@jgdina/kernels-js

Pure TypeScript numerical backend for the binary, single-group jGDINA v1 estimator. It supports per-item GDINA, DINA, and DINO models; estimated saturated or fixed latent-class priors; missing responses; deterministic multiple starts; and full or scores-only posterior output.

Numerical conventions

• Attribute profiles use GDINA's alpha2 order: the zero profile followed by profiles in increasing mastery count and lexicographic subset order.
• GDINA design columns use the same subset order: intercept, main effects, then increasing-order interactions. DINA and DINO use intercept plus their ideal response indicator.
• The E-step uses row-wise log-sum-exp. Missing responses contribute zero to the conditional log-likelihood.
• The closed-form M-step applies smallSampleCorrection to each free success probability and then applies strict-interior probabilityBounds. Exact 0/1 item bounds are rejected during validation so all log likelihoods stay finite. DINA pools all non-master groups; DINO pools all nonzero groups.
• Estimated saturated class probabilities are floored at Number.MIN_VALUE after each M-step and renormalized. Fixed priors, including explicit zeros, are never changed.
• Convergence is the maximum absolute change across item success probabilities and, for a saturated prior, class probabilities.
• Multiple starts follow GDINA's fast workflow: evaluate every candidate under the initial prior, select the largest initial observed likelihood (lowest index on ties), and run EM only from that candidate. Callers may provide all candidates through initialItemProbabilityCandidates; the legacy initialItemProbabilities continues to define only start 0.

Reproducibility

Random candidates use xoshiro128** with SplitMix32 state expansion. Every operation is explicit unsigned 32-bit arithmetic, so the same unsigned seed, start index, input, and package version produce identical candidates in Node and browsers. This is deterministic across JavaScript runtimes but is not intended to reproduce R's random-number stream.

The public backend is available as jsBackend or via createJsBackend(). fitValidated() is the direct entry point for worker adapters, while evaluateValidated() evaluates supplied parameters without fitting for golden likelihood and posterior fixtures.

Numerical parity and convergence are not evidence of substantive model fit. The complete local jGDINA workspace contains the validation and statistical responsibility evidence. This archive includes the preferred TypeScript source and exact package-local rebuild procedure in SOURCE.md, compatibility provenance in UPSTREAM.md, and the GPL-3.0-only license with NOTICE.