moved into a six year old home with 2 1/2 baths. Two full baths on the upper level and a half bath on the main floor.
The problem I am having is in the half bath with the toilet randomly clogging. I have plunged, snaked and removed toilet to verify that nothing is stuck in the trap. By randomly clogging I mean I can flush the toilet multiple times with only clean water and after a few flushes the water will rise to the top of the bowl and then drain out slowly. If I plunge it after this occurs it will be fine for a while.
The toilets in the upstairs baths work fine but I notice a large bubble coming from the supply inlet in the bowl each time any of the toilets is flushed. I also have noticed the two upstairs flush very quickly and only empty about half the tank where the problem toilet empties the entire tank after every flush.
Any advice you can offer will be greatly appreciated.

My best guess is that you might have a vent problem. Possibly your rooftop vent is partially blocked. I would start there.

The half bath toilet may be much older and is no longer getting an effective siphon out of the trap, such as from a clogged jetway (small hole towards the front). It is not quite clear about what bubbles where and when. There could be a partial blockage in the line from that toilet but before it joins the main line.
I'll bet that it is not a vent problem.

Check the chains on the flappers for the upstairs toilets. The chain should have only enough slack to allow the flapper to seal. This will give you a "full" flush.
If other toilets bubble when another is flushed, I would check the vent line going out the roof. Good luck.

Thank you for your replies.
Further details are. All the toilets were installed at the time the home was built. The vent sytem seems to be such that all run up the exterior wall and are connected in the attic and then one vent runs through the roof. Since the two upstairs toilets work fine I don't believe the vent is plugged unless something was possibly left in the branch for the downstairs half bath at the time of construction.
As far as the bubbling all three toilets do this and it is at every flush. The large bubble seems to be coming from the jet in the front of the bowl and is almost as if when the toilet is flushed air gets trapped in a pocket and is released at the next flush. The manufacturer of the toilets is Mansfield and they all appear to be the same model but I am not sure what that is.
There are no bubbles in other fixtures of the sound of air being pulled in from the sink or tub when any of the toilets is flushed.
Could the downstairs toilet just be defective in some way?

Since you have already checked the trap on the problem toilet, that only leaves the drainline leaving the toilet. You may need to pull the toilet again and snake out the drain line. Sorry, thats all I can think of since you have covered most other bases. Good luck.

Thanks I'll have another go at it.

A little added information, perhaps. I'm having a similar problem with one toilet on the first floor of my two-story house. I get an air bubble, too, but I think it's coming from the, forgot what it's called, the waste drain hole. I went in the basement and noticed a slight leak stained on the side of the drain going from the toilet to the stack. That may be from last week or ten years ago, I don't know. I, too, think there might be something stuck under the toilet so I guess I may have to pull it to check.