If you build it properly this shouldn't happen. If my ceiling sagged overnight I'd assess what I might have done wrong while constructing it, or what I could have done better. Did the pile set properly before I started to hollow it out? Dig I dig the walls too thin? Did I not shape the arch of my ceiling propely?
Instead of figuring out how to predict how much sag you're going to have, you should learn how to build a snow shelter without any resulting sag whatsoever.
Selection of snow is your first and most important task. The absolute best snow to build a shelter in is a wind drift that was laid down in a single storm. The crystalline structure of the snow in wind drifts is already broken, and won't settle much if at all when you cut into it and build your shelter. Wind drifts are also a good indicator of where you should build your shelter, because they only form where there's a break in the wind.
Building a cave in fresh snow or at the top of a loose snow pack is not the best thing to do structurally, because the snow is not settled and is full of air. It's best to first pack the snow down with your snow shoes and let the snow set a bit before you start digging into it. Fluffy snow is great for insulation, but not for structure. The best shelter is one that is built just before a snow, a blanket of fresh fallen snow on top of a solid quinzhee is the type of shelter you could live in for the winter.
In an emergency situation you may be forced to forgo proper site selection and dig-in wherever you can. In these situations, where you do not necessarily build your shelter in ideal structural snow, then how much your shelter may shrink will depend on how loose the snow is, so plan on building your shelter a little bigger than necessary if you think you're going to be in it for longer than waiting out a storm, or spending only one night.