Appendix F — Software and Computation
This appendix orients rather than instructs. The Associate Editor’s third demand asked for a worked code example, and decision OQ-1 placed it in the companion repository DPMirt-case-study/, not here. What follows says what each piece of software does, where its documentation is, and — more usefully — the two places where a default choice inside the software is a modelling decision that this book has an opinion about.
Everything below was read from the packages’ DESCRIPTION, NAMESPACE and source on 2026-08-05. Package documentation sits at the bottom of this book’s authority order (Chapter 2), so nothing here is used to support a claim in the body.
F.1 The three project packages
DPMirt (version 0.2.0) is the fitting package (Lee 2026c). Its own description states what it covers: Bayesian semiparametric IRT with Dirichlet process mixture priors via NIMBLE, supporting Rasch, 2PL and 3PL models under both Normal and DPM latent-trait priors, and providing posterior mean, constrained Bayes and triple-goal summaries. It exposes 26 functions, organized around a compile-once, sample-many workflow: dpmirt_compile() builds and compiles the NIMBLE model, dpmirt() fits, and dpmirt_draws(), dpmirt_estimates(), dpmirt_loss() and dpmirt_diagnostics() read the result. nimble (≥ 1.0.0) is a hard dependency; the model is not portable to another sampler without rewriting it.
IRTsimrel (version 0.2.0) is the design package, and it is the one that makes Chapter 9’s argument operational (Lee 2026e). Its title is “Reliability-Targeted Simulation for Item Response Data,” and its exported API is built around solving for a design that hits a target reliability: eqc_calibrate(), spc_calibrate() and sac_calibrate() are three calibration routes, compute_rho_bar(), compute_rho_tilde() and compute_rho_both() compute the competing coefficients Chapter 8 distinguishes, and check_feasibility() and rho_curve() say whether a target is reachable at all. The calibration algorithms themselves are developed in the package’s companion paper (Lee 2026f).
That the package computes \(\bar\rho\) and \(\tilde\rho\) separately is worth noticing here: it is the software counterpart of Theorem 8.1, and a design calibrated to one is not calibrated to the other.
DPprior (version 1.1.0) is a separate package, not vendored, that performs the \(\alpha\)-elicitation of Chapter 15 — choosing a Gamma hyperprior for the concentration parameter from a belief about the number of clusters, with the dual-anchor extension that constrains the induced weight behaviour at the same time (Lee 2026d, 2026b). One implementation bound belongs on the record because the case-study volume met it in production: the package’s Antoniak tabulation currently stops at \(J = 500\) persons, so every elicitation in that volume ran at \(n \le 500\) (Chapter 29).
F.2 Two defaults that are modelling decisions
F.2.1 The \(\alpha\) prior falls back silently in substance
DPprior is a Suggests dependency of DPMirt, not a requirement. Reading R/alpha_prior.R, when the package is absent dpmirt_alpha_prior() emits a message and falls back to Gamma(1, 3), Paganin et al.’s default.
The fallback is announced, so nothing is hidden. But the two paths are not the same modelling decision. The elicited prior encodes a belief about \(K\) and inverts Antoniak’s law to reach \(\alpha\) (Section A.2.4); the fallback encodes someone else’s default at a different sample size. Chapter 16’s realized fit is one instance of how far prior and posterior on \(K\) can sit apart, and Chapter 23 records the interaction between the \(\alpha\) prior and the identification convention as unresolved. A reader reproducing this work should check which of the two paths ran, because the message is easy to lose in MCMC output.
When mu_K is not supplied the elicitation itself defaults to \(\max(3, \lceil \log N \rceil)\) clusters — a rule of thumb, not a result.
F.2.2 The item prior is centred and its variance is fixed
DPMirt’s implemented item prior is beta.tmp[i] ~ N(0, sigma2_beta) with beta = beta.tmp - mean(beta.tmp) and sigma2_beta fixed at 3. There is no \(\mu_\beta\) parameter and no hyperprior on the item variance.
This matters twice over. The centring is the identification constraint of Chapter 4 as actually implemented — Proposition 10.1 works out what a centred item prior is as a distribution — and the fixed variance means the item side carries no learned dispersion. It also matters because the submitted manuscript’s Appendix D describes a different prior, with a flat \(\mu_\beta\) and an inverse-\(\chi^2\) hyperprior. That is correction C-013, and the ruling was that the appendix follows the implemented model, since every number the paper reports came from it.
F.3 External software
NIMBLE is the sampler DPMirt compiles to, and its DP machinery is what makes the semiparametric prior tractable. Documentation: https://r-nimble.org.
TAM is used by IRTsimrel for the validation path — TAM::tam.mml() and TAM::tam.mml.2pl() fit the reference model and TAM::tam.wle() produces the weighted likelihood estimates that Chapter 6 discusses. It is the independent check that a simulated design behaves as intended, not part of the DPM fitting path.
Stan and brms are not used by any package in this project. They are named here only because a reader coming from the Bayesian IRT literature will expect them, and because Chapter 10 mentions HMC as the alternative to NIMBLE’s samplers for this model class.
F.4 Where the worked example lives
Decision OQ-1 assigned the Associate Editor’s code example to the case-study repository, so this appendix does not carry one. In the first edition of this book this section reported an empty scaffold; that report is superseded twice over. The case-study volume is complete and now stands in its second edition (Lee 2026a): nineteen chapters and four appendices over thirteen Item Response Warehouse cases, each fitted under both item models and all three latent-trait priors (78 production fits, replicated in full at a second seed), with the three posterior summaries of Chapter 17 read from every fit, materiality thresholds declared before fitting, a frozen claim register with its corrections on the record, and a verdict layer joining each case-cell to its matched simulation cell. The second edition rewrote the reader-facing volume; it added no fits and recomputed no frozen number, and its analysis layer — the P-series tables, the manifest, the run records — remains in the first edition’s repository at DPMirt-case-study/, which is what this book’s evidence pipeline reads. The five acceptance criteria this appendix used to list are met in the volume’s own appendices, and OQ-6 is closed; the claim-map rows AE-03 and R2-05 move to addressed on that basis, which decision (a7) records. What this book takes from the volume — and the vocabulary rules under which it takes it — is Chapter 28’s business.
A reader who wants to run the machinery today has a better starting point than this appendix: DPMirt’s own vignettes, at https://joonho112.github.io/DPMirt/.
F.5 What this appendix does not do
It does not benchmark, compare run times, or recommend one sampler over another. It does not report what any of this software produced when run — that is the companion simulation study’s authority, and Chapter 21 and Chapter 23 draw the same line. And it does not certify that the package versions named above are the ones used for the manuscript’s results; the reproduction record for that belongs with the simulation study’s own build report.