gtheory-app: a Shiny app for generalizability theory analyses

Generalizability theory (G-theory) extends classical reliability theory by partitioning measurement error into multiple, separable sources, thereby supporting the design of more dependable measurement procedures. Existing software for G-theory — most notably the GENOVA Suite and EduG — is widely used but predates contemporary R-based reproducible workflows and lacks interactive exploration of decision (D) study trade-offs. We introduce gtheory-app, a free and open-source Shiny application that brings G-theory analysis into the browser. The application accepts long-format data uploads with auto-detected delimiters or score-only files paired with a user-specified design, supports balanced and unbalanced data, and handles fully crossed, nested, and mixed (random + fixed) designs with an arbitrary number of facets. Variance components are estimated via lme4 (REML) with a classical ANOVA cross-check available for balanced data. The application then reports universe-score variance, relative and absolute error variances, the generalizability coefficient (Eρ²), the index of dependability (Φ), Φ(λ) for criterion-referenced decisions, a G-facets sensitivity table, and an interactive 3D surface graph over any pair of user-selected facets with the resulting D-study. Every numerical output is paired with a context-sensitive, plain-language interpretation that names the user's actual facets, places reliability values in conventional bands, and identifies the largest single error term as a target for redesign. We illustrate the application on three classes of designs: a fully crossed three-facet design, a nested-items design, and a multi-facet chain-nested design. We argue that gtheory-app fills a clear gap in the open-source psychometric software ecosystem and lowers the barrier to G-theory for applied researchers, educators, and assessment professionals.

CHANGELOG:

v0.2.1 (May 2026)

Changed

- Documentation DOI in the in-app introductory panel updated to
  the concept DOI <https://doi.org/10.5281/zenodo.20086375>, which
  resolves to the latest version of the Zenodo deposit rather than to
  a specific frozen version.
- Long-format example in the data-upload help block now uses
  plural column names (`persons, items, raters, scores`) and shows
  additional rows so the long-format pattern is clearer to first-time
  users.

Added

- App version visible in the UI. The title bar shows a `v0.2.1`
  chip next to the title; a small footer at the bottom of every page
  repeats the version and links to the documentation DOI.

v0.2.0 (May 2026)

Added

- Always-visible introductory panel above section 1 that explains
  Generalizability Theory for non-initiated users, ending with the
  full documentation DOI: <https://doi.org/10.5281/zenodo.20115464>.
- New file `AUDIT.md` documenting the full code audit performed for
  this release: REML/lme4 correctness, G-coefficient assembly,
  plain-language interpretations, and comparability with EduG and the
  GENOVA Suite.
- `tests/test_vc.R` now asserts REML/ANOVA agreement to 1e-4 on
  balanced data — a regression test for the v0.1.x ANOVA bug.

Fixed

- ANOVA-path EMS matrix. The expected-mean-square coefficient rule
  in `estimate_vc_anova()` was inverted in v0.1.x — it computed
  "facets in B but not in A" rather than the correct "facets not in
  B" (Henderson Method 1 / Cornfield–Tukey rule). The default REML
  path used by the UI was never affected, but ANOVA-based variance
  estimates were systematically wrong for any design with unequal
  facet sizes. See `AUDIT.md` §4 for the full derivation and fix.

Removed

- "Score column only" upload mode. The expand-grid-based row order
  was fragile and produced incorrect facet assignments when the user's
  row order did not match R's `expand.grid` convention. The long-format
  upload (with automatic separator and score-column detection) is the
  single supported path.

v0.1.x (prior development)

Initial public preview. Three-facet crossed and nested designs,
four-facet crossed designs, chain-nested designs, mixed-model designs
with fixed facets, interactive 3D D-study surface, plain-language
interpretations on every output, automatic delimiter and score-column
detection.