@palday, what would you think of changing the structure of the fitlog to be a

Vector{NamedTuple{(:θ, :obj),(NTuple{K,T}, T)}} so that it can be displayed as a Table? If I understand correctly using an NTuple{K,T} instead of a Vector{T} to store each parameter vector in the fit log should even save a bit of storage.

I am also considering changing the format of the allpars property of a parametric bootstrap to be like that of the tbl property of a MixedModelProfile. That is, a Vector{<:NamedTuple} which can be displayed as a Table. @palday, I would defer to you regarding the implications of such changes for version numbers under semantic versioning. It is probably best to save up several such incompatible changes for one, massive, break with the past. It is such a pity that we have to go through the stages of "keep doing it wrong until you do it right" in this type of design.

An alternative for the parametric bootstrap is just to introduce a new property, say tbl, which has the Table-compatible structure and deprecate the allpars property.

Ergonomic design is only "obvious" in retrospect.

We do a decent job of keeping release notes and haven't had a breaking release in a while, so I'm not terribly opposed to having a clean-up cycle + major release in the near future. If the breaking changes don't impact a particular user, then they can feel free to have MixedModels = "4, 5" in their compat entry.

That said, I haven't yet thought about the proposal. I would suggest implementing it and seeing how much we like it for a little bit. As soon as we have something breaking on main, I can split off a release-4.x branch for any small things we want to backport. Then we can tinker on main for a little while before tagging 5.0 (and I can get to work on all the breaking changes I want to do in 5.0, such as some consistency stuff and stripping out the multithreading -- it's better to let the BLAS do multithreading and maybe add a nice example of doing multiprocessing to the docs).

Another couple of things to throw in the hopper for a breaking version is to change the name and default value of the argument to fit that causes the fitlog to be created. In retrospect, calling this thin was inappropriate. I, at least, have never used it as other than a toggle to keep the fitlog or not so the concept of "thinning" the fitlog and keeping only every 10'th value is not particularly valuable to me. If one really wanted that then it would be possible to post-process the fitlog. I doubt that the amount of memory required to keep the entire fitlog is ever going to be the limiting factor for fitting a model.

I am also thinking of changing the structure to be a row-oriented table (Vector{NamedTuple}) with the first column being the objective and the remaining columns being the values of the theta parameters.

see also #618

Exactly. I am getting to the point where I keep coming up with the same ideas, over and over, and considering them to be novel approaches. I suppose in a way that this is better than coming up with contradictory ideas and considering them to be worthwhile, novel approaches.