Status: accepted · Date: 2026-09-14 · Applies: 0074, 0075, 0095

#338 had three subjects. Decision 0104 took the link function and 0105 the time index. Mixed and hierarchical models were read by neither — 0104 says so in its own consequences — and #621 exists so that closing #338 did not drop them: statsmodels' MixedLM, fixed and random effects, random intercepts and slopes, nested and crossed grouping.

The issue put two things on record before anything was read. The reading was owed under decision 0074, which twice found the naive expectation wrong. And the verdict was allowed to be no: the subject is the hardest of the three, and its audience is the narrowest.

nuget.org, 2026-09-14:

Every package below was read with tools/survey.cs (decision 0110) against one pattern, and every licence from the package, per decision 0075:

dotnet run tools/survey.cs -- <package> <version> \
  '(Mixed|RandomEffect|FixedEffect|VarianceComponent|Reml|Multilevel|Hierarch|RandomIntercept|RandomSlope|Satterthwaite|KenwardRoger)'

Dew.Stats.Core is the managed edition of Dew.Stats; the Windows edition was not loaded, and its description names ANOVA, ANCOVA and no mixed model.

Nothing in .NET fits a linear mixed model, free or commercial. The nearest things are classical ANOVA with a random or repeated factor — Accord, NMath — which is the balanced-design special case a mixed model exists to replace. Infer.NET is the one honest caveat: its Variable API can express a hierarchical model by hand, a Gaussian per group drawn from a Gaussian over groups, and infers it by message passing. That is a Bayesian modelling language, not an estimator with statsmodels' output, and it is named so it is not mistaken for an absence.

So the gap is real, and wider than any 0074 has recorded: 0096 and 0105 each found the computation somewhere and the apparatus missing. Here neither exists.

statsmodels 0.15.0 is already in tools/requirements.lock.txt, and one fit settles more than any argument. A random intercept and a random slope over 20 groups of 10, fitted by REML:

              Coef. Std.Err.   z    P>|z| [0.025 0.975]
Intercept     1.318    0.228  5.774 0.000  0.871  1.766
x             1.879    0.080 23.583 0.000  1.723  2.036
Group Var     0.927    0.354
Group x x Cov 0.002    0.102
x Var         0.000    0.119

Two things follow.

The inference is z, not Satterthwaite or Kenward-Roger. statsmodels reports Wald tests against the normal distribution. Across its source, Kenward-Roger appears nowhere and Satterthwaite only in stats/oneway.py, stats/weightstats.py, stats/multicomp.py and stats/nonparametric.py — the unequal-variance corrections of classical tests. The part #621 feared most is not part of this reference: parity with MixedLM needs REML or ML, the profiled likelihood and its Hessian, and nothing from lmerTest.

The estimate belongs to the optimizer, and the oracle gate cannot hold it. The slope's variance sits on its boundary, and statsmodels warns "The MLE may be on the boundary of the parameter space". The same data refitted with each method it accepts:

The default does not reach the best likelihood statsmodels itself finds on this data, and two solvers stop 16 log-likelihood units away. The oracle gate compares at 1e-9 (decision 0073); here the reference disagrees with itself at 1e-5 on a coefficient and 3e-3 on the likelihood. A corpus would freeze one optimizer's path, and a correct implementation reaching a better optimum would fail it.

Moving away from the boundary narrows the disagreement without closing it. A random intercept alone, over 30 groups of 10 with a group variance near 1.7, converges under all five solvers with no warning, and they agree on the REML log-likelihood to 3e-8, on the coefficients to 2e-7, and on the group variance only to 1.4e-4 (1.73992 to 1.74006): the likelihood is flat along the variance, so every solver stops where its own tolerance says the surface is level. A variance shrinking to zero is the ordinary case, not an edge, and even the interior one is not pinned to 1e-9 by the reference's defaults.

Mixed models are not written now. The void is recorded, scoped, and left for a caller, under decision 0095's rule that what ships is what a caller needs rather than what a gap permits.

It is not refused forever, and the reason is not that .NET has an answer — it has none. It is that the lot would be the largest in Lodestar.Stats.Regression, its audience is the narrowest of the three subjects in #338, and its conformance cannot be proven the way everything else in this repository is proven. Writing it on the strength of the gap alone would ship the one estimator here whose numbers no corpus stands behind.

What reopens it: a caller who needs MixedLM's table from .NET. The lot it would be is written down so it does not have to be rediscovered:

• linear mixed models only — random intercepts and slopes over one grouping factor, variance components for nested ones — by REML and ML on the profiled likelihood, with statsmodels' z-based table;
• a conformance method decided before any code: the log-likelihood held to the best the reference's solvers reach, and the parameters to the tolerance that likelihood's curvature allows rather than to one solver's stopping point — a divergence from the 1e-9 gate that docs/equivalence.md and a decision would both have to carry;
• generalized linear mixed models, crossed random effects beyond variance components, and Satterthwaite or Kenward-Roger degrees of freedom out of scope: statsmodels fits the first only by Bayesian approximation (BinomialBayesMixedGLM, PoissonBayesMixedGLM), and names the last only for one-way ANOVA and two-sample tests, never for a mixed model;
• placement answered then, against decision 0076 and the two-level naming rule. Lodestar.Stats.Regression is the obvious candidate and the answer is not taken here, because nothing is being placed.

• Write it as the next lot. The gap is genuine, and this project's thesis is to write where .NET is empty. It lost on the conformance table above, not on effort: an estimator whose reference disagrees with itself cannot be held to the tolerance every other estimator here meets, and choosing a weaker one belongs to the lot that has a caller to judge it against.
• Delegate to Infer.NET. First-party and MIT, and it can express the model. It cannot print the table: no REML, no standard errors from the observed information, no z test. A migration row sending a MixedLM user to a message-passing compiler would be a row that fails them.
• Delegate to a commercial ANOVA. NMath's repeated-measures ANOVA answers the balanced design a mixed model generalises, and nothing more. Naming it is a courtesy to a reader with that design; delegating to it would be a claim it does not meet.

• docs/migration/statsmodels.md's mixed-models row stops reading "the only one still unread": it reads no .NET package, with this record, the Infer.NET and repeated-measures caveats, and the reopening condition.
• #621 closes with this record. #338 loses its last unread subject.