DPMirt: Bayesian Semiparametric IRT with DPM Priors • DPMirt

Bayesian Semiparametric Item Response Theory Models Using Dirichlet Process Mixture Priors

DPMirt fits Bayesian IRT models with flexible, nonparametric ability distributions via NIMBLE. It supports Rasch, 2PL, and 3PL models under both a standard Normal prior and a Dirichlet Process Mixture (DPM) prior, and provides three posterior summary methods — PM, CB, and GR — designed for different inferential goals.

Key Features

Feature	Description
Three IRT models	Rasch, 2PL, and 3PL
Two latent priors	Parametric (Normal) and semiparametric (DPM)
Triple-goal estimation	Posterior Mean (PM), Constrained Bayes (CB; Ghosh 1992), Triple-Goal (GR; Shen & Louis 1998)
Compile-once workflow	Compile the NIMBLE model once, then draw additional sequential samples while the compiled object is live
Principled prior elicitation	Optional concentration-parameter calibration via DPprior, with a Gamma(1, 3) fallback
Reliability-targeted simulation	Generate Rasch/2PL test data at a specified marginal reliability via IRTsimrel; 3PL uses DPMirt’s fallback simulator and does not target reliability
Rich diagnostics	ESS, optional chain-aware R-hat, WAIC provenance, posterior predictive checks, trace and density plots

Installation

Install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("joonho112/DPMirt")

DPMirt requires R ≥ 4.1 and nimble ≥ 1.0.0. NIMBLE needs a working C++ compiler; see the NIMBLE installation guide if you do not already have one set up.

Optional packages

DPprior and IRTsimrel are optional GitHub packages. DPMirt installs and runs without them: without DPprior, alpha-prior elicitation falls back to Gamma(1, 3); without IRTsimrel, simulation uses DPMirt’s internal fallback generator without reliability targeting.

# Principled alpha prior elicitation
remotes::install_github("joonho112/DPprior")

# Reliability-targeted simulation
remotes::install_github("joonho112/IRTsimrel")

# Enhanced plotting
install.packages(c("ggplot2", "bayesplot"))

Quick Start

library(DPMirt)

# 1. Simulate a bimodal population (200 persons, 20 items)
sim <- dpmirt_simulate(
  n_persons = 200, n_items = 20,
  model = "rasch", latent_shape = "bimodal",
  target_rho = 0.8, seed = 42
)

# 2. Fit a Rasch model with a DPM prior
fit <- dpmirt(
  sim$response,
  model = "rasch", prior = "dpm",
  niter = 10000, nburnin = 3000, seed = 123
)

# 3. Inspect results
summary(fit)
plot(fit, type = "density")

# 4. Compute triple-goal estimates (PM, CB, GR)
est <- dpmirt_estimates(fit)
plot(est, type = "shrinkage")

# 5. Compare Normal vs DPM priors
fit_normal <- dpmirt(
  sim$response,
  model = "rasch", prior = "normal",
  niter = 10000, nburnin = 3000, seed = 123
)
dpmirt_compare(fit_normal, fit)

Step-by-Step Pipeline

For finer control, use the modular pipeline instead of the all-in-one dpmirt() wrapper:

# Specify
spec <- dpmirt_spec(sim$response, model = "2pl", prior = "dpm")

# Compile (slow — only done once)
compiled <- dpmirt_compile(spec)

# Sample
samples <- dpmirt_sample(compiled, niter = 10000, nburnin = 3000)

# Rescale (post-hoc identification)
fit <- dpmirt_rescale(samples)

# Continue sampling without recompiling
resumed <- dpmirt_resume(fit, niter_more = 5000)
fit2 <- dpmirt_rescale(resumed)

Compiled NIMBLE objects contain external pointers and cannot be restored from RDS. dpmirt_resume() therefore requires the original live compiled object stored in the dpmirt_samples or dpmirt_fit object.

Posterior Summary Methods

DPMirt implements three complementary estimators for person abilities:

PM (Posterior Mean) — minimises individual-level mean squared error but can severely compress the ability distribution, especially when test reliability is low.
CB (Constrained Bayes) — inflates the PM distribution so that the first two moments of the estimates match the posterior predictive distribution (Ghosh, 1992).
GR (Triple-Goal) — places each estimate at the midpoint of its corresponding quantile interval of the estimated empirical distribution function, optimising simultaneous estimation, ranking, and distributional recovery (Shen & Louis, 1998).

est <- dpmirt_estimates(fit, methods = c("pm", "cb", "gr"))

# Compare estimator distributions against truth
dpmirt_loss(est, true_theta = sim$theta, metrics = c("msel", "ks"))

Diagnostics and Draws

diag <- dpmirt_diagnostics(fit)
diag$chain_info
diag$waic_aggregation

theta_draws <- dpmirt_draws(fit, vars = "theta", format = "long")
head(theta_draws)

dpmirt_fit objects store chain/run provenance through schema_version, chain_info, draw_index, and run_history. R-hat is reported when at least two labeled chains have retained draws; single-chain fits and the compact vignette fixtures return NULL R-hat and should be judged with ESS, trace plots, and substantive diagnostics.

dpmirt_draws() currently extracts the rescaled posterior draws used by summary and plotting methods. Raw, unrescaled draw extraction and disk-backed draw storage (save_draws = FALSE or save_path) are reserved for a future release.

Current Scope Notes

sampler_config supports an advanced function hook with signature function(conf, model, spec). List-based sampler schemas are reserved.
item_priors is reserved; use NULL or list() for DPMirt’s fixed item priors.
3PL models include item guessing parameters (delta). Some identification combinations are intentionally unavailable, including constrained_item for 3PL and constrained_ability for DPM models.
3PL simulation uses DPMirt’s fallback generator with Beta-distributed guessing parameters and does not use target_rho.
dpmirt_dp_density() can be computationally expensive because it rebuilds the NIMBLE DP-measure workflow and loads retained DP draws through public modelValues accessors; compact vignette fixtures store thinned posterior draws and plot-ready DP-density summaries.

Vignettes

DPMirt ships with eight source vignettes:

Vignette	Topic
`vignette("introduction")`	Package overview and reading guide
`vignette("quick-start")`	First model fit in 5 minutes
`vignette("models-and-workflow")`	All models, priors, and the step-by-step pipeline
`vignette("posterior-summaries")`	PM vs CB vs GR with shrinkage diagnostics
`vignette("prior-elicitation")`	Principled DPM hyperprior selection
`vignette("simulation-study")`	Replicating the evaluation framework from Lee & Wind
`vignette("theory-irt-dpm")`	Mathematical foundations
`vignette("nimble-internals")`	Custom samplers and advanced NIMBLE configuration

References

Lee, J. & Wind, S. Targeting toward inferential goals in Bayesian Rasch models for estimating person-specific latent traits. OSF Preprint. https://doi.org/10.31219/osf.io/qrw4n
Paganin, S., Paciorek, C. J., Wehrhahn, C., Rodriguez, A., Rabe-Hesketh, S., & de Valpine, P. (2023). Computational strategies and estimation performance with Bayesian semiparametric item response theory models. Journal of Educational and Behavioral Statistics, 48(2), 147–188.
Ghosh, M. (1992). Constrained Bayes estimation with applications. Journal of the American Statistical Association, 87(418), 533–540.
Shen, W., & Louis, T. A. (1998). Triple-goal estimates in two-stage hierarchical models. Journal of the Royal Statistical Society: Series B, 60(2), 455–471.

DPMirt