Theory, Identification, and the Literature Behind the Estimators
JoonHo Lee · The University of Alabama · jlee296@ua.edu
A web monograph on what it takes to report a person's latent trait honestly: the measurement models and their identification, information and the reliability coefficients that summarise it, hierarchical shrinkage and the empirical-Bayes tradition it comes from, Dirichlet process mixture priors on the latent-trait distribution, and the decision-theoretic case that three inferential goals — an individual's score, a ranking, and the distribution itself — imply three different posterior summaries rather than one set of numbers.
📖 Read it: https://joonho112.github.io/dpmirt-theory-book/
The book runs to 29 chapters in nine parts, plus seven appendices.
| Part | What it does |
|---|---|
| I–II | The estimation problem; the Rasch and 2PL models, identification, and item/person estimation |
| III | Information, measurement error, and the reliability coefficients — including why several defensible coefficients disagree |
| IV | The Bayesian hierarchical model, the conditional posterior, shrinkage, and its empirical-Bayes lineage |
| V | What happens when normality is relaxed: flexible and semiparametric alternatives, the Dirichlet process, and DPM priors |
| VI | Three goals, three losses: posterior means, constrained Bayes, and triple-goal estimation |
| VII | Positioning against the nearest neighbour in the literature, scope, and open problems |
| VIII | What changes under the 2PL — information, reliability, and identification with free discriminations |
| IX | The realized evidence: what a companion simulation settled, what real tests look like, and what remains open |
The title is a Rasch-centred umbrella, not a claim of parallel depth across the two models: Parts I–VII form the theory spine and Part VIII is a focused two-parameter extension of the mechanisms for which free discriminations materially change the argument.
Two disciplines shape the repository, and both are auditable.
Provenance. Every numbered result carries a tag — restated, adapted, or
derived here — together with a source locator, and manifest/ holds the
registers that make this checkable: the result register, the notation register,
the corrections to the manuscript this book supports, the reviewer claim map,
and the source-reading receipts. A derived-here tag asserts no priority.
Generated artifacts. Chapters read frozen tables under tables/ and figures
under book/figures/; they compute nothing. Where the book quotes a companion
volume, manifest/evidence-claim-register.csv binds each imported claim to its
source edition, snapshot locator, and field. Appendix G states exactly what that
machinery guarantees and what it does not.
| Path | Contents |
|---|---|
book/ |
Quarto sources, figures, and bibliography. The rendered site is published from the gh-pages branch |
code/R/ |
The build pipeline: table and figure generators, the bibliography harvester, and the verifiers |
manifest/ |
Provenance registers |
tables/ |
Frozen .rds artifacts with CSV mirrors under tables/supplement/ |
refs/ |
The bibliography and its acquisition ledger |
verification/ |
Verifier outputs from the release build |
Rendering the book needs only this repository:
quarto render bookThe rendered site is served from the gh-pages branch; main carries the
sources that produce it.
The full verification pipeline does not. Rscript code/R/14-build-all.R
regenerates every artifact and runs the verifiers, but it reads inputs that are
deliberately not published: nine reference libraries of licensed third-party
PDFs that back the citation audit, the companion simulation and case-study
repositories, and two Item Response Warehouse corpus studies. Point
DPMIRT_PROJECT_ROOT at a directory holding those alongside this repository and
the pipeline runs; without them it will stop at the first missing input, by
design. The verifier outputs from the release build are included under
verification/ so the result of that run can be inspected without re-running it.
Environment: R 4.6.0, Quarto 1.9.x.
This project is published as three linked volumes. Each stands on its own; read together they separate what is true of a model, what is true in a study, and what changes on a real test.
| Volume | What it owns |
|---|---|
| Theory (this repository) | The mathematics and its sources: the measurement models, identification, reliability, shrinkage, DP mixture priors, and why three inferential goals imply three posterior summaries |
| Simulation study | Realized outcomes under known truth: the preregistered design grid, the confirmatory record, Monte Carlo error, and the gate verdicts |
| Case studies | What changes on real tests: thirteen Item Response Warehouse cases under both item models, reported as consequence rather than correctness |
See CITATION.cff, or:
Lee, JoonHo (2026). Bayesian Semiparametric Item Response Modelling for Person-Specific Latent Traits: Theory, Identification, and the Literature Behind the Estimators.
Text, figures, and tables under book/ are CC BY 4.0; code under code/ is
MIT. Cited sources are the copyright of their publishers and are not
distributed here. See LICENSE.