| ID | Severity | Where | Book chapter | Ruled |
|---|---|---|---|---|
| C-009 | moderate | Reviewer 2 comment 3 and the manuscript’s implicit framing | ch. 4 | 2026-08-05 |
| C-011 | moderate | Manuscript sec. 2.1 | ch. 6 | — |
| C-013 | moderate | Appendix D draft sec. D.2.3, level-3 item prior | ch. 10 | 2026-08-05 |
| C-010 | moderate | Scope caveat, not a manuscript error | ch. 16 | — |
| C-014 | moderate | Appendix F draft sec. F.4, partial identifiability of G | ch. 16 | 2026-08-05 |
| C-012 | minor | Manuscript sec. 2.1, standard error | ch. 6 | — |
| C-001 | minor | Table 2, S and H columns | ch. 8 | 2026-08-05 |
| C-004 | minor | Estimator vs design parameter | ch. 8 | — |
| C-005 | minor | Appendix C draft eq. (C.13) | ch. 8 | — |
| C-006 | minor | Appendix C draft eq. (C.23)-(C.24) | ch. 8 | — |
| C-008 | minor | Manuscript reference list | ch. 21 | 2026-08-05 |
| C-007 | none | Manuscript sec. 6.1, sample-size context | ch. 1 | — |
| C-002 | none | Reliability attribution | ch. 8 | — |
| C-003 | none | Strata formula provenance | ch. 8 | — |
Appendix C — Corrections to the Submitted Manuscript
This appendix is the revision’s worklist. It collects every place where writing this book required going back to a primary source and finding that the submitted manuscript — APM-25-04-056, Targeting Toward Inferential Goals in Bayesian Rasch Models for Estimating Person-Specific Latent Traits — says something wrong, imprecise, or merely unclear.
It exists because the book was written under a rule stated in the front matter: a claim enters only when the source that established it has been read at the locator cited, not when the manuscript’s or a reviewer’s summary of it has been read. Applying that rule produced findings. Rather than fix them silently in the book and leave the paper unchanged, each one is recorded here with the source consulted, so the revision can be worked through entry by entry and the response letter can point at specific text.
C.1 What counts as an entry, and what the severities mean
An entry is not a difference of emphasis or a place where the manuscript is terser than the book. It is a statement whose truth value or attribution changes once the source is opened.
| Severity | Meaning | Count |
|---|---|---|
| moderate | A substantive statement is wrong, or a citation attributes a result to a source that does not contain it. Fixing it changes what the paper claims | 5 |
| minor | A number, a formula, or a piece of wording is wrong or imprecise, but the surrounding argument survives the fix | 6 |
| none | Checked against the primary source and found sound. Recorded so the revision does not spend effort re-verifying, and so a reviewer can see the check was made | 3 |
The none rows are not padding. Three of them are places where an earlier draft of this appendix asserted an error that a second reading withdrew; keeping them makes the audit trail honest and stops the same false alarm from being raised twice. C-007 is the clearest case — a first pass mixed rows and units and produced a correction that was itself wrong.
3 entries are limitations rather than errors: C-010 records that the semiparametric 2PL identification problem is open, which the manuscript does not disclose, and C-002 and C-003 record provenance that was previously unchecked and is now sourced.
C.2 Index
Where an entry required a decision that only the author could make — because more than one fix was defensible — the ruling and its date are recorded with the entry. 5 entries carry rulings; the rest have a single defensible fix and needed none.
C.3 The entries
Each entry gives, in order: where in the manuscript, what it says, why that is wrong (or why it is sound), the source consulted at its locator, what the revision should do, and the author’s ruling.
C.3.1 C-009 — Reviewer 2 comment 3 and the manuscript’s implicit framing
Severity: moderate. Treated in ch. 4 of this book.
The assumption theta_p ~ N(0,1) is typically used to fix the location and scale of the latent trait. However, the authors consider models where the mean and variance of the latent trait are estimated from the data … In such settings, the model is not identifiable without additional constraints
Why that is wrong. San Martin (2016, sec. 8.5.1) establishes scale identification only for a random-effects Rasch model in which the shape of G is known and a scale parameter sigma is unknown: a strictly increasing bivariate-probability map identifies sigma when I >= 2, after which item difficulties follow. This does not establish identification when G is an unknown semiparametric or Dirichlet-process-mixture distribution. Location still requires anchoring. The revision must state the known-shape theorem narrowly and treat unknown-G identification separately.
Source consulted. San Martin (2016, sec. 8.5.1 and Table 8.1)
What the revision should do. ch. 4 secs. 4-5; the response letter to R2-3
Author ruling. Adopt the book’s narrower reading. San Martin (2016, sec. 8.5.1) identifies the scale only when the shape of G is known and sigma alone is unknown, so it supplies no scale-identification warrant for a flexible-G model. Chapter 4 and the R2-3 response state the constraint actually imposed rather than claiming the mean and variance are freely estimated. (ruled 2026-08-05)
C.3.2 C-011 — Manuscript sec. 2.1
Severity: moderate. Treated in ch. 6 of this book.
Estimates for theta_p can be derived through maximum likelihood (Baker & Kim, 2004) or least squares estimation (Fox, 2010), based solely on the within-person item response vector
Why that is wrong. This is exact only when the item parameters are treated as known. With calibrated item estimates, the ability estimator also depends on the calibration sample. Whether the omitted item-parameter uncertainty is negligible cannot be inferred from P alone: it depends on calibration design and size, overlap between calibration and scoring samples, and the target estimand. The book should state those conditions and avoid claiming that P in the tens by itself makes the term important.
Source consulted. Warm (1989), which treats item parameters as known; law of total variance and two-stage-estimation logic
What the revision should do. ch. 6 sec. 5
Author ruling. No author decision required; the fix has one form.
C.3.3 C-013 — Appendix D draft sec. D.2.3, level-3 item prior
Severity: moderate. Treated in ch. 10 of this book.
beta_i | mu_beta, sigma2_beta ~ iid N(mu_beta, sigma2_beta), with a flat prior on mu_beta and an inverse-chi-squared hyperprior on sigma2_beta
Why that is wrong. The fitted model does neither. Read from the companion package model source (R/model_spec.R, item-centered Rasch specification and default constants): beta.tmp[i] ~ iid 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. The drafted specification is strictly more general than the one that produced the results, and the induced prior on beta does NOT factor over items (PROP-10-2), so writing the level-3 term as a product of independent item densities is correct for the drafted model and false for the fitted one.
Source consulted. DPMirt R/model_spec.R lines 242-253 and 933-937; Appendix D draft sec. D.2.3-D.2.4
What the revision should do. ch. 10 sec. 2 – bring Appendix D into line with the implemented model
Author ruling. Correct Appendix D to the implemented model: beta.tmp[i] ~ N(0, sigma2_beta) with beta = beta.tmp - mean(beta.tmp) and sigma2_beta fixed at 3. No mu_beta and no item variance hyperprior. Refitting the drafted model was rejected as costly and unnecessary: every reported number comes from the implemented one. (ruled 2026-08-05)
C.3.4 C-010 — Scope caveat, not a manuscript error
Severity: moderate. Treated in ch. 16 of this book.
The manuscript and the companion simulation both fit Dirichlet process mixtures under the 2PL as well as the Rasch model
Why that is wrong. NOT an error in the manuscript, but a limitation that must be disclosed: the identification of the SEMIPARAMETRIC 2PL is an open problem. San Martin (2016) marks it with question marks in Table 8.1 and states so in sec. 8.7. Every semiparametric identification result the book proves is proved for the Rasch model; the meaning of the 2PL results is correspondingly less secure. Inherited from the literature, not created here.
Source consulted. San Martin (2016, sec. 8.7 and Table 8.1)
What the revision should do. ch. 4 sec. 8, ch. 16, ch. 23
Author ruling. No author decision required; the fix has one form.
C.3.5 C-014 — Appendix F draft sec. F.4, partial identifiability of G
Severity: moderate. Treated in ch. 16 of this book.
San Martin et al. (2011, Theorem 3) rigorously demonstrated that in the semiparametric 1PL (Rasch) model, the full distribution G is not identifiable from a finite test of length I
Why that is wrong. Wrong theorem, and the named theorem concerns a different model. Read directly: their Theorem 3 is about the semiparametric Rasch POISSON COUNTS model and gives FULL identification of beta and G with at least two probes. The Rasch partial-identification result is their THEOREM 5: the item parameters and exactly n+1 functionals of G are b-identified IF AND ONLY IF one item parameter is a.s. constant, given at least two items. The appendix’s functional form (F.7) and the count I+1 are correct; the attribution is not. The appendix also states the restriction as sum-to-zero centering, whereas Theorem 5 is stated as an iff with an anchor item.
Source consulted. San Martin et al. (2011), Theorems 3, 4, 5 and 6 and expression (11); Appendix F draft sec. F.4
What the revision should do. ch. 16 sec. 4 – correct the citation to Theorem 5 and state the anchor-item form of the restriction
Author ruling. Cite Theorem 5, not Theorem 3, and state the anchor-item form of the restriction. Their Theorem 3 concerns the semiparametric Rasch Poisson counts model and gives full identification. (ruled 2026-08-05)
C.3.6 C-012 — Manuscript sec. 2.1, standard error
Severity: minor. Treated in ch. 6 of this book.
The squared standard error for person p is calculated as the inverse of the Fisher information function
Why that is wrong. The inverse information is a local/asymptotic variance conditional on fixed known item parameters (and, for plug-in scoring, evaluated at estimated item parameters). An unconditional variance requires a two-stage or joint analysis whose extra term depends on the calibration/scoring design and covariance structure; the law of total variance alone does not determine its magnitude. This qualification propagates to MSEM and reliability summaries.
Source consulted. Warm (1989); conditional information identity; two-stage-estimation qualification
What the revision should do. ch. 6 sec. 5; ch. 7 sec. 5
Author ruling. No author decision required; the fix has one form.
C.3.7 C-001 — Table 2, S and H columns
Severity: minor. Treated in ch. 8 of this book.
Table 2 columns: RMSEM 1.0/0.8/0.7/0.5/0.3, separation S 1.0/1.3/1.4/2.0/3.3, strata H 1.7/2.0/2.4/3.0/4.3, test information 1.0/1.5/2.3/4.0/9.0, for target reliabilities 0.5-0.9
Why that is wrong. RE-VERIFIED 2026-08-04 after C-007 was withdrawn; the earlier wording was too broad and framed the issue as rounding. Corrected finding: three of the four derived columns are computed from the EXACT target reliability and agree with it to the displayed precision – RMSEM (5/5), H (5/5) and test information (5/5). The SEPARATION column alone is computed from the ROUNDED RMSEM column: half-up rounding of 1/RMSEM_printed reproduces 1.0/1.3/1.4/2.0/3.3 exactly, while the exact values are 1.0/1.2/1.5/2.0/3.0. S is therefore wrong in the first decimal at w=0.6, 0.7 and 0.9. DECISIVE EVIDENCE that this is a slip and not a display convention: the manuscript’s own prose uses the EXACT values. It says that at w=0.9 the between-person SD is ‘about three times greater than’ RMSEM (S = 3.0, not the printed 3.3) and that at w=0.5 they are equal (S = 1.0, consistent). Prose and table disagree at the largest row.
Source consulted. Manuscript Table 2 and its preceding paragraph; Wright & Masters (1982, sec. 5.5)
What the revision should do. ch. 8 sec. 5 – regenerate the separation column from the target reliability
Author ruling. Regenerate the separation column from the exact target reliability. The other three derived columns are already correct to the displayed precision. (ruled 2026-08-05)
C.3.8 C-004 — Estimator vs design parameter
Severity: minor. Treated in ch. 8 of this book.
sigma_theta^2 fixed at 1 in the simulation, then w-bar computed
Why that is wrong. Wright & Masters obtain adjusted variance by SUBTRACTION, SA^2 = SD^2 - MSE, while the simulation SETS sigma^2 = 1 as a generating parameter. They may target the same population quantity under the measurement-error model, but nonlinear plug-in scoring and finite-sample or boundary handling prevent an automatic equality-in-expectation claim.
Source consulted. Wright & Masters (1982, sec. 5.5); external review
What the revision should do. ch. 8 sec. 4 and ch. 7 MSEM callout
Author ruling. No author decision required; the fix has one form.
C.3.9 C-005 — Appendix C draft eq. (C.13)
Severity: minor. Treated in ch. 8 of this book.
SD_P^2 approx SA_P^2 + MSE_P, presented as an approximation
Why that is wrong. Wright & Masters (1982, sec. 5.5) DEFINE the adjusted variance as SA_P^2 = SD_P^2 - MSE_P. The decomposition is therefore an identity, not an approximation, and the draft’s use of ‘approx’ weakens it without reason. This matters because it is the step that makes the CTT correspondence exact: with equality, Rel = SA2/SD2 = G2/(1+G2) follows algebraically rather than approximately.
Source consulted. Wright & Masters (1982, sec. 5.5)
What the revision should do. ch. 8 sec. 2 – restore equality
Author ruling. No author decision required; the fix has one form.
C.3.10 C-006 — Appendix C draft eq. (C.23)-(C.24)
Severity: minor. Treated in ch. 8 of this book.
Average shrinkage weight equals Rasch reliability under approximately constant standard errors
Why that is wrong. The Jensen direction is exact for the conditional normal–normal shrinkage weights w_p = sigma2/(sigma2+s_p^2): because x -> sigma2/(sigma2+x) is convex, mean(w_p) >= sigma2/(sigma2+mean(s_p^2)), with equality iff the s_p^2 are constant. The further identification of these weights with Rasch EAP weights is only a local normal approximation and must not be stated as an exact Rasch identity.
Source consulted. this book’s algebra under the stated normal–normal approximation; no originality claim
What the revision should do. ch. 8 sec. 4 – separate the exact Jensen inequality from the local-normal EAP approximation
Author ruling. No author decision required; the fix has one form.
C.3.11 C-008 — Manuscript reference list
Severity: minor. Treated in ch. 21 of this book.
Lee, J., Che, J., Rabe-Hesketh, S., Feller, A., & Miratrix, L. (2024). … Journal of Educational and Behavioral Statistics, 0(0). Advance online publication.
Why that is wrong. Not an error at the time of writing, but now completable: the article has final pagination, Journal of Educational and Behavioral Statistics, 50(5), 731-764, DOI 10.3102/10769986241254286 (confirmed against Crossref 2026-08-03). The revision should cite the final version, since ch. 21 takes page-level locators from it.
Source consulted. Crossref 10.3102/10769986241254286
What the revision should do. manuscript reference list; ch. 21 locators
Author ruling. Resolved in this book on 2026-08-05: the bibliography now carries the final version (2025, 50(5), 731-764) under key lee_improving_2025, tier primary-read, and ch. 21 takes its locators from it. The manuscript reference list still needs the same repair. (ruled 2026-08-05)
C.3.12 C-007 — Manuscript sec. 6.1, sample-size context
Severity: none. Treated in ch. 1 of this book.
Conoyer et al. (2022) analyzed 20 curriculum-based measurement assessments, reporting examinee counts ranging from 25 to 967, with the first, median, and third quartiles being 62, 147, and 245
Why that is wrong. The earlier correction was itself wrong because it mixed rows and units. Table 1 contains 20 assessment-level N values: 25, 51, 51, 58, 58, 63, 106, 106, 117, 146, 148, 153, 198, 202, 205, 367, 547, 746, 799, and 967. R type-7 quartiles are 61.75, 147, and 245.5, so the manuscript’s rounded 62/147/245 and range 25–967 are supported. The value 1,545 is the combined sample for the Ford and Hosp study, whereas Table 1 reports separate grade-level assessment samples of 799 and 746. WITHDRAW the 2026-08-03 correction; retain the manuscript claim with a precise Table 1 locator.
Source consulted. Conoyer et al. (2022, Table 1), visually checked against the held PDF
What the revision should do. ch. 1 sec. 6.1 – retain the values and add the assessment-level/table locator
Author ruling. No author decision required; the fix has one form.
C.3.13 C-002 — Reliability attribution
Severity: none. Treated in ch. 8 of this book.
w-bar = sigma2/(sigma2 + MSE) attributed to Wright & Masters (1982)
Why that is wrong. Not an error. VERIFIED against the primary source: Wright & Masters (1982, sec. 5.5) define Test Reliability of Person Separation as R_P = SA_P2/SD_P2 = 1 - MSE_P/SD_P^2 = G_P2/(1+G_P2), with SA_P^2 = SD_P^2 - MSE_P. Identifying sigma^2 with SA_P^2 makes the manuscript formula exactly R_P.
Source consulted. Wright & Masters (1982, sec. 5.5)
What the revision should do. ch. 8 — cite with locator
Author ruling. No author decision required; the fix has one form.
C.3.14 C-003 — Strata formula provenance
Severity: none. Treated in ch. 8 of this book.
H = (4S+1)/3 following Wright and Masters (1982)
Why that is wrong. Not an error. VERIFIED: Wright & Masters (1982, sec. 5.5) give Number of Person Strata H_P = (4G_P+1)/3, derived from defining strata with centers THREE measurement errors apart. The three-error convention was previously unchecked and is now sourced.
Source consulted. Wright & Masters (1982, sec. 5.5)
What the revision should do. ch. 8 — state the three-error convention explicitly
Author ruling. No author decision required; the fix has one form.
C.4 What is not here
Three classes of thing are deliberately absent.
Results. No entry concerns whether a simulated condition came out one way or another. That boundary is the companion simulation study’s, and this book does not cross it; the front matter sets out which document is authority for what.
Presentation. Places where the manuscript would read better are not corrections. The three that came out of Part VI and were ratified for the revision are recorded in DECISIONS.md rather than here: naming \(G_N\) as the realized empirical distribution (Chapter 17), stating that \(\bar G_N\) is a probability rather than a trait estimate (Chapter 19), and saying in one sentence that test length was the instrument by which reliability was set rather than a crossed design factor (Chapter 9).
Errors in this book. They exist, and external review found them. They are recorded in the project’s step logs, which are not part of the published release, rather than here, because this appendix is about the manuscript. The distinction matters for one reason worth stating plainly: several of the corrections above were found only because a check was written that could fail, and the same discipline applied to the book’s own prose refuted claims this book had made. An appendix that listed only the manuscript’s errors would misrepresent where the errors were.
C.5 Using this appendix for the response letter
The entries map onto the reviewers’ comments unevenly. C-009 is the substance of the answer to Reviewer 2’s third comment and should be quoted in the response, not merely fixed in the text: the identification warrant the manuscript implicitly claims is narrower than stated, and saying so is stronger than defending the wider claim. C-014 and C-010 both bear on Reviewer 2’s identifiability question and are best answered together, since one is a misattributed theorem and the other an undisclosed open problem in the same literature. C-008 is a reference-list repair that Reviewer 2’s overlap comment makes conspicuous. The remaining entries are text repairs that need no comment in the letter.