
doi: 10.5281/zenodo.20141023 , 10.5281/zenodo.20129884 , 10.5281/zenodo.20149006 , 10.5281/zenodo.20136652 , 10.5281/zenodo.20149276 , 10.5281/zenodo.20149608 , 10.5281/zenodo.20130293 , 10.5281/zenodo.20115464 , 10.5281/zenodo.20129615 , 10.5281/zenodo.20143116 , 10.5281/zenodo.20123935 , 10.5281/zenodo.20136744 , 10.5281/zenodo.20138568
doi: 10.5281/zenodo.20141023 , 10.5281/zenodo.20129884 , 10.5281/zenodo.20149006 , 10.5281/zenodo.20136652 , 10.5281/zenodo.20149276 , 10.5281/zenodo.20149608 , 10.5281/zenodo.20130293 , 10.5281/zenodo.20115464 , 10.5281/zenodo.20129615 , 10.5281/zenodo.20143116 , 10.5281/zenodo.20123935 , 10.5281/zenodo.20136744 , 10.5281/zenodo.20138568
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: 0.8.1 (May 2026) Fixed - Mixed variance components now match EduG exactly. v0.8.0 computed Mixed VCs by solving `M_mixed × σ² = MS` where `M_mixed` was built from `M_random` by zeroing entries whose `β\α` set contained any fully-fixed facet. For many components (notably D in example 16) every off-diagonal collapsed and the equation returned `σ²_random` instead of the correct Mixed value. v0.8.1 replaces that matrix solve with the EduG-equivalent additive correction: ``` σ²_mixed(α) = σ²_random(α) + Σ_β σ²_random(β) × M_random[α,β] / M_random[α,α] ``` where β ranges over components strictly containing α, with `β\α` consisting entirely of **fully-fixed** facets (`N = n`). Hand-verified against EduG's example 16 on D, M, C:DS, P:C:DS, K:O, and I:K:O — all six recover EduG's reported Mixed values to displayed precision. σ²(X̄..) computed from the corrected Mixed values lands on 0.015, matching EduG. - G-Study contributions and final Coef_G now match EduG. With the corrected Mixed VCs flowing through `compute_g_coefficients`, the dependent quantities — `σ²(τ)`, `σ²(δ)`, `σ²(Δ)`, `Coef_G_rel`, `Coef_G_abs`, `σ²(X̄..)`, and the per-component `Differ./Rel/Abs` cells — all align with EduG to displayed precision. The visible discrepancies you saw in v0.8.0 (D's absolute err. var. 0.0111 vs 0.005; σ²(X̄..) 0.0213 vs 0.015; Coef_G_abs 0.5752 vs 0.65) are all eliminated. Cosmetic - Intro paragraph no longer lists per-version highlights.- Author and personal website (`carloscollares.com`) added to intro.- Footer credits GNU General Public License v3.0 alongside the documentation link. Inherited from v0.8.0 - `(N − n)/(N − 1)` correcting coefficient (per EduG).- Coefficient applied only to MAIN (effect) fixed facets in each component, never to transitive nesting parents.- All `D × I` components route to relative error.- Universe-size column accepts `INF` / `Inf` / `infinite`.- Restricted Φ(λ) fallback. Known limitation - The Universe radio still uses "random / fixed" rather than inferring sampling status from N vs n the way EduG does. A future version will drop the radio and let N alone determine fixed / finite random / infinite random. Earlier versions See v0.8.0, v0.7.0, v0.6.0, v0.5.0, v0.4.0, v0.3.0, v0.2.x, v0.1.xentries in those folders' CHANGELOGs.
psychometrics, reliability, Shiny, R, variance components, generalizability theory, lme4
psychometrics, reliability, Shiny, R, variance components, generalizability theory, lme4
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