General Dynamic Parameter Models via Reference Anchoring

Implements a unified predictive framework in which individual parameters are decomposed as theta_i equal to theta_ref plus Delta(x_i, theta_ref), with theta_ref a population reference and Delta an explicit deviation function. The decomposition follows the Additive-Multiplicative-Modulated canonical form and is estimated through three complementary paths: hierarchical Bayesian inference via 'Stan', varying-coefficient models via penalized splines, and amortized inference via hypernetworks in 'torch'. The package provides identifiability diagnostics, validity tests for the population reference, and benchmarks against canonical zero-inflated count datasets and avian abundance data from the eBird Status and Trends project. The framework and its estimation paths are described in Gomez Julian (2026) .

gdpar

General Dynamic Parameter Models via Reference Anchoring

gdpar is an R package implementing a unified predictive framework in which each unit's parameter is decomposed around a population reference:

theta_i = theta_ref + Delta(x_i, theta_ref)

with Delta following the canonical Additive--Multiplicative--Modulated (AMM) form a(x) + b(x) * theta + W(theta) x. Here theta_ref is a population reference estimated from the data and Delta is an explicit, identifiable deviation function. The package provides identifiability diagnostics, validity tests for the population reference, distributional (multi-slot) regression, empirical-Bayes and full-Bayes estimation, a causal-inference bridge, a geometric-robustness sampling engine, and dependence-robust inference.

Installation

Path 1 (the operational estimation path) uses Stan via cmdstanr. Install the back-end once per machine:

install.packages(
  "cmdstanr",
  repos = c("https://stan-dev.r-universe.dev", getOption("repos"))
)
cmdstanr::install_cmdstan()

Then install gdpar from GitHub:

# install.packages("remotes")
remotes::install_github("IsadoreNabi/gdpar")

Quick start

library(gdpar)

set.seed(20260526)
n <- 200L
x <- rnorm(n)
y <- 1.5 + 0.8 * x + rnorm(n, sd = 0.3)   # theta_ref = 1.5, a = 0.8
dat <- data.frame(y = y, x = x)

fit <- gdpar(
  formula = y ~ x,
  data    = dat,
  family  = gdpar_family("gaussian"),
  path    = "bayes"
)

summary(fit)
coef(fit)
predict(fit, newdata = data.frame(x = seq(-2, 2, length.out = 11)), level = 0.9)

See the vop00_quickstart vignette for a line-by-line walk-through.

The three estimation paths

gdpar specifies three estimation paths for the AMM decomposition:

Path 1 --- hierarchical Bayesian (path = "bayes"): the operational path, via Stan / cmdstanr.
Path 2 --- varying-coefficient (path = "vcm"): reference-grade asymptotic theory; implementation queued for a future version.
Path 3 --- hypernetwork (path = "hyper"): reference-grade; implementation queued for a future version.

Calls to the not-yet-implemented paths abort with gdpar_unsupported_feature_error.

Capabilities

Distributional regression (K >= 1 slots): Gaussian, Student-t, Gamma, Beta, Tweedie, Poisson, negative-binomial, zero-inflated and hurdle families, plus heterogeneous per-slot families; B-spline W bases; arbitrary covariate dimension p; grouped references.
Empirical-Bayes and full-Bayes estimation, with EB-vs-FB comparators (marginal total variation and joint KSD).
Causal positioning: a T-learner CATE/ITE bridge on the AMM side and an external meta-learner comparator (grf, EconML via reticulate).
Geometric-robustness sampling engine: an opt-in, default-bit-identical Riemannian / sub-Riemannian / Finsler metric stack with a certifying orchestrator, for stiff and near-deterministic posteriors.
Dependence-robust inference: diagnostics (lag-1 / Durbin-Watson; Moran's I) and block-bootstrap robust standard errors for temporally and spatially dependent data, with a data-driven (Politis-White) block length, on both the empirical-Bayes and full-Bayes paths. gdpar does not model the dependence; only its inference is made robust to it.
Residual diagnostics (Dunn-Smyth quantile residuals; G1/G2/G3) and a golden-regression test suite.

Validation

gdpar was re-validated against mgcv, brms, INLA and rstanarm:

A synthetic recovery benchmark with known ground truth (3200 cells): gdpar leads on the distributional structure it models (heavy-tail quantiles, zero-inflated count means, heteroscedastic scale), is robust where it makes no modelling claim (e.g. autocorrelation it does not model), and is the most computationally expensive method in the roster.
An organic eBird benchmark (80 cells): gdpar is statistically indistinguishable from mgcv on the held-out predictive density.

Reports: inst/benchmarks/results/block9_synthetic_recovery.md and inst/benchmarks/results/block9_revalidation.md.

Documentation

The package ships an extensive set of vignettes: an operational track (vop00--vop09, from quickstart to dependence-robust inference) and a theoretical track (v00--v09, covering the canonical form, identifiability, the gnoseological validity of the population reference, the per-path asymptotic theory, the empirical-Bayes versus full-Bayes comparison, and the causal-inference positioning).