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).

Author and citation

José Mauricio Gómez Julián (ORCID 0009-0000-2412-3150).

License

GPL (>= 3).