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DPMirt: Bayesian Semiparametric IRT Models Using DPM Priors

DPMirt-package.Rd

Fits Bayesian semiparametric Item Response Theory (IRT) models using Dirichlet Process Mixture (DPM) priors via NIMBLE. Supports Rasch, 2PL, and 3PL models with parametric (Normal) or semiparametric (Dirichlet Process Mixture) priors on the latent ability distribution, and provides triple-goal posterior summaries (PM, CB, GR) for simultaneous estimation and ranking of person abilities.

Details

The DPMirt package supports:

  • Three IRT models: Rasch, 2PL, and 3PL

  • Two latent trait priors: parametric (Normal) and semiparametric (DPM)

  • Three identification strategies where compatible: constrained_item, constrained_ability, unconstrained

  • Three posterior summary methods: PM, CB (Ghosh 1992), GR (Shen & Louis 1998)

  • Compile-once, sample-many MCMC workflow

  • Optional alpha hyperprior elicitation via DPprior, with Gamma(1, 3) fallback

  • Rasch/2PL reliability-targeted simulation when IRTsimrel is installed; fallback simulation otherwise, including 3PL without reliability targeting

The backbone NIMBLE model code is adapted from Paganin et al. (2023). MCMC compilation, sampling, and model management are handled by NIMBLE's C++ infrastructure.

Typical Workflow

A standard DPMirt analysis proceeds in five steps:

  1. Simulate or load data: Use dpmirt_simulate or provide a binary response matrix.

  2. Fit the model: Call dpmirt for one-step fitting, or use the step-by-step pipeline dpmirt_spec \(\rightarrow\) dpmirt_compile \(\rightarrow\) dpmirt_sample \(\rightarrow\) dpmirt_rescale.

  3. Summarize: Compute triple-goal estimates with dpmirt_estimates and extract posterior draws with dpmirt_draws.

  4. Diagnose: Evaluate convergence and model comparison via dpmirt_diagnostics and dpmirt_compare.

  5. Visualize: Use plot(fit) and the dpmirt_plot_* family for publication-quality figures.

Model Fitting

dpmirt

One-step model fitting (specification + compilation + sampling + rescaling)

dpmirt_spec

Create model specification

dpmirt_compile

Compile NIMBLE model and MCMC

dpmirt_sample

Run MCMC sampling

dpmirt_resume

Continue sampling from a fitted model

Estimation and Rescaling

dpmirt_rescale

Post-hoc identification rescaling (Rasch, IRT, SI)

dpmirt_estimates

Compute PM, CB, and GR triple-goal posterior summaries

dpmirt_draws

Extract posterior draws as matrix or long-format data frame

Diagnostics and Model Comparison

dpmirt_diagnostics

MCMC convergence diagnostics (ESS, optional chain-aware R-hat, trace summaries, and WAIC provenance)

dpmirt_compare

WAIC-based model comparison with aggregation provenance

Simulation

dpmirt_simulate

Simulate IRT data with flexible latent distributions and reliability targeting

dpmirt_loss

Evaluate estimator loss (MSEL, MSELR, KS, custom)

Prior Specification

dpmirt_alpha_prior

Principled DPM concentration parameter elicitation

DP Density Estimation

dpmirt_dp_density

Posterior density estimation from the Dirichlet Process mixture, most directly interpretable for Rasch/location-shift settings

Visualization

S3 plot methods:

plot(fit)

Trace plots, density plots, and caterpillar plots for fitted models

plot(estimates)

Caterpillar plots of PM/CB/GR estimates and PM-vs-CB shrinkage plots

plot(sim)

True-parameter histograms and response-matrix heatmaps for simulated data

Standalone ggplot2 functions (require ggplot2): dpmirt_plot_trace, dpmirt_plot_density, dpmirt_plot_caterpillar, dpmirt_plot_items, dpmirt_plot_icc, dpmirt_plot_info, dpmirt_plot_dp_density, dpmirt_plot_clusters, dpmirt_plot_wright_map, dpmirt_plot_parameter_trace, dpmirt_plot_density_compare, dpmirt_plot_pp_check

References

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.

See also

Useful links:

Author

Maintainer: JoonHo Lee jlee296@ua.edu

Authors: