pith. sign in

arxiv: 2607.01971 · v1 · pith:V5WJNSFKnew · submitted 2026-07-02 · 📊 stat.ME · stat.ML

Moment-Based Selection of Multiresponse Linear Mixed-Effects Models

Yifan Chen , Yuedong Wang , Guo Yu This is my paper

Pith reviewed 2026-07-03 08:04 UTC · model grok-4.3

classification 📊 stat.ME stat.ML
keywords MOMENTmoment-based selectionmultiresponse linear mixed-effects modelsrandom-effects selectionfixed-effects selectionsub-Weibull errorsconvex optimizationmultivariate longitudinal data
0
0 comments X

The pith

MOMENT uses second-order cross-moment identities to select random effects in multiresponse linear mixed models and establishes finite-sample consistency.

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

The paper proposes MOMENT, a stage-wise moment-based framework for selecting and estimating parameters in multiresponse linear mixed-effects models. It exploits second-order cross-moment identities to reduce random-effects selection to a smooth constrained convex optimization problem under a positive semidefinite constraint. Finite-sample theoretical guarantees are established for random-effects and fixed-effects selection consistency when errors follow a joint sub-Weibull distribution. Simulations show competitive performance that improves over univariate analyses when responses are correlated, with an application to hemodialysis data illustrating use for multivariate longitudinal data.

Core claim

MOMENT is a stage-wise moment-based framework that exploits second-order cross-moment identities to select and estimate the random-effects covariance matrix and fixed-effects coefficients. By inducing sparsity through its diagonal under a positive semidefinite constraint, the random-effects selection problem reduces to a smooth constrained convex optimization problem that can be solved efficiently by projected gradient descent. We further establish finite-sample theoretical guarantees for the proposed procedure, including random-effects selection consistency and fixed-effects selection consistency under joint sub-Weibull errors.

What carries the argument

MOMENT framework that exploits second-order cross-moment identities and induces sparsity via the diagonal of the random-effects covariance matrix under a positive semidefinite constraint to enable smooth constrained convex optimization.

If this is right

  • Random-effects selection reduces to an efficiently solvable smooth constrained convex optimization problem using projected gradient descent.
  • Both random-effects and fixed-effects selection achieve consistency in finite samples under the joint sub-Weibull error condition.
  • The method can substantially outperform separate univariate analyses when responses are correlated.
  • It yields an interpretable and flexible approach for analyzing multivariate longitudinal data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The convex formulation may remain computationally feasible when the number of responses grows moderately if the positive semidefinite constraint is handled efficiently.
  • Alternative tail conditions weaker than joint sub-Weibull could be tested to see whether consistency still holds in practice.
  • The stage-wise structure could be combined with existing penalized likelihood approaches to trade off computational speed against statistical efficiency.

Load-bearing premise

The errors follow a joint sub-Weibull distribution to obtain the selection consistency results.

What would settle it

Repeated simulations drawn from error distributions that violate the joint sub-Weibull tail condition in which the procedure fails to achieve random-effects selection consistency.

Figures

Figures reproduced from arXiv: 2607.01971 by Guo Yu, Yifan Chen, Yuedong Wang.

Figure 1
Figure 1. Figure 1: Estimated population trajectories for the 20 response variables. Red points represent empirical monthly averages of the observed responses, and blue curves represent the estimated trajectories [PITH_FULL_IMAGE:figures/full_fig_p027_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Summary of fixed-effect selection and dependence structure in the hemodialysis multiresponse linear mixed model. Panel (a) shows selected demographic and vascular-access fixed effects for each re￾sponse; blue and red points indicate positive and negative selected coefficients, respectively. Panel (b) shows the patient-level correlation graph estimated from Σˆ B, and Panel (c) shows the monthly within￾patie… view at source ↗
Figure 3
Figure 3. Figure 3: Spaghetti plots of anxiety, depress, and aep score for each subject [PITH_FULL_IMAGE:figures/full_fig_p040_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The heatmap of the covariance matrix Σˆ B. The first block diagonal represents the covariance matrix for response anxiety. The second block diagonal represents the covariance matrix for response depress. The third block diagonal represents the covariance matrix for response aep. The off-diagonal blocks represent the covariance structure among responses. D Proof of Proposition 1 Let Σ ∈ R qd×qd be the decis… view at source ↗
read the original abstract

We propose MOMENT (\textbf{MO}ment-Based \textbf{M}ixed-\textbf{E}ffects Selectio\textbf{N} and Es\textbf{T}imation), a stage-wise moment-based framework that exploits second-order cross-moment identities to select and estimate the random-effects covariance matrix and fixed-effects coefficients. By inducing sparsity through its diagonal under a positive semidefinite constraint, the random-effects selection problem reduces to a smooth constrained convex optimization problem that can be solved efficiently by projected gradient descent. We further establish finite-sample theoretical guarantees for the proposed procedure, including random-effects selection consistency and fixed-effects selection consistency under joint sub-Weibull errors. Simulation studies show that MOMENT performs competitively overall and can substantially outperform separate univariate analyses when responses are correlated. An application to the hemodialysis dataset demonstrates that the proposed method yields an interpretable and flexible approach for multivariate longitudinal data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript proposes MOMENT, a stage-wise moment-based procedure for simultaneous selection and estimation in multiresponse linear mixed-effects models. It exploits second-order cross-moment identities to reduce random-effects covariance selection to a smooth, PSD-constrained convex program solved by projected gradient descent, while separately handling fixed-effects selection. Finite-sample consistency guarantees are claimed for both random- and fixed-effects selection under a joint sub-Weibull error assumption. Simulations compare performance against univariate analyses and existing methods, and an application to hemodialysis data is included.

Significance. If the stated consistency results hold, the work supplies a computationally efficient, likelihood-free alternative for multivariate longitudinal modeling that directly exploits cross-response dependence. The convex formulation and moment identities are attractive for high-dimensional or non-Gaussian settings, and the reported simulation gains when responses are correlated suggest practical utility beyond separate univariate fits.

minor comments (3)
  1. The abstract and introduction state that the random-effects problem reduces to a 'smooth constrained convex optimization problem,' but the precise form of the objective (including any penalty or constraint linearization) is not shown until the methods section; adding an early equation reference would improve readability.
  2. Simulation tables report point estimates of selection accuracy and MSE but do not include standard errors or the number of Monte Carlo replications used to generate the reported values; this makes it difficult to assess whether observed differences are statistically meaningful.
  3. The sub-Weibull tail condition is invoked for the consistency theorems; a brief remark on whether the same rates can be obtained under weaker moment conditions (e.g., finite fourth moments) would clarify the necessity of the assumption.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful summary of the manuscript and for the positive significance assessment. The recommendation for minor revision is noted. No major comments were provided in the report, so we have no specific points requiring point-by-point rebuttal or revision at this stage.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation begins from second-order cross-moment identities, formulates random-effects selection as a PSD-constrained convex program solved by projected gradient descent, and states finite-sample consistency results under an explicitly external joint sub-Weibull tail condition. None of the load-bearing steps (moment identities to optimization, or consistency proofs) reduce by the paper's own equations to a fitted parameter or self-citation chain; the sub-Weibull assumption is invoked as a sufficient condition rather than derived internally. The procedure is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the joint sub-Weibull error assumption for consistency and on the validity of second-order cross-moment identities for the selection procedure; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Errors are jointly sub-Weibull distributed
    Invoked to establish finite-sample selection consistency for both random and fixed effects.
  • domain assumption Second-order cross-moment identities hold and can be exploited for selection
    Basis for the stage-wise moment-based framework.

pith-pipeline@v0.9.1-grok · 5675 in / 1299 out tokens · 27774 ms · 2026-07-03T08:04:34.322329+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 1 internal anchor

  1. [1]

    Annals of the Institute of Statistical Mathematics , volume=

    New variable selection for linear mixed-effects models , author=. Annals of the Institute of Statistical Mathematics , volume=. 2017 , publisher=

    work page 2017

  2. [2]

    Feature Extraction: Modern Questions and Challenges , pages=

    Covariance Selection in the Linear Mixed Effect Model , author=. Feature Extraction: Modern Questions and Challenges , pages=. 2015 , organization=

    work page 2015

  3. [3]

    Journal of the American statistical association , volume=

    Functional data analysis for sparse longitudinal data , author=. Journal of the American statistical association , volume=. 2005 , publisher=

    work page 2005

  4. [4]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=

    Dimension reduction and coefficient estimation in multivariate linear regression , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2007 , publisher=

    work page 2007

  5. [5]

    Biometrika , volume=

    Reduced rank regression via adaptive nuclear norm penalization , author=. Biometrika , volume=. 2013 , publisher=

    work page 2013

  6. [6]

    2022 , publisher=

    Multivariate Reduced-rank Regression: Theory, Methods and Applications , author=. 2022 , publisher=

    work page 2022

  7. [7]

    Wiley Interdisciplinary Reviews: Computational Statistics , volume=

    Estimation of the error structure in multivariate response linear regression models , author=. Wiley Interdisciplinary Reviews: Computational Statistics , volume=. 2025 , publisher=

    work page 2025

  8. [8]

    The Annals of Statistics , volume=

    Support union recovery in high-dimensional multivariate regression , author=. The Annals of Statistics , volume=. 2011 , publisher=

    work page 2011

  9. [9]

    Machine learning , volume=

    Convex multi-task feature learning , author=. Machine learning , volume=. 2008 , publisher=

    work page 2008

  10. [10]

    Journal of Computational and Graphical Statistics , volume=

    Sparse multivariate regression with covariance estimation , author=. Journal of Computational and Graphical Statistics , volume=. 2010 , publisher=

    work page 2010

  11. [11]

    Journal of the American Statistical Association , volume=

    Newton—Raphson and EM algorithms for linear mixed-effects models for repeated-measures data , author=. Journal of the American Statistical Association , volume=. 1988 , publisher=

    work page 1988

  12. [12]

    Journal of the Royal Statistical Society: Series B (Methodological) , volume=

    Modelling variance heterogeneity: residual maximum likelihood and diagnostics , author=. Journal of the Royal Statistical Society: Series B (Methodological) , volume=. 1993 , publisher=

    work page 1993

  13. [13]

    2007 , publisher=

    Linear and generalized linear mixed models and their applications , author=. 2007 , publisher=

    work page 2007

  14. [14]

    Statistica Sinica , volume=

    Estimating Covariance Matrices at Different Levels in Repeated Measurements , author=. Statistica Sinica , volume=

    work page

  15. [15]

    Covariance regularization by thresholding , year =

    Bickel, Peter J and Levina, Elizaveta , journal =. Covariance regularization by thresholding , year =

    work page

  16. [16]

    Regularized estimation of large covariance matrices , volume =

    Bickel, Peter J and Levina, Elizaveta , journal =. Regularized estimation of large covariance matrices , volume =

    work page

  17. [17]

    2012 , publisher=

    Matrix analysis , author=. 2012 , publisher=

    work page 2012

  18. [18]

    Biometrics , volume=

    Fixed and random effects selection in linear and logistic models , author=. Biometrics , volume=. 2007 , publisher=

    work page 2007

  19. [19]

    Biometrics , volume=

    Random effects selection in linear mixed models , author=. Biometrics , volume=. 2003 , publisher=

    work page 2003

  20. [20]

    Annals of statistics , volume=

    Variable selection in linear mixed effects models , author=. Annals of statistics , volume=

    work page

  21. [21]

    Biometrics , volume=

    Joint variable selection for fixed and random effects in linear mixed-effects models , author=. Biometrics , volume=. 2010 , publisher=

    work page 2010

  22. [22]

    Statistics and its Interface , volume=

    Doubly regularized estimation and selection in linear mixed-effects models for high-dimensional longitudinal data , author=. Statistics and its Interface , volume=

    work page

  23. [23]

    Biometrics , volume=

    Fixed and random effects selection in mixed effects models , author=. Biometrics , volume=. 2011 , publisher=

    work page 2011

  24. [24]

    The R journal , volume=

    glmmpen: High dimensional penalized generalized linear mixed models , author=. The R journal , volume=

    work page

  25. [25]

    Statistica Sinica , pages=

    Hierarchical selection of fixed and random effects in generalized linear mixed models , author=. Statistica Sinica , pages=. 2017 , publisher=

    work page 2017

  26. [26]

    Journal of the American Statistical Association , volume=

    Joint selection in mixed models using regularized PQL , author=. Journal of the American Statistical Association , volume=. 2017 , publisher=

    work page 2017

  27. [27]

    Journal of Computational and Graphical Statistics , volume=

    A relaxation approach to feature selection for linear mixed effects models , author=. Journal of Computational and Graphical Statistics , volume=. 2024 , publisher=

    work page 2024

  28. [28]

    Scalable Subset Selection in Linear Mixed Models

    Scalable Subset Selection in Linear Mixed Models , author=. arXiv preprint arXiv:2506.20425 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  29. [29]

    Journal of Multivariate Analysis , volume=

    Model selection in linear mixed effect models , author=. Journal of Multivariate Analysis , volume=. 2012 , publisher=

    work page 2012

  30. [30]

    Statistica Sinica , volume=

    Moment-based method for random effects selection in linear mixed models , author=. Statistica Sinica , volume=

    work page

  31. [31]

    Proceedings of the 25th international conference on Machine learning , pages=

    Bolasso: model consistent lasso estimation through the bootstrap , author=. Proceedings of the 25th international conference on Machine learning , pages=

    work page

  32. [32]

    IEEE transactions on information theory , volume=

    Sharp thresholds for High-Dimensional and noisy sparsity recovery using _1 -Constrained Quadratic Programming (Lasso) , author=. IEEE transactions on information theory , volume=. 2009 , publisher=

    work page 2009

  33. [33]

    Information and Inference: A Journal of the IMA , volume=

    Moving beyond sub-Gaussianity in high-dimensional statistics: Applications in covariance estimation and linear regression , author=. Information and Inference: A Journal of the IMA , volume=. 2022 , publisher=

    work page 2022

  34. [34]

    BMC medical research methodology , volume=

    joineRML: a joint model and software package for time-to-event and multivariate longitudinal outcomes , author=. BMC medical research methodology , volume=. 2018 , publisher=

    work page 2018

  35. [35]

    The Lancet , volume=

    The SANAD study of effectiveness of carbamazepine, gabapentin, lamotrigine, oxcarbazepine, or topiramate for treatment of partial epilepsy: an unblinded randomised controlled trial , author=. The Lancet , volume=. 2007 , publisher=

    work page 2007

  36. [36]

    Epilepsia , volume=

    Quality-of-life outcomes of initiating treatment with standard and newer antiepileptic drugs in adults with new-onset epilepsy: findings from the SANAD trial , author=. Epilepsia , volume=. 2015 , publisher=

    work page 2015

  37. [37]

    arXiv preprint arXiv:2304.08020 , year=

    Sparse positive-definite estimation for covariance matrices with repeated measurements , author=. arXiv preprint arXiv:2304.08020 , year=

    work page arXiv

  38. [38]

    Journal of computational and Graphical Statistics , volume=

    Computational strategies for multivariate linear mixed-effects models with missing values , author=. Journal of computational and Graphical Statistics , volume=. 2002 , publisher=

    work page 2002

  39. [39]

    Biometrics , volume=

    Multivariate multilevel nonlinear mixed effects models for timber yield predictions , author=. Biometrics , volume=. 2004 , publisher=

    work page 2004

  40. [40]

    2008 , publisher=

    Econometrics , author=. 2008 , publisher=

    work page 2008

  41. [41]

    Journal of Computational and Graphical Statistics , volume=

    Fixed and random effects selection by REML and pathwise coordinate optimization , author=. Journal of Computational and Graphical Statistics , volume=. 2013 , publisher=

    work page 2013

  42. [42]

    Foundations and trends

    Proximal algorithms , author=. Foundations and trends. 2014 , publisher=

    work page 2014

  43. [43]

    Mathematical programming , volume=

    Gradient methods for minimizing composite functions , author=. Mathematical programming , volume=. 2013 , publisher=

    work page 2013

  44. [44]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=

    Regression shrinkage and selection via the lasso , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 1996 , publisher=

    work page 1996

  45. [45]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=

    Model selection and estimation in regression with grouped variables , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2006 , publisher=

    work page 2006

  46. [46]

    Journal of the American statistical Association , volume=

    Variable selection via nonconcave penalized likelihood and its oracle properties , author=. Journal of the American statistical Association , volume=. 2001 , publisher=

    work page 2001

  47. [47]

    Annals of Statistics , volume=

    Nearly unbiased variable selection under minimax concave penalty , author=. Annals of Statistics , volume=. 2010 , publisher=

    work page 2010

  48. [48]

    Journal of the American statistical association , volume=

    The adaptive lasso and its oracle properties , author=. Journal of the American statistical association , volume=. 2006 , publisher=

    work page 2006

  49. [49]

    Random Matrices: Theory and Applications , volume=

    Matrix deviation inequality for -p norm , author=. Random Matrices: Theory and Applications , volume=. 2023 , publisher=

    work page 2023

  50. [50]

    2011 , publisher=

    Statistics for high-dimensional data: methods, theory and applications , author=. 2011 , publisher=

    work page 2011

  51. [51]

    2018 , publisher=

    High-dimensional probability: An introduction with applications in data science , author=. 2018 , publisher=

    work page 2018

  52. [52]

    Nephrology Dialysis Transplantation , volume=

    Variation in intravenous iron use internationally and over time: the Dialysis Outcomes and Practice Patterns Study (DOPPS) , author=. Nephrology Dialysis Transplantation , volume=. 2013 , publisher=

    work page 2013

  53. [53]

    BMC nephrology , volume=

    Evaluating the effectiveness of IV iron dosing for anemia management in common clinical practice: results from the Dialysis Outcomes and Practice Patterns Study (DOPPS) , author=. BMC nephrology , volume=. 2017 , publisher=

    work page 2017

  54. [54]

    American Journal of Kidney Diseases , volume=

    Analytical and biological variation in measures of anemia and iron status in patients treated with maintenance hemodialysis , author=. American Journal of Kidney Diseases , volume=. 2010 , publisher=

    work page 2010

  55. [55]

    Kidney international , volume=

    Interdialytic weight gain as a marker of blood pressure, nutrition, and survival in hemodialysis patients , author=. Kidney international , volume=. 2005 , publisher=

    work page 2005

  56. [56]

    Kidney and Blood Pressure Research , volume=

    Causes and consequences of interdialytic weight gain , author=. Kidney and Blood Pressure Research , volume=. 2016 , publisher=

    work page 2016