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REVIEW 3 major objections 2 minor 39 references

Multinomial probit model based on joint quantile regression

T0 review · 3 major / 2 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper proposes a multinomial probit model that estimates conditional quantiles of latent relative utilities in multiple-choice data by combining joint quantile regression with Gibbs sampling.

desk verdict The full text is an unrelated physics paper, so the statistical claims are unverifiable; the abstract alone is a plausible but unsubstantiated proposal. read the letter →

arxiv 2508.13556 v1 pith:I4VT3YXN submitted 2025-08-19 stat.ME

Masaaki Okabe , Koki Matsuoka , Jun Tsuchida , Hiroshi Yadohisa This is my paper
classification stat.ME
keywords multinomialprobitjointquantileregressionlatentutilitiesinferencediscretechoiceGibbssamplingBayesianestimationcorrelationstructure
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Standard multinomial probit can only interpret the expectation of the latent relative utilities that drive a multiple-choice decision. This paper proposes a model that instead estimates conditional quantiles of those relative utilities, so a covariate's effect can be tracked at the median, tails, or any chosen quantile rather than at the mean alone. The proposal combines joint quantile regression with the multinomial probit framework, which lets the model describe the correlation structure among latent variables explicitly while targeting quantiles. The authors derive full conditional distributions under several priors and estimate parameters from the posterior by Gibbs sampling; they argue this is computationally less expensive and easier to implement than Metropolis-Hastings, and they report quantile-dependent estimates on several datasets.

What carries the argument

The joint quantile regression structure placed on the latent relative utilities. It is what lets the model speak about conditional quantile points of relative utilities in a multinomial probit setup, and it is structured enough that the full conditionals under the chosen priors become tractable for Gibbs sampling. The explicit latent correlation structure is part of the same machinery: it adds the dependence information that a set of separate quantile regressions would lose.

What would settle it

Simulate multinomial choices from latent utilities with an asymmetric error distribution so that the 0.9-quantile slope genuinely differs from the median slope, then fit the proposed Gibbs sampler under its stated priors and check whether posterior credible intervals for the quantile-specific coefficients contain the true values. If reparameterizations that leave the likelihood unchanged shift the inferred quantile coefficients, the quantile effects are not identified.

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Extended reading notes

Core claim

The central claim is that quantile-specific inference for multinomial choice data can be achieved through a multinomial probit model built on joint quantile regression. In this model, latent relative utilities are regressed on covariates conditionally at chosen quantile levels rather than only in expectation, and the latent variables carry an explicit correlation structure. The paper derives the full conditional distributions of the parameters under several prior distributions and estimates them from the posterior by Gibbs sampling. Applied to several datasets, the fitted model yields interpretable parameters that vary by quantile, which is exactly the information that ordinary multinomial p

Load-bearing premise

The model's quantile estimates are identifiable: a baseline alternative, a scale or covariance normalization, and a quantile-fixing error specification must pin down the latent relative utilities; without them, different model parameterizations could produce the same observed choices with different quantile interpretations.

Editorial extensions

If this is right

  • Researchers can compare how a covariate shifts the median, lower-tail, and upper-tail of relative utilities in discrete choice data, not just the average.
  • The model supplies an explicit correlation structure among latent utilities together with quantile-specific coefficients, enabling dependence-aware quantile comparisons across alternatives.
  • Gibbs sampling makes the quantile multinomial probit model practical to fit without the tuning and computational cost of Metropolis-Hastings.
  • Applying the model to several datasets provides evidence that different covariates can matter at different quantiles, which mean-based probit would miss.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The supplied full-text body appears to belong to a different manuscript (an analysis of the trace of higher-derivative gravity field equations); the fields above are grounded only in the supplied abstract and metadata for the multinomial-probit paper.
  • A reader should verify the identification constraints in the full paper: multinomial probit requires a baseline alternative and a scale or covariance normalization, and quantile interpretation additionally requires the error distribution and link to fix what 'quantile' means for latent relative utilities.
  • If identification is secured, natural next steps are extensions to heteroskedastic or panel discrete choice, where tail behavior of utilities can be tied to unobserved heterogeneity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 2 minor

Summary. The submission's abstract announces a multinomial probit model based on joint quantile regression, in which conditional quantiles of latent relative utilities are compared, an explicit latent correlation structure is estimated, and full conditional distributions are derived for Gibbs sampling under several priors, followed by applications to several datasets. However, the attached full text is an unrelated higher-derivative gravity paper (arXiv:2508.13549v3) by Jun-Jin Peng and Hua Li. It contains no statistical model, no prior specifications, no Gibbs conditionals, no identifiability discussion, and no data analysis. Consequently, the central statistical claims cannot be checked from the submitted manuscript.

Significance. If the proposed method worked as advertised, a multinomial probit model with joint quantile regression could be a genuinely useful extension: quantile-specific inference about relative utilities would complement mean-based probit analyses and the claimed Gibbs sampler would offer computational advantages. The abstract's program is coherent and the topic is relevant for stat.ME readership. However, none of the technical apparatus—model equations, identification restrictions, full conditionals, MCMC details, or empirical results—is present in the submitted full text. There are no machine-checked proofs, reproducible code, or falsifiable predictions to assess. The physical manuscript that is attached may be internally consistent, but it is irrelevant to the statistical abstract.

major comments (3)
  1. [Full text (entireties)] The body of the submission is arXiv:2508.13549v3, 'The trace of field equations for higher-derivative gravity...', not the multinomial probit paper announced in the abstract. Equations (1)-(38) and Sections 1-4 concern gravitational Lagrangians, field equations, and divergence identities. None of the promised content—model specification, priors, full conditional distributions, Gibbs updates, or data applications—appears. This is a load-bearing mismatch: the central claim cannot be reviewed.
  2. [Abstract] The abstract's central object, 'conditional quantile points of relative utilities,' is not identified by anything stated. Multinomial probit is identified only after choosing a baseline alternative and imposing a scale or covariance normalization (e.g., fixing one diagonal element or total variance). Quantile interpretation additionally requires the latent error distribution to be fixed so that the quantile function is well-defined. The abstract states none of these restrictions, and the full text supplies none. Without them, the reported quantile comparisons would not be invariant under equivalent parameterizations.
  3. [Abstract (computational claim)] The claim that 'the ability to calculate by Gibbs sampling is computationally less expensive than Metropolis-Hastings' is unsupported because no full conditional distributions are derived or displayed anywhere in the submitted document. Even setting aside the unrelated full text, the abstract gives no model equation or prior family for which the conditionals would hold, so the computational efficiency claim is not assessable.
minor comments (2)
  1. [Metadata] The arXiv ID in the full text (2508.13549, gr-qc) differs from the submission ID (2508.13556, stat.ME), and the title and authors are completely different. The submission appears to contain the wrong paper body.
  2. [References] The full text's references are all to the general relativity and gravity literature; there are no citations to the quantile regression or multinomial probit literature advertised in the abstract. This reinforces that the statistical paper is absent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity visible; the supplied full text is an unrelated physics paper, so the abstract's derivation cannot be checked, but nothing in the abstract reduces to its own inputs.

full rationale

The abstract promises a multinomial probit model based on joint quantile regression, with full conditional distributions derived under priors and Gibbs sampling for posterior estimation. No equation in the abstract defines the proposed quantile parameters in terms of the quantities they are said to predict, and no fitted parameter is relabeled as a prediction. The identification concerns raised by the reader are real statistical prerequisites, but they are not circularity: a model can be unidentified without being circular. The supplied full text is a higher-derivative gravity paper (arXiv:2508.13549) unrelated to the abstract, so the derivation chain cannot be audited; however, a document mismatch is not evidence of circularity and cannot support an allegation that the statistical derivation is equivalent to its inputs. Accordingly, no circular step can be exhibited, and the honest finding is no significant circularity.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The abstract alone discloses no quantitative parameters. The entries below are the minimal load-bearing components of any multinomial probit + quantile regression model inferred from the abstract; the full text, which concerns higher-derivative gravity, provides no information about them.

free parameters (2)
  • User-chosen quantile levels (tau)
    The method's output is conditional quantiles of relative utilities; which quantile levels are used is an analyst choice not stated in the abstract.
  • Prior hyperparameters for the latent covariance and regression coefficients
    The abstract says the model is fit 'under several prior distributions' but does not specify them; posterior quantities and Gibbs updates depend on these choices.
assumptions (3)
  • domain assumption Multinomial probit identification restrictions (baseline category and scale/covariance normalization) are imposed and are compatible with quantile inference.
    Any multinomial probit model is only identified under such restrictions; the abstract's quantile reports depend on them without mention.
  • domain assumption The joint quantile regression specification is a valid representation of the conditional quantiles of the latent relative utilities.
    This is the modeling step that gives the quantile interpretation; the abstract states it as fact with no supporting argument.
  • domain assumption The derived full conditional distributions are correct and the Gibbs sampler converges to the target posterior.
    The computational claim of the paper rests on this; no derivation or convergence analysis is available in the provided document.

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Cite this review

Pith. "Pith review of Multinomial probit model based on joint quantile regression." pith.science (2026). https://pith.science/paper/I4VT3YXN

@misc{pith2026250813556,
  author       = {Pith},
  title        = {Pith review of: Multinomial probit model based on joint quantile regression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I4VT3YXN}},
  note         = {Machine review of arXiv:2508.13556}
}
read the original abstract

The multinomial probit model is a typical statistical model for multiple-choice data applied in many research areas. When we are interested in some quantiles of relative utilities for understanding the distribution of these utilities, the multinomial probit model is unsuitable because we only interpret the expectation of relative utilities based on it. We thus propose quantile regression analysis methods for multinomial choice data based on joint quantile regression and multinomial probit models to compare relative utilities with some quantiles. Using a joint quantile regression model allows us to consider the conditional quantile points of relative utilities and explicitly describe the correlation structure in the latent variables. We derive the full conditional distribution under several prior distributions and estimate the model's parameters from the posterior distribution by Gibbs sampling. The ability to calculate by Gibbs sampling is not only computationally less expensive than the Metropolis--Hastings method, but also easier to implement. We also apply the proposed model to several datasets. Consequently, we obtain interpretable results about different parameters by quantile.

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Works this paper leans on

39 extracted references · 14 canonical work pages

  1. [1]

    Stelle, Renormalization of higher derivative quantum gravity, Phys

    K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D16, 953 (1977)

    work page 1977

  2. [2]

    Stelle, Classical gravity with higher derivatives, Gen

    K.S. Stelle, Classical gravity with higher derivatives, Gen. Rel. Grav.9, 353 (1978)

    work page 1978

  3. [3]

    Myers, Higher derivative gravity, surface terms and string theory, Phys

    R.C. Myers, Higher derivative gravity, surface terms and string theory, Phys. Rev. D 36, 392 (1987)

    work page 1987

  4. [4]

    I.G. Avramidi, Covariant methods for the calculation of the effective action in quan- tum field theory and investigation of higher derivative quantum gravity, arXiv:hep- th/9510140 [hep-th]

    work page arXiv

  5. [5]

    Iyer and R.M

    V . Iyer and R.M. Wald, Some properties of the Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D50, 846 (1994) [arXiv:gr-qc/9403028]

    arXiv 1994

  6. [6]

    Jacobson, G

    T. Jacobson, G. Kang and R.C. Myers, On black hole entropy, Phys. Rev. D49, 6587 (1994) [arXiv:gr-qc/9312023 [gr-qc]]

    arXiv 1994

  7. [7]

    Dong, Holographic entanglement entropy for general higher derivative gravity, JHEP01, 044 (2014) [arXiv:1310.5713 [hep-th]]

    X. Dong, Holographic entanglement entropy for general higher derivative gravity, JHEP01, 044 (2014) [arXiv:1310.5713 [hep-th]]

    arXiv 2014

  8. [8]

    Dyer and K

    E. Dyer and K. Hinterbichler, Boundary terms, variational principles and higher derivative modified gravity, Phys. Rev. D79, 024028 (2009) [arXiv:0809.4033 [gr- qc]]

    arXiv 2009

Show all 39 references
  1. [9]

    Sotiriou and V

    T.P. Sotiriou and V . Faraoni, f(R) theories of gravity, Rev. Mod. Phys.82, 451 (2010) [arXiv:0805.1726 [gr-qc]]

    2010 arXiv

  2. [10]

    Felice and S

    A.D. Felice and S. Tsujikawa, f(R) theories, Living Rev. Rel.13, 3 (2010) [arXiv:1002.4928 [gr-qc]]

    2010 arXiv

  3. [11]

    Nojiri and S.D

    S. Nojiri and S.D. Odintsov, Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept.505, 59 (2011) [arXiv:1011.0544 [gr-qc]]. 11

    2011 arXiv

  4. [12]

    Modesto, Super-renormalizable quantum gravity, Phys

    L. Modesto, Super-renormalizable quantum gravity, Phys. Rev. D86, 044005 (2012) [arXiv:1107.2403 [hep-th]]

    2012 arXiv

  5. [13]

    Camps, Generalized entropy and higher derivative gravity, JHEP03, 070 (2014) [arXiv:1310.6659 [hep-th]]

    J. Camps, Generalized entropy and higher derivative gravity, JHEP03, 070 (2014) [arXiv:1310.6659 [hep-th]]

    2014 arXiv

  6. [14]

    Biswas and S

    T. Biswas and S. Talaganis, String-inspired infinite-derivative theories of gravity: a brief overview, Mod. Phys. Lett. A30, 1540009 (2015) [arXiv:1412.4256 [gr-qc]]

    2015 arXiv

  7. [15]

    Biswas, A.S

    T. Biswas, A.S. Koshelev and A. Mazumdar, Consistent higher derivative gravita- tional theories with stable de Sitter and anti-de Sitter backgrounds, Phys. Rev. D95, 043533 (2017) [arXiv:1606.01250 [gr-qc]]

    2017 arXiv

  8. [16]

    Bueno, P.A

    P. Bueno, P.A. Cano, J. Moreno and A. Murcia, All higher-curvature gravities as gen- eralized quasi-topological gravities, JHEP11, 062 (2019) [arXiv:1906.00987 [hep- th]]

    2019 arXiv

  9. [17]

    Mignemi and D.L

    S. Mignemi and D.L. Wiltshire, Black holes in higher derivative gravity theories, Phys. Rev. D461475 (1992) [arXiv:hep-th/9202031 [hep-th]]

    1992 arXiv

  10. [18]

    Cai and N

    R.G. Cai and N. Ohta, Black holes in pure Lovelock gravities, Phys. Rev. D74, 064001 (2006) [arXiv:hep-th/0604088 [hep-th]]

    2006 arXiv

  11. [19]

    H. L ¨u, A. Perkins, C.N. Pope and K.S. Stelle, Black holes in higher-derivative gravity, Phys. Rev. Lett.114, 171601 (2015) [arXiv:1502.01028 [hep-th]]

    2015 arXiv

  12. [20]

    H. L ¨u, A. Perkins, C.N. Pope and K.S. Stelle, Spherically symmetric solutions in higher-derivative gravity, Phys. Rev. D92, 124019 (2015) [arXiv:1508.00010 [hep- th]]

    2015 arXiv

  13. [21]

    Kokkotas, R.A

    K. Kokkotas, R.A. Konoplya and A. Zhidenko, Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: analytical approximation, Phys. Rev. D 96, 064007 (2017) [arXiv:1705.09875 [gr-qc]]

    2017 arXiv

  14. [22]

    Bueno and P.A

    P. Bueno and P.A. Cano, On black holes in higher-derivative gravities, Class. Quant. Grav.34, 175008 (2017) [arXiv:1703.04625 [hep-th]]

    2017 arXiv

  15. [23]

    P.A. Cano, B. Ganchev, D.R. Mayerson and A. Ruip ´erez, Black hole multipoles in higher-derivative gravity, JHEP12, 120 (2022) [arXiv:2208.01044 [gr-qc]]

    2022 arXiv

  16. [24]

    Amirabi, M

    Z. Amirabi, M. Halilsoy and S.H. Mazharimousavi, Generation of spherically sym- metric metrics in f(R) gravity, Eur. Phys. J. C76, 338 (2016) [arXiv:1509.06967 [gr-qc]]

    2016 arXiv

  17. [25]

    Myers and J.Z

    R.C. Myers and J.Z. Simon, Black hole thermodynamics in Lovelock gravity, Phys. Rev. D38, 2434 (1988)

    1988

  18. [26]

    Nojiri and S.D

    S. Nojiri and S.D. Odintsov, Anti-de Sitter black hole thermodynamics in higher derivative gravity and new confining deconfining phases in dual CFT, Phys. Lett. B521, 87 (2001) [�������: Phys. Lett. B542, 301 (2002)] [arXiv:hep-th/0109122 [hep-th]]. 12

    2001 arXiv

  19. [27]

    Deser and B

    S. Deser and B. Tekin, Energy in generic higher curvature gravity theories, Phys. Rev. D67, 084009 (2003) [arXiv:hep-th/0212292 [hep-th]]

    2003 arXiv

  20. [28]

    Biswas, A

    T. Biswas, A. Mazumdar and W. Siegel, Bouncing universes in string-inspired gravity, JCAP03, 009 (2006) [arXiv:hep-th/0508194 [hep-th]]

    2006 arXiv

  21. [29]

    Cai and L.M

    R.G. Cai and L.M. Cao, Unified first law and thermodynamics of apparent horizon in FRW universe, Phys. Rev. D75, 064008 (2007) [arXiv:gr-qc/0611071 [gr-qc]]

    2007 arXiv

  22. [30]

    Odintsov and V .K

    S.Nojiri, S.D. Odintsov and V .K. Oikonomou, Modified gravity theories on a nutshell: inflation, bounce and late-time evolution, Phys. Rept.692, 1 (2017) [arXiv:1705.11098 [gr-qc]]

    2017 arXiv

  23. [31]

    Reall and J.E

    H.S. Reall and J.E. Santos, Higher derivative corrections to Kerr black hole thermo- dynamics, JHEP04, 021 (2019) [arXiv:1901.11535 [hep-th]]

    2019 arXiv

  24. [32]

    Querella, Variational principles and cosmological models in higher order gravity, arXiv:gr-qc/9902044 [gr-qc]

    L. Querella, Variational principles and cosmological models in higher order gravity, arXiv:gr-qc/9902044 [gr-qc]

    arXiv

  25. [33]

    Peng, A note on field equations in generalized theories of gravity, Phys

    J.J. Peng, A note on field equations in generalized theories of gravity, Phys. Scr.99, 105229 (2024) [arXiv:2306.11561 [gr-qc]]

    2024 arXiv

  26. [34]

    Oliva and S

    J. Oliva and S. Ray, Classification of six derivative Lagrangians of gravity and static spherically symmetric solutions, Phys. Rev. D82, 124030 (2010) [arXiv:1004.0737 [gr-qc]]

    2010 arXiv

  27. [35]

    Xiao, First order corrections to the black hole thermodynamics in higher curvature theories of gravity, Phys

    Y . Xiao, First order corrections to the black hole thermodynamics in higher curvature theories of gravity, Phys. Rev. D106, 064041 (2022) [arXiv:2207.00967 [grqc]]

    2022 arXiv

  28. [36]

    Y . Xiao, Q. Wang and A. Zhang, A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories, arXiv:2508.05326 [gr-qc]

  29. [37]

    Padmanabhan, Some aspects of field equations in generalised theories of gravity, Phys

    T. Padmanabhan, Some aspects of field equations in generalised theories of gravity, Phys. Rev. D84, 124041 (2011) [arXiv:1109.3846 [gr-qc]]

    2011 arXiv

  30. [38]

    S. W. Hawking and D. N. Page, Thermodynamics of black holes in Anti-De Sitter space, Commun. Math. Phys.87, 577 (1983)

    1983

  31. [39]

    Peng and H

    J.J. Peng and H. Li, Field equations and Noether potentials for higher-order theories of gravity with Lagrangians involving� iR,� iRµν and� iRµνρσ, arXiv:2402.17429 [gr-qc]. 13

    arXiv

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