Add Cronbach alpha and Feldt (1965) exact-F confidence interval

[seonghobae]

Iteration 10 of the paper-implementation loop. Stacked on #226 (base seonghobae-tenberge-mu).

What

• mlsirm_core::reliability::cronbach_alpha — raw-covariance Cronbach's alpha: p/(p-1) * (1 - tr(C)/sum(C)) (Cronbach, 1951).
• mlsirm_core::reliability::feldt_alpha_ci — Feldt (1965) exact-F CI: pivot (1-alpha)/(1-alpha_hat) ~ F(n-1, (n-1)(p-1)); lower = 1-(1-a)*qF(1-d/2), upper = 1-(1-a)*qF(d/2); plus implied r_bar. In-crate F quantile (Lentz continued-fraction incomplete beta + bisection; endpoints guarded to 0/+inf).
• PyO3 bindings + Python wrappers cronbach_alpha / feldt_alpha_ci / AlphaCiResult.

Sources actually verified

Claim	Source	Status
CI bound mapping, dfs, r_bar	psych 2.6.5 alpha.ci (R/alpha.R)	read line by line
Numeric bounds	scipy.stats.f.ppf	independent fixture replication
Feldt (1965) paper	doi:10.1007/BF02289499	unobtainable — as cited in Revelle (2025)
Cronbach covariance form	psych raw-alpha computation	verified; 1951 paper not re-read

Evidence

• Spec-verify (adversarial, before impl): GO-WITH-FIXES, all applied — pivot wording inverted; negative alpha admitted to CI; zero-variance guard documented as divergence; identity anchor demoted from EXACT to 1e-10; reviewer numeric cross-check (alpha=.8, n=30, p=6) matched R oracle to full precision.
• Impl-review (adversarial, after impl): 2 confirmed defects, both fixed — (1) f_quantile returned a finite bisection cap at prob>=1 where qf/scipy give inf → endpoint guards + regression test; (2) wrapper docstrings were "..." + CONST expressions (__doc__ None) → literal docstring + __doc__ +=.
• Fixtures pinned at 1e-9 from independent NumPy+scipy replication: A (n=30, p=6, unequal variances), B (n=24, p=5), negative-alpha p=2 (CI not clamped). Identity anchor: alpha on z-scored data == guttman_lambdas lambda3 at 1e-10 (crate-vs-crate).
• Mutation kills (4/4): tail swap d/2<->1-d/2 → 3 fixtures FAIL; f_cdf z-orientation flip → 3 FAIL; df2=n-1 → A/B FAIL (p=2 passes by identity, documented); tr/sum inversion → 3 FAIL. Disclosed equivalent mutant: dropping the inc_beta symmetry branch survives (convergence acceleration only at these dfs; scipy literals anchor everything coarser).
• MC (#[ignore], 500 reps): empirical 95% CI coverage of true tau-equivalent reliability within [0.925, 0.975] — passed.
• Full crate suite: 492 passed. Python: 6 reliability tests passed.

Divergences from psych (documented in module docs)

Raw-data input only (no reverse-keying/check.keys); zero-variance items rejected; confidence level instead of p.val; hard errors instead of NA; bounds not clamped (negative alpha allowed, matching psych).

[Copilot]

Pull request overview

Adds coefficient alpha reliability support (Cronbach’s alpha) and Feldt (1965) exact-F confidence intervals to the mlsirm_core::reliability Rust crate, exposes them through the PyO3 core module, and provides Python-facing wrappers + tests to pin the numeric contract against independent NumPy/SciPy fixtures.

Changes:

• Implement cronbach_alpha (raw-covariance form) and feldt_alpha_ci (Feldt exact-F CI) in crates/mlsirm-core.
• Add PyO3 bindings and Python wrapper API (cronbach_alpha, feldt_alpha_ci, AlphaCiResult) and export them from fast_mlsirm.
• Add Rust + Python fixtures/rejection tests and document the feature in CHANGELOG.md.

Reviewed changes

Copilot reviewed 8 out of 8 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
tests/unit/reliability_tests.rs	Adds Rust-side fixture tests, regression for extreme CI endpoint behavior, and rejection coverage.
tests/test_paper_features.py	Adds Python-level fixture test and boundary rejection tests for the new reliability APIs.
python/fast_mlsirm/reliability.py	Introduces Python wrappers + AlphaCiResult dataclass and appends reference text to docstrings.
python/fast_mlsirm/init.py	Re-exports the new reliability functions/types at the package top-level.
crates/mlsirm-core/src/reliability.rs	Implements Cronbach alpha, Feldt CI, and internal F CDF/quantile utilities (incomplete beta + bisection).
crates/mlsirm-core/src/fitstats.rs	Makes ln_gamma pub(crate) for reuse in the new incomplete-beta implementation.
crates/fast-mlsirm-py/src/lib.rs	Adds PyO3 functions cronbach_alpha / feldt_alpha_ci and wires them into the module init.
CHANGELOG.md	Documents the newly added reliability metrics and key behavioral divergences from psych.

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[seonghobae]

@copilot Fix the code for all comments in this review thread.

When a review comment includes a suggested change, apply the suggestion exactly.

Do not make changes beyond what is described in the linked review thread.

[Copilot]

@copilot Fix the code for all comments in this review thread.

When a review comment includes a suggested ch...

Implemented the requested review-thread fix in commit 66048a2: f_quantile now bisects directly in z-space (inc_beta(...) in-loop) and only converts z -> x once at return.

[Copilot]

Pull request overview

Copilot reviewed 8 out of 8 changed files in this pull request and generated 1 comment.

Comments suppressed due to low confidence (1)

crates/mlsirm-core/src/reliability.rs:632

• df2 is computed as ((n - 1) * (p - 1)) as f64; the (n-1)*(p-1) multiplication can overflow usize in release builds before the cast. Please use checked_mul (as elsewhere in the crate) so extreme inputs fail fast with a clear error instead of wrapping to an incorrect df2.

    let df1 = (n - 1) as f64;
    let df2 = ((n - 1) * (p - 1)) as f64;
    let delta = 1.0 - level;