Greenacre 2023 - Aitchison CoDA 40 Years On
Routing Summary
Captures Greenacre, Grunsky, Bacon-Shone, Erb and Quinn (2023), Aitchison’s Compositional Data Analysis 40 Years On: A Reappraisal (Statistical Science): simplex, closure, coherence, ALR/CLR/ILR, log-contrasts, the Tellus geochemistry example, correspondence analysis, wide data, zeros and quasi-coherence. 5 notes plus overview. Motivating PyMC example: E70.
- Need the one-page summary and source map? → Greenacre 2023 - Aitchison CoDA 40 Years On - Overview
- Need closure, the simplex, coherence, dominance, distributional equivalence? → Greenacre 2023 - Simplex, Closure and Core CoDA Properties
- Need ALR / CLR / ILR / log-contrast definitions and the variation matrix? → Greenacre 2023 - Logratios ALR CLR ILR and Log-Contrasts
- Need the Tellus numbers, ALR reference selection, CA with Box-Cox power? → Greenacre 2023 - Tellus Application, Variable Selection and Correspondence Analysis
- Need wide data, zeros, SLR amalgamation, incoherence measures? → Greenacre 2023 - Wide Data, Zeros and Quasi-Coherence
- Need PyMC logistic-normal / Dirichlet / Dirichlet-multinomial? → Greenacre 2023 - Compositional Outcome Models in PyMC
Concept Map
| Concept | Note | Type | Depends On | Key Result |
|---|---|---|---|---|
| Simplex, closure, scale invariance | Greenacre 2023 - Simplex, Closure and Core CoDA Properties | definition | - | only ratios matter; |
| Subcompositional coherence | Greenacre 2023 - Simplex, Closure and Core CoDA Properties | definition | closure | La-Y correlation 0.479 vs -0.344 |
| LR, ALR, CLR, ILR | Greenacre 2023 - Logratios ALR CLR ILR and Log-Contrasts | definition | coherence | CLR isometric; ALR coherent |
| Variation matrix | Greenacre 2023 - Logratios ALR CLR ILR and Log-Contrasts | theorem | LR | covariances from |
| FINDALR reference choice | Greenacre 2023 - Tellus Application, Variable Selection and Correspondence Analysis | example | ALR | Al: Procrustes 0.990 |
| CA and Box-Cox power | Greenacre 2023 - Tellus Application, Variable Selection and Correspondence Analysis | concept | CLR | optimal power 0.5 |
| Incoherence / anisometry | Greenacre 2023 - Wide Data, Zeros and Quasi-Coherence | definition | subcompositions | stress, Procrustes |
| Summed logratio | Greenacre 2023 - Wide Data, Zeros and Quasi-Coherence | definition | amalgamation | zero-friendly |
| Compositional likelihoods | Greenacre 2023 - Compositional Outcome Models in PyMC | concept | ALR | logistic-normal, Dirichlet, DM |
Notes
- Greenacre 2023 - Aitchison CoDA 40 Years On - Overview — CONTAINS: question, thesis, motivating example E70, source map.
- Greenacre 2023 - Simplex, Closure and Core CoDA Properties — CONTAINS: Def. simplex, scale invariance, coherence, dominance, distributional equivalence; correlation paradox; Tellus zeros.
- Greenacre 2023 - Logratios ALR CLR ILR and Log-Contrasts — CONTAINS: Defs. LR, ALR, CLR, log-contrast, ILR; variation matrix theorem; comparison table; numpy.
- Greenacre 2023 - Tellus Application, Variable Selection and Correspondence Analysis — CONTAINS: data description; weighting; FINDALR; CA/Box-Cox; quasi-coherence; LR selection table.
- Greenacre 2023 - Wide Data, Zeros and Quasi-Coherence — CONTAINS: genomics, incoherence measures, SLR, zero discussion, conclusion.
- Greenacre 2023 - Compositional Outcome Models in PyMC — CONTAINS: logistic-normal with LKJ, Dirichlet, DM sketches; Jacobian for LOO.
Sources
- Greenacre 2023 - Aitchison’s Compositional Data Analysis 40 Years On — Greenacre M, Grunsky E, Bacon-Shone J, Erb I, Quinn T (2023), Statistical Science; arXiv:2201.05197v3 (30 pp.).