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gdpar — Complete Technical Wiki

General Dynamic Parameter Models via Reference Anchoring

Package version: 0.1.0 · License: GPL (≥ 3) · Author: José Mauricio Gómez Julián (ORCID 0009-0000-2412-3150) · Repository: https://github.com/IsadoreNabi/gdpar

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0. About this document

This is an exhaustive, self-contained technical reference for the gdpar R package. It documents, in three layers and at maximal depth:

1. Conceptualization — the cognitive and statistical idea behind the framework, its desiderata, and the family of problems it addresses (Part I).
2. Mathematics — the canonical decomposition, identifiability theory, the three estimation paths and their asymptotics, the distributional-family algebra, the spline bases, the causal-inference bridge, the geometry-adaptive sampling engine, and the dependence-robust inference machinery (Part II).
3. Computation — how the mathematics is realized in code: the Stan code generator and every Stan template (line by line), the fitting engines, the family code generation, the geometry engine, and every one of the package's 469 functions organized by module (Parts III–V).

Parts VI and the appendices cover the bundled data, the benchmark harness, the test suite, the symbol glossary, and the bibliographic anchors.

0.1 How this document is organized

Part	Content
I	Conceptual framework: motivation, the anchoring equation, the AMM form, the three paths, EB vs FB, distributional regression, the causal bridge, geometric robustness, dependence-robust inference
II	Mathematical foundations: AMM algebra, identifiability theorems (C1–C7), parametrizations (CP/NCP, linear reparametrization), asymptotics of Paths 1/2/3, Empirical-Bayes theory (Theorems 7A–7D) and its multivariate extension, families and links, B-spline W bases, grouped references, causal identification, geometric metrics, dependence diagnostics and block bootstrap
III	Computational architecture: the Stan code generator, the fitting engines (gdpar, .gdpar_multi, .gdpar_K), the Empirical-Bayes engine, the family/codegen layer, the geometry engine/orchestrator
IV	Exhaustive function reference: all 44 R source files, all 469 functions, grouped by module, each with purpose, signature, arguments, mathematics, and return value
V	Stan templates: all 13 .stan files, block by block
VI	Data, benchmarks, tests, appendices, references

0.2 Notation and conventions

Mathematics is written in GitHub-flavored LaTeX: inline as $ … $ and display as $$ … $$. Code identifiers, file names, and Stan symbols are in monospace. Internal (non-exported) R functions are named with a leading dot, e.g. .gdpar_multi; exported functions have no leading dot, e.g. gdpar.

The single most important object in the entire package is the reference-anchoring decomposition

$$\theta_i ;=; \theta_{\text{ref}} ;+; \Delta(x_i,; \theta_{\text{ref}}),$$

read throughout as: the parameter of individual $i$ equals a population reference plus a deviation that is itself a function of the individual's covariates and of the reference. Every layer of the package — conceptual, mathematical, computational — is an elaboration of this one equation.

0.3 Global symbol table

Symbol	Meaning
$\theta_i$	parameter (vector) for individual / observation $i$
$\theta_{\text{ref}}$	population reference parameter, $\theta_{\text{ref}} = \mathbb{E}[\theta]$
$\Delta(x_i,\theta_{\text{ref}})$	individual deviation function
$x_i$	observable covariates of individual $i$
$a(x)$	additive component of the AMM deviation
$b(x)$	multiplicative (Hadamard) component of the AMM deviation
$W(\theta_{\text{ref}})$	reference-modulated mixing matrix of the AMM deviation
$\odot$	Hadamard (elementwise) product
$K$	number of distributional parameter slots (e.g. $\mu,\sigma,\nu,\pi,\dots$)
$p$	dimension of the parameter at a slot (number of coordinates of $\theta$)
$\mathcal{D}(\theta_i)$	observation distribution given $\theta_i$
$\xi$	EB hyperparameter / canonical-piece reduced parameter vector
$g(\cdot),\ g^{-1}(\cdot)$	link and inverse-link (response) function of a slot
$G(\theta)$	Riemannian metric tensor used by the geometry engine
$\phi$	temporal persistence (AR) parameter; also hypernetwork weights in Path 3
$\pi_i$	structural-zero probability for individual $i$ (zero-inflation / hurdle)

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Contents

This wiki is split across the following pages (GitHub renders at most ~512 KB per page, so the single-file version is paginated here). Use the sidebar for quick navigation.

• Part I — Conceptual Framework
• Part II — Mathematical Foundations
• Part III — Computational Architecture
• Part IV — Exhaustive Function Reference (1/7) — _{R/adapter_econml.R … R/compare_eb_fb.R}
• Part IV — Exhaustive Function Reference (2/7) — _{R/compare_meta_learners_methods.R … Functions in R/eb.R (section 3 of 8)}
• Part IV — Exhaustive Function Reference (3/7) — _{.gdpar_eb_make_random_init(stan_data, seed_offset = 1L, base_seed = NULL) … R/gdpar-package.R}
• Part IV — Exhaustive Function Reference (4/7) — _{R/gdpar.R … Geometry Diagnostic — Culprit Localisation, Difficulty Curve, and Rule-Based Classifier}
• Part IV — Exhaustive Function Reference (5/7) — _{R/geometry_engine.R … R/geometry_suite.R}
• Part IV — Exhaustive Function Reference (6/7) — _{R/golden_compare.R … R/preflight.R}
• Part IV — Exhaustive Function Reference (7/7) — _{Pre-flight Diagnostics (Section 2) … .gdpar_validate_bspline_boundary_range(W, projected_range)}
• Part V — Stan Templates (1/3) — _{inst/stan/_canonical_pieces/amm_canonical_distrib_K.stan … inst/stan/_canonical_pieces/amm_canonical_eb_conditional.stan}
• Part V — Stan Templates (2/3) — _{inst/stan/_canonical_pieces/amm_canonical_eb_marginal_K.stan … inst/stan/_canonical_pieces/amm_canonical_pmulti_KxP.stan}
• Part V — Stan Templates (3/3) — _{inst/stan/_canonical_pieces/amm_canonical_pmulti.stan … inst/stan/amm_eb_marginal_KxP.stan}
• Part VI — Data, Benchmarks, Tests & References