Index: Stasinopoulos 2007 - GAMLSS in R

Stasinopoulos 2007 - GAMLSS in R

Routing Summary

This folder captures Stasinopoulos and Rigby (2007), Generalized Additive Models for Location, Scale and Shape (GAMLSS) in R (J. Stat. Softw. 23(7)): the model class, distribution and smoother catalogue, RS/CG algorithms, GAIC/VGD selection, four worked examples and the LMS/BCT growth-centile methodology. 7 notes. Motivating PyMC example: E41 (growth centile charts).

• Need the paper in one page and the section-to-note map? → Stasinopoulos 2007 - GAMLSS in R - Overview
• Need the formal GAMLSS definition, links, penalized likelihood, censoring, mixtures? → Stasinopoulos 2007 - GAMLSS Model Framework
• Need the list of distributions (BCCG, BCT, SHASH, NBI, ZIP…) or the P-spline definition? → Stasinopoulos 2007 - Distributions and Additive Terms
• Need RS vs CG, GAIC, validation deviance, stepwise selection? → Stasinopoulos 2007 - Fitting Algorithms and Model Selection
• Need the lice / CD4 / insurance-claims numbers? → Stasinopoulos 2007 - Lice, CD4 and Claims Examples
• Need LMS, BCT centile formula, worm plots, Q statistics, head-circumference tables? → Stasinopoulos 2007 - Centile Curves, LMS and Residual Diagnostics
• Need a PyMC model with P-splines for each distribution parameter? → Stasinopoulos 2007 - Bayesian P-Splines and Distributional Regression in PyMC

Concept Map

Concept	Note	Type	Depends On	Key Result
GAMLSS model	Stasinopoulos 2007 - GAMLSS Model Framework	definition	Generalized Linear Models	$g_k({\theta }_k)=X_k{\beta }_k+{\sum }_j{Z}_{jk}{\gamma }_{jk}$ for $\mu ,\sigma ,\nu ,\tau$
Penalized likelihood	Stasinopoulos 2007 - GAMLSS Model Framework	definition	GAMLSS model	${\ell }_p=\ell -\frac{1}{2}\sum \lambda {\gamma }^{\top }G\gamma$
Family catalogue	Stasinopoulos 2007 - Distributions and Additive Terms	concept	Framework	BCCG = LMS; BCT adds kurtosis
P-spline term	Stasinopoulos 2007 - Distributions and Additive Terms	definition	B-splines	$D\gamma \sim N(0,{\lambda }^{-1}I)$
RS / CG algorithms	Stasinopoulos 2007 - Fitting Algorithms and Model Selection	algorithm	Penalized likelihood	RS ignores cross derivatives
GAIC, VGD	Stasinopoulos 2007 - Fitting Algorithms and Model Selection	definition	likelihood	penalty $\#$ is a tuning choice
Lice, CD4, claims	Stasinopoulos 2007 - Lice, CD4 and Claims Examples	example	Algorithms	Sichel AIC 4646.2; smooth $\sigma$ simplifies $\mu$
LMS / BCT centile	Stasinopoulos 2007 - Centile Curves, LMS and Residual Diagnostics	theorem	Family catalogue	$y_{\alpha }=\mu \{1+\nu \sigma t_{\tau ,\alpha }{\}}^{1/\nu }$
Worm plot, Q statistics	Stasinopoulos 2007 - Centile Curves, LMS and Residual Diagnostics	definition	Quantile residuals	BCT 0 violations vs LMS 16
Bayesian P-splines	Stasinopoulos 2007 - Bayesian P-Splines and Distributional Regression in PyMC	concept	Penalized likelihood	RW2 prior per parameter

Notes

• Stasinopoulos 2007 - GAMLSS in R - Overview — CONTAINS: question, contribution, key result, motivating PyMC examples, source map.
• Stasinopoulos 2007 - GAMLSS Model Framework — CONTAINS: Def. GAMLSS (Eq. 1), sub-models (Eqs. 2-5), Def. penalized likelihood (Eq. 6), censoring, mixtures, CD4 example.
• Stasinopoulos 2007 - Distributions and Additive Terms — CONTAINS: Tables 1-3 (selected rows with links), parameterisations, Def. P-spline, backfitting conventions.
• Stasinopoulos 2007 - Fitting Algorithms and Model Selection — CONTAINS: Def. CG, RS, GAIC, VGD; package map; stepwise selection; caveats; penalty-choice example.
• Stasinopoulos 2007 - Lice, CD4 and Claims Examples — CONTAINS: AIC table for count families; CD4 mean/variance smoothing comparison; claims term selection.
• Stasinopoulos 2007 - Centile Curves, LMS and Residual Diagnostics — CONTAINS: Def. LMS/BCT, Thm. centile formula, Eq. 10 model, hyperparameter table, worm plot, Q statistics table, Python.
• Stasinopoulos 2007 - Bayesian P-Splines and Distributional Regression in PyMC — CONTAINS: Bayesian reading of Eq. 6, RW2 P-spline definition, untested PyMC sketch for E41.

Sources

• Stasinopoulos 2007 - GAMLSS in R — Stasinopoulos DM, Rigby RA (2007), J. Stat. Softw. 23(7), 46 pp. Open access.

See Also

• Generalized Linear Models, Quantile Regression, Hilbert Space Gaussian Processes, Hierarchical Models
• Ji 2024 - Valid Standard Errors for Bayesian Quantile Regression - Overview — quantile alternative to modelling the full distribution.