Profile the objective

[dmbates]

• The profile method for LinearMixedModel currently profiles w.r.t. σ, the fixed-effects coefficients, the σ parameters, and the θ parameters (but not the correlation parameters).
• The MixedModelProfile struct returned contains a table, tbl, of values of ζ (the signed square root of the change in objective from the optimum) and β and θ as a Vector{NamedTuple}. The TypedTables.Table generic is re-exported from this package to allow for presenting this row-table in a table format.
• Forward and reverse interpolation splines are added for parameters to and from ζ

Did behavior change? Did you add need features? If so, please update NEWS.md

• add entry in NEWS.md
• after opening this PR, add a reference and run docs/NEWS-update.jl to update the cross-references.

Should we release your changes right away? If so, bump the version:

• I've bumped the version appropriately

[codecov]

Codecov Report

Patch coverage: 94.04% and project coverage change: -0.26 ⚠️

Comparison is base (d946f6f) 95.90% compared to head (8977dc1) 95.64%.

❗ Current head 8977dc1 differs from pull request most recent head f8f4559. Consider uploading reports for the commit f8f4559 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #639      +/-   ##
==========================================
- Coverage   95.90%   95.64%   -0.26%     
==========================================
  Files          29       35       +6     
  Lines        2732     3189     +457     
==========================================
+ Hits         2620     3050     +430     
- Misses        112      139      +27     

Impacted Files	Coverage Δ
src/MixedModels.jl	100.00% <ø> (ø)
src/utilities.jl	96.92% <ø> (ø)
src/linearmixedmodel.jl	94.88% <28.57%> (-3.23%)	⬇️
src/profile/utilities.jl	94.31% <94.31%> (ø)
src/profile/thetapr.jl	97.14% <97.14%> (ø)
src/remat.jl	96.69% <97.22%> (-0.04%)	⬇️
src/bootstrap.jl	93.93% <100.00%> (+2.15%)	⬆️
src/profile/fixefpr.jl	100.00% <100.00%> (ø)
src/profile/profile.jl	100.00% <100.00%> (ø)
src/profile/sigmapr.jl	100.00% <100.00%> (ø)
... and 1 more

... and 1 file with indirect coverage changes

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[dmbates]

If you have time to look at that, sure. I expect that the periodic splines, which were introduced in BSplineKit v0.12.0, will be needed in MixedModelsMakie but probably not in MixedModels.

The way I imagine the division of responsibility is that MixedModels will add the forward and backward splines to the MixedModelProfile, because they are used to obtain profile-based confidence intervals. These splines are natural cubic splines. The reverse splines, mapping the zeta values to the fixed-effects coefficients, are used to create these profile-based confidence intervals. The periodic splines are used for contour interpolation, which should be in MixedModelsMakie, I think.

That is, we can probably live with a compat entry in MixedModels.jl allowing 0.11,0.12 for BSplineKit.

[palday]

I think this is mostly good to go for an initial merge and release.

• I've marked all comment-conversations as resolved that I think are nonblocking.
• I've added a number of docstring suggestions that also highlight where the API guarantees are and which things might still change in the 4.x series. There are three broad things that I think we might revisit:
  • The exact internal structure of MixedModelProfile, but I think that is not really interesting for most users, who just want the profile to compute the CI.
  • The concrete Tables.jl-compatible return types. I don't really have any objection to the current DictTable, but I suspect that we'll only really know what works as we get more experience with using this feature in practice.
  • The parameter names in the various tables. For the fixed effects, I would really like to see these match coefnames or fixefnames, but that is the type of polish that we can make in a smaller, more focused PR.
• Related to nonblocking polish, I've opened up a discussion for that: Polish for profiling #688.
• I've added a NEWS entry that tries to highlight the "awesome new feature but some details might change!" nature of the release. Feel free to modify.
• I've bumped the version appropriately.

Feel free to keep or reject all my suggestions.

[palday]

@dmbates I think I've messed up the indents on some of the !!! note blocks. When you're all done, I make those changes locally and push before you merge.

[palday]

@dmbates I think I've messed up the indents on some of the !!! note blocks. When you're all done, I make those changes locally and push before you merge.

fixed

[palday]

@dmbates merge and release when ready 🚀