Status: accepted · Date: 2026-09-12 · Applies: 0008, 0095

#686 names two families of absence in Lodestar.Stats.Regression, both recorded in docs/equivalence.md:

• The covariances. sm.WLS, sm.GLS and .get_robustcov_results("HC0".."HC3") are "out of scope for 0.1.0".
• The links. The GLM wires logit and log; "the other families sm.families publishes (Gamma, inverse Gaussian, negative binomial, Tweedie) have no counterpart yet."

Taken together that is several lots. This record fixes the order and says what each later one waits for, so the sequence is a decision rather than whatever gets written next.

The heteroskedasticity-consistent covariances come first, and ship here: CovarianceType with Nonrobust, Hc0, Hc1, Hc2 and Hc3, chosen on OlsOptions and echoed on OlsSummary.

They come first because of what this package claims to be. README.md sells it as the inference table — "coefficients everywhere and inference nowhere" — and a robust covariance is what an analyst reaches for when the assumption behind the standard errors fails, which is the ordinary case rather than the exotic one. Shipping the table without HC0–HC3 ships the numbers that are easiest to compute and hardest to defend. Nothing else on the list has that property: a missing family stops a fit outright, which is visible, where a standard error computed under an assumption nobody checked is wrong and silent.

The order after it, each opening when the one before has shipped:

1. WLS, which is this solve over rows scaled by the square root of a weight — the operation LeastSquares already performs for IRLS every iteration.
2. Negative binomial, the family a count model reaches for when Poisson's variance assumption fails, and the natural sibling of the Poisson that ships.
3. Gamma, with the .scale handling docs/equivalence.md has already written against.
4. GLS, which is not the same solve: it needs a full covariance from the caller and a whitening factorization, so it is a lot rather than a parameter.
5. Inverse Gaussian and Tweedie, deferred under decision 0095's rule — nothing has asked, and publishing later is always available.

Under any cov_type, statsmodels flips use_t from True to False. Measured rather than read: the coefficient p-values become 2·Φ̄(|z|) against the normal, the interval multiplier becomes the normal quantile, and — asymmetrically — f_pvalue stays on the F distribution, f.sf(fvalue, k, df_resid) matching to the last bit while chi2.sf(fvalue·k, k) does not.

Reproducing that follows decision 0008's standing tie-breaker: parity with the library a user migrates from, over what is tidier. A reader who expected both tests to move together would be wrong about statsmodels, and a package that quietly corrected the asymmetry would make every p-value disagree with the reference for a reason no oracle could explain.

The cost is that OlsSummary.TStatistics holds a z under a robust type, which is what statsmodels' own tvalues does. OlsSummary.CovarianceType exists for that: a summary that changes the meaning of two of its properties has to carry the thing that says so, or the shape advertises a promise it does not keep — which is #668's lesson applied before the fact rather than after it.

The normal p-value needs Φ̄, and Distributions publishes five members of which that is not one — Normal.Sf is on the list 0095 explicitly keeps internal. The obvious move was the one 0097 and 0098 already made twice: publish it, bump Lodestar.Stats, release it, then floor on it — a two-package sequence across two pull requests.

It was not needed. The square of a standard normal is chi-squared on one degree of freedom, so the two-sided normal p-value is ChiSquaredSf(z², 1), and that member has been public since 0097. The identity is exact, not an approximation, and measured against scipy it agrees to 1.8e-16 relative at z = 0.5 and 1.1e-13 at z = 37 — the worst case being a p-value of 1e-299, and the tolerance the corpora compare at being 1e-9.

So the rule this record applies is 0095's, by reading it and finding it did not apply: publishing later is always available has a companion worth writing down — before asking the layer to publish, check whether what it already publishes answers the question. Two of the four published tails are related by an identity to a third, and that will not be the last time.

• Publish Normal.Sf anyway, for the name. ChiSquaredSf(z * z, 1.0) needs a comment where NormalSf(z) would not. Refused because the comment is two lines and the alternative is a release of another package to add a member nothing else wants — and an unused published member cannot be unpublished, which is the asymmetry 0081 and 0095 are both built on.
• Keep Student's t under a robust covariance. Defensible on its own terms, and it would make TStatistics mean one thing always. Refused on 0008's rule: every p-value would then disagree with statsmodels for a migrating reader, and the oracle would have to be weakened to let it.
• Name the properties Statistics and drop TStatistics. A breaking rename that would say what the numbers are under both modes. Refused as out of scope here, and it is worth recording that it was refused for scope rather than on merit: 0.x is where such a rename is cheap, and #689 is where that window is tracked.
• Take WLS in the same lot. It shares the solve and would have been cheap. Refused because it changes what a fit is rather than how its covariance is estimated, and a reviewer reading one branch should not have to hold both.

• Lodestar.Stats.Regression reaches 0.3.0, a minor bump: new members, no behaviour changed for a caller who does not ask for one.
• The corpus grows from six cases to twelve, six of them robust, and the four types are fitted on one heteroskedastic design rather than four — they differ only in a row weight, so a shared design tells them apart where separate ones would confound the estimator with the data.
• LeastSquares.Solve returns its factorization instead of discarding it, because the leverages HC2 and HC3 need are a row of Q against itself. The IRLS caller discards it, so nothing pays for what only one mode uses.
• A third tight loop now reads QrDecomposition.Q through IReadOnlyList<double>, which is #669's subject. This record does not act on it; it adds one more consumer to the case that issue is making.
• A leverage of exactly one leaves HC2 and HC3 dividing by zero. statsmodels returns infinity rather than raising, and so does this — the row is what is degenerate, and a summary naming it is more use than an exception naming the call.