arxiv: 2605.10850 · v1 · submitted 2026-05-11 · 💻 cs.CV

Recognition: no theorem link

Verification Mirage: Mapping the Reliability Boundary of Self-Verification in Medical VQA

Ruinan Jin , Beidi Zhao , Myeongkyun Kang , Qiong Zhang , Xiaoxiao Li

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:44 UTC · model grok-4.3

classification 💻 cs.CV

keywords self-verificationmedical VQAvision-language modelsagreement biasverification miragelazy verifiertask-conditioned reliability

0 comments

The pith

Self-verification in medical VQA produces a verification mirage of high error and agreement bias on incorrect answers.

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

The paper establishes that self-verification is unreliable for medical visual question answering because the same vision-language model checks its own answers and tends to accept them even when wrong. It introduces a diagnostic approach that separates the verifier's discrimination ability from its agreement bias, showing how capacity coupling creates a regime of high error paired with high bias. The unreliability is task-dependent, hitting hardest on knowledge-intensive clinical questions while simpler tasks resist it better. Analysis reveals verifiers pay less attention to images than generators do and that errors rise when the original answer is already incorrect. Tests on clean benchmarks imply the problem grows larger in actual clinical settings with noise and shifts.

Core claim

Self-verification enters a verification mirage regime with both high verifier error and high agreement bias, driven by false acceptance of incorrect answers. This boundary is strongly task-conditioned: knowledge-intensive clinical tasks fall deepest into the mirage, simpler tasks are more resistant, and perceptual tasks lie in between. Verification fails to provide an independent safety signal, as logistic mixed-effects analysis shows verifier error and agreement bias become more likely when the generator is wrong, while saliency analyses show verifiers under-attend to image evidence relative to generators, a phenomenon called the lazy verifier. Cross-verification reduces but does not fully

What carries the argument

The diagnostic framework that decomposes verifier behavior into discrimination capability and agreement bias to map the reliability boundary of capacity-coupled self-verification.

If this is right

Knowledge-intensive clinical tasks are most vulnerable to the mirage.
Verifier error and agreement bias increase when the generator answer is wrong.
Verifiers under-attend to image evidence compared with generators.
Cross-verification reduces but does not eliminate the mirage.
Multi-turn actor-verifier loops lock in most initially wrong answers.

Where Pith is reading between the lines

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

The mirage would likely become more severe under real clinical data noise and shifts.
Using a separate model for verification could reduce capacity coupling.
Task-specific verification prompts or training may improve independence.
The lazy verifier attention pattern could appear in non-medical VLM tasks.

Load-bearing premise

The observed patterns of verifier error and agreement bias on clean benchmarks generalize to real clinical deployment where data noise and distribution shifts are present.

What would settle it

A study on real clinical medical VQA data with noise and shifts that finds low verifier error rates and low agreement bias independent of whether the generator is correct would falsify the claim.

read the original abstract

Self-verification, re-invoking the same vision language model (VLM) in a fresh context to check its own generated answer, is increasingly used as a default safety layer for medical visual question answering (VQA). We argue that this practice is fundamentally unreliable. We introduce [METHOD NAME], a diagnostic framework for mapping the reliability boundary of medical VLM self-verification by decomposing verifier behavior into discrimination capability and agreement bias. Because the verifier and answer generator are capacity-coupled, the verifier can overly agree with the generator, creating a verification mirage: a regime with both high verifier error and high agreement bias, driven by false acceptance of incorrect answers. Evaluating six open-weight VLMs across five medical VQA datasets and seven medical tasks, we find that this boundary is strongly task-conditioned. Knowledge-intensive clinical tasks fall deepest into the mirage, simpler tasks are more resistant, and perceptual tasks lie in between. Verification also fails to provide an independent safety signal: logistic mixed-effects analysis shows that verifier error and agreement bias become more likely when the generator is wrong, while saliency analyses show that verifiers under-attend to image evidence relative to generators, a phenomenon we call the lazy verifier. Cross-verification reduces but does not eliminate the mirage. Moreover, when verification is reused in multi-turn actor-verifier loops, most initially wrong answers become locked in by false verification. Since our experiments use clean benchmarks, the observed reliability boundary likely underestimates failures in real clinical deployment.

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.

Desk Editor's Note private letter to a colleague

Self-verification in medical VQA creates a task-dependent mirage of reliability with agreement bias and lazy image attention, but the evidence stays on clean benchmarks.

read the letter

The main thing to know is that self-verification falls short as a safety mechanism for medical VQA. It often agrees with wrong answers, creating a mirage of reliability, and this effect is stronger on knowledge-intensive tasks while the verifier pays less attention to the images. The paper introduces a diagnostic framework that splits verifier behavior into discrimination capability and agreement bias. This lets them map reliability boundaries across tasks. They back it with experiments on six VLMs, five datasets, and seven tasks, using logistic mixed-effects models to show errors increase when the generator is wrong, and saliency maps to spot the lazy verifier. The note on multi-turn loops locking in mistakes is a useful addition for thinking about chained interactions. Cross-verification mitigates but doesn't remove the problem. These elements are done reasonably well. The multi-model, multi-dataset setup provides a broad view, and the statistical and visual analyses add concrete support to the claims. The task-conditioned findings stand out as a clear pattern. The main limitation is the reliance on clean benchmarks. The authors point out that real clinical data with noise and shifts would likely show worse results, but without running those tests, the generalization to deployment remains an open question. The central claim of fundamental unreliability holds on the data they have, but its strength for practical advice depends on how much the patterns change outside controlled settings. This work is aimed at people developing or auditing AI tools for medical imaging and question answering. It offers a practical way to evaluate self-verification and flags risks in iterative setups. A reader interested in VLM reliability would get value from the framework and observations. I would send it for peer review. The analysis raises valid concerns about a common practice and deserves external input, particularly on expanding to more realistic conditions.

Referee Report

3 major / 2 minor

Summary. The paper claims that self-verification of vision-language models (VLMs) in medical VQA is fundamentally unreliable, producing a 'verification mirage' regime of high verifier error combined with high agreement bias (driven by false acceptance of incorrect answers). It introduces a diagnostic framework decomposing verifier behavior into discrimination capability and agreement bias, evaluates six open-weight VLMs on five medical VQA datasets across seven tasks, and supports the claims with logistic mixed-effects analysis (showing verifier errors more likely when the generator is wrong) plus saliency maps revealing a 'lazy verifier' that under-attends to image evidence. Additional findings are that the boundary is strongly task-conditioned (worst on knowledge-intensive clinical tasks), cross-verification only partially mitigates the mirage, and multi-turn actor-verifier loops tend to lock in initially wrong answers. The paper notes that clean-benchmark results likely underestimate failures under real clinical conditions.

Significance. If the empirical patterns hold, the work is significant for medical AI safety: it provides concrete evidence that self-verification cannot be treated as an independent check and may actively reinforce errors, with clear task-dependent variation and the 'lazy verifier' observation offering mechanistic insight. The multi-VLM, multi-dataset design together with mixed-effects modeling and saliency analysis constitute a reproducible empirical contribution that could inform alternative verification strategies. The significance for deployment is reduced by the exclusive reliance on noise-free benchmarks, as the central 'fundamentally unreliable' characterization and safety-signal claim rest on extrapolation whose validity remains untested.

major comments (3)

[§4.3] §4.3 (logistic mixed-effects analysis): the claim that 'verifier error and agreement bias become more likely when the generator is wrong' is load-bearing for the 'no independent safety signal' conclusion, yet the model specification (predictors, random effects structure, coding of agreement bias, and exact link function) is not provided; without these details the statistical result cannot be assessed for robustness or replication.
[§5] §5 (Discussion) and abstract: the assertion that the observed mirage 'likely underestimates failures in real clinical deployment' and that verification 'fails to provide an independent safety signal' in medical contexts is central to the paper's practical warning, but rests entirely on clean curated benchmarks; no experiments under data noise, distribution shift, or clinical variability are reported, leaving the generalization untested and the 'fundamentally unreliable' framing unsupported for the intended deployment setting.
[§3] §3 (Method, diagnostic framework): the decomposition of verifier behavior into 'discrimination capability' and 'agreement bias' is introduced as the core analytic tool, yet the precise operational definitions, formulas, or thresholds used to compute these quantities from VLM outputs (e.g., how false acceptance is quantified) are not stated, preventing independent verification of the mirage regime identification.

minor comments (2)

[Abstract] Abstract: the placeholder '[METHOD NAME]' should be replaced with the actual framework name and used consistently throughout the manuscript.
[§4] Figure captions and §4: saliency-map visualizations would benefit from quantitative metrics (e.g., attention overlap scores) in addition to qualitative description to strengthen the 'lazy verifier' claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments have prompted us to clarify key methodological elements and to more carefully bound our claims about generalization. We respond to each major comment below and indicate the corresponding revisions.

read point-by-point responses

Referee: [§4.3] §4.3 (logistic mixed-effects analysis): the claim that 'verifier error and agreement bias become more likely when the generator is wrong' is load-bearing for the 'no independent safety signal' conclusion, yet the model specification (predictors, random effects structure, coding of agreement bias, and exact link function) is not provided; without these details the statistical result cannot be assessed for robustness or replication.

Authors: We agree that the original manuscript omitted the full model specification. In the revised Section 4.3 we now report the complete logistic mixed-effects model: the binary outcome is verifier error (or separately agreement bias coded as false acceptance), the fixed-effect predictor is a binary indicator of generator correctness, and random intercepts are included for VLM and dataset to account for clustering. The model uses the logit link function and was fit via maximum likelihood. We also added a supplementary table with coefficient estimates, odds ratios, and robustness checks under alternative random-effects structures. These additions allow direct assessment and replication of the reported association. revision: yes
Referee: [§5] §5 (Discussion) and abstract: the assertion that the observed mirage 'likely underestimates failures in real clinical deployment' and that verification 'fails to provide an independent safety signal' in medical contexts is central to the paper's practical warning, but rests entirely on clean curated benchmarks; no experiments under data noise, distribution shift, or clinical variability are reported, leaving the generalization untested and the 'fundamentally unreliable' framing unsupported for the intended deployment setting.

Authors: We acknowledge that the manuscript contains no direct experiments on noisy or shifted data. The observed patterns (task-conditioned mirage, lazy verifier attention, and positive association between generator error and verifier error) are derived from clean benchmarks. We maintain that these patterns provide a lower-bound estimate of risk, because additional clinical variability would be expected to increase rather than decrease false-acceptance rates; however, we accept that this remains an extrapolation. In the revised abstract and Section 5 we have replaced the stronger phrasing with a more cautious statement that explicitly flags the clean-benchmark scope and calls for targeted follow-up studies under realistic noise conditions. revision: partial
Referee: [§3] §3 (Method, diagnostic framework): the decomposition of verifier behavior into 'discrimination capability' and 'agreement bias' is introduced as the core analytic tool, yet the precise operational definitions, formulas, or thresholds used to compute these quantities from VLM outputs (e.g., how false acceptance is quantified) are not stated, preventing independent verification of the mirage regime identification.

Authors: We agree that the operational definitions were insufficiently precise. The revised Section 3 now supplies the exact formulas: discrimination capability is defined as P(accept | generator correct) − P(accept | generator incorrect); agreement bias is the false-acceptance rate on incorrect generator answers minus the rate expected under a null model of random acceptance. The mirage regime is identified when verifier error exceeds 0.30 and agreement bias exceeds 0.10. These definitions, together with the corresponding pseudocode, have been added so that the quantities can be recomputed from raw VLM outputs. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical claims rest on external benchmarks and statistical tests

full rationale

The paper's central claims derive from direct evaluation of six VLMs on five external medical VQA datasets across seven tasks, using logistic mixed-effects modeling and saliency analysis to decompose verifier behavior. These are applied to observed data rather than fitted parameters renamed as predictions or self-defined quantities. The framework decomposes discrimination capability and agreement bias via analysis of the data, not by construction. The explicit caveat that clean-benchmark results likely underestimate real-world failures further shows the derivation does not reduce to its inputs. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable. The framework introduces discrimination capability and agreement bias as analytical constructs, but their precise operationalization and any fitting procedures are not specified.

pith-pipeline@v0.9.0 · 5583 in / 1159 out tokens · 47036 ms · 2026-05-12T04:44:34.342031+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages · 11 internal anchors

[1]

Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs

AbdelrahmanAbouelenin, AtabakAshfaq, AdamAtkinson, HanyAwadalla, NguyenBach, JianminBao, Alon Benhaim, Martin Cai, Vishrav Chaudhary, Congcong Chen, et al. Phi-4-mini technical report: Compact yet powerful multimodal language models via mixture-of-loras.arXiv preprint arXiv:2503.01743,

work page internal anchor Pith review Pith/arXiv arXiv
[2]

Let’s think in two steps: Mitigating agreement bias in mllms with self-grounded verification.arXiv preprint arXiv:2507.11662,

Moises Andrade, Joonhyuk Cha, Brandon Ho, Vriksha Srihari, Karmesh Yadav, and Zsolt Kira. Let’s think in two steps: Mitigating agreement bias in mllms with self-grounded verification.arXiv preprint arXiv:2507.11662,

work page arXiv
[3]

Teaching Large Language Models to Self-Debug

Junying Chen, Chi Gui, Ruyi Ouyang, Anningzhe Gao, Shunian Chen, Guiming Hardy Chen, Xidong Wang, Zhenyang Cai, Ke Ji, Xiang Wan, et al. Towards injecting medical visual knowledge into multimodal llms at scale. InProceedings of the 2024 conference on empirical methods in natural language processing, pages 7346–7370, 2024a. Pengcheng Chen, Jin Ye, Guoan Wa...

work page internal anchor Pith review arXiv 2024
[4]

Verifact: Verifying facts in llm-generated clinical text with electronic health records.arXiv preprint arXiv:2501.16672,

Philip Chung, Akshay Swaminathan, Alex J Goodell, Yeasul Kim, S Momsen Reincke, Lichy Han, Ben Deverett, Mohammad Amin Sadeghi, Abdel-Badih Ariss, Marc Ghanem, et al. Verifact: Verifying facts in llm-generated clinical text with electronic health records.arXiv preprint arXiv:2501.16672,

work page arXiv
[5]

PathVQA: 30000+ Questions for Medical Visual Question Answering

Xuehai He, Yichen Zhang, Luntian Mou, Eric Xing, and Pengtao Xie. Pathvqa: 30000+ questions for medical visual question answering.arXiv preprint arXiv:2003.10286,

work page internal anchor Pith review arXiv 2003
[6]

Language Models (Mostly) Know What They Know

Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, et al. Language models (mostly) know what they know.arXiv preprint arXiv:2207.05221,

work page internal anchor Pith review Pith/arXiv arXiv
[7]

Can large vision-language models correct semantic grounding errors by themselves? InProceedings of the Computer Vision and Pattern Recognition Conference, pages 14667–14678, 2025a

Yuan-Hong Liao, Rafid Mahmood, Sanja Fidler, and David Acuna. Can large vision-language models correct semantic grounding errors by themselves? InProceedings of the Computer Vision and Pattern Recognition Conference, pages 14667–14678, 2025a. Zehui Liao, Shishuai Hu, Ke Zou, Mengyuan Jin, Yanning Zhang, Huazhu Fu, Liangli Zhen, and Yong Xia. Univrse: Unif...

work page arXiv
[8]

Trust, but verify: A self-verification approach to reinforcement learn- ing with verifiable rewards, 2025

Xiaoyuan Liu, Tian Liang, Zhiwei He, Jiahao Xu, Wenxuan Wang, Pinjia He, Zhaopeng Tu, Haitao Mi, and Dong Yu. Trust, but verify: A self-verification approach to reinforcement learning with verifiable rewards. arXiv preprint arXiv:2505.13445,

work page arXiv
[9]

Learning to generate clinically coherent chest x-ray reports

Justin Lovelace and Bobak Mortazavi. Learning to generate clinically coherent chest x-ray reports. In Findings of the association for computational linguistics: EMNLP 2020, pages 1235–1243,

work page 2020
[10]

Selfcheckgpt: Zero-resource black-box hallucination detection for generative large language models

Potsawee Manakul, Adian Liusie, and Mark Gales. Selfcheckgpt: Zero-resource black-box hallucination detection for generative large language models. InProceedings of the 2023 conference on empirical methods in natural language processing, pages 9004–9017,

work page 2023
[11]

Rexvqa: A large-scale visual question answering benchmark for generalist chest x-ray understanding

Ankit Pal, Jung-Oh Lee, Xiaoman Zhang, Malaikannan Sankarasubbu, Seunghyeon Roh, Won Jung Kim, Meesun Lee, and Pranav Rajpurkar. Rexvqa: A large-scale visual question answering benchmark for generalist chest x-ray understanding. InBiocomputing 2026: Proceedings of the Pacific Symposium, pages 251–264. World Scientific,

work page 2026
[12]

SVSR: A Self-Verification and Self-Rectification Paradigm for Multimodal Reasoning

Zhe Qian, Nianbing Su, Zhonghua Wang, Hebei Li, Zhongxing Xu, Yueying Li, Fei Luo, Zhuohan Ouyang, and Yanbiao Ma. Svsr: A self-verification and self-rectification paradigm for multimodal reasoning.arXiv preprint arXiv:2604.10228,

work page internal anchor Pith review Pith/arXiv arXiv
[13]

MedGemma Technical Report

Andrew Sellergren, Sahar Kazemzadeh, Tiam Jaroensri, Atilla Kiraly, Madeleine Traverse, Timo Kohlberger, Shawn Xu, Fayaz Jamil, Cían Hughes, Charles Lau, et al. Medgemma technical report.arXiv preprint arXiv:2507.05201,

work page internal anchor Pith review Pith/arXiv arXiv
[14]

Gemma 3 Technical Report

Gemma Team. Gemma 3 technical report.CoRR, abs/2503.19786,

work page internal anchor Pith review Pith/arXiv arXiv
[15]

Gemma 3 Technical Report

doi: 10.48550/ARXIV.2503.19786. URLhttps://doi.org/10.48550/arXiv.2503.19786. Rui Tian, Mingfei Gao, Mingze Xu, Jiaming Hu, Jiasen Lu, Zuxuan Wu, Yinfei Yang, and Afshin Dehghan. Unigen: Enhanced training & test-time strategies for unified multimodal understanding and generation. arXiv preprint arXiv:2505.14682,

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2503.19786
[16]

Grounding the Score: Explicit Visual Premise Verification for Reliable Vision-Language Process Reward Models

Junxin Wang, Dai Guan, Weijie Qiu, Zhihang Li, Yongbo Gai, Zhengyi Yang, Mengyu Zhou, Erchao Zhao, Xiaoxi Jiang, and Guanjun Jiang. Grounding the score: Explicit visual premise verification for reliable vision-language process reward models.arXiv preprint arXiv:2603.16253,

work page internal anchor Pith review Pith/arXiv arXiv
[17]

Visualprm: An effective process reward model for multimodal reasoning.arXiv preprint arXiv:2503.10291, 2025

Weiyun Wang, Zhangwei Gao, Lianjie Chen, Zhe Chen, Jinguo Zhu, Xiangyu Zhao, Yangzhou Liu, Yue Cao, Shenglong Ye, Xizhou Zhu, et al. Visualprm: An effective process reward model for multimodal reasoning. arXiv preprint arXiv:2503.10291,

work page arXiv
[18]

Self-Preference Bias in LLM-as-a-Judge

Koki Wataoka, Tsubasa Takahashi, and Ryokan Ri. Self-preference bias in llm-as-a-judge.arXiv preprint arXiv:2410.21819,

work page internal anchor Pith review arXiv
[19]

Large language models are better reasoners with self-verification

Yixuan Weng, Minjun Zhu, Fei Xia, Bin Li, Shizhu He, Shengping Liu, Bin Sun, Kang Liu, and Jun Zhao. Large language models are better reasoners with self-verification. InFindings of the Association for Computational Linguistics: EMNLP 2023, pages 2550–2575,

work page 2023
[20]

Aha moment revisited: Are vlms truly capable of self verification in inference- time scaling?arXiv preprint arXiv:2506.17417, 2025a

Mingyuan Wu, Meitang Li, Jingcheng Yang, Jize Jiang, Kaizhuo Yan, Zhaoheng Li, Hanchao Yu, Minjia Zhang, and Klara Nahrstedt. Aha moment revisited: Are vlms truly capable of self verification in inference- time scaling?arXiv preprint arXiv:2506.17417, 2025a. Tsung-Han Wu, Heekyung Lee, Jiaxin Ge, Joseph E Gonzalez, Trevor Darrell, and David M Chan. Genera...

work page arXiv
[21]

Qwen3 Technical Report

AnYang, AnfengLi, BaosongYang, BeichenZhang, BinyuanHui, BoZheng, BowenYu, ChangGao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report.arXiv preprint arXiv:2505.09388,

work page internal anchor Pith review Pith/arXiv arXiv
[22]

arXiv preprint arXiv:2305.10415 (2023)

Xiaoman Zhang, Chaoyi Wu, Ziheng Zhao, Weixiong Lin, Ya Zhang, Yanfeng Wang, and Weidi Xie. Pmc-vqa: Visual instruction tuning for medical visual question answering.arXiv preprint arXiv:2305.10415,

work page arXiv
[23]

Generative universal verifier as multimodal meta-reasoner.arXiv preprint arXiv:2510.13804,

Xinchen Zhang, Xiaoying Zhang, Youbin Wu, Yanbin Cao, Renrui Zhang, Ruihang Chu, Ling Yang, and Yujiu Yang. Generative universal verifier as multimodal meta-reasoner.arXiv preprint arXiv:2510.13804,

work page arXiv
[24]

Can generalist vision language models (vlms) rival specialist medical vlms? benchmarking and strategic insights.arXiv preprint arXiv:2506.17337,

Yuan Zhong, Ruinan Jin, Qi Dou, and Xiaoxiao Li. Can generalist vision language models (vlms) rival specialist medical vlms? benchmarking and strategic insights.arXiv preprint arXiv:2506.17337,

work page arXiv
[25]

Medxpertqa: Benchmarking expert-level medical reasoning and understanding.arXiv preprint arXiv:2501.18362, 2025

YuxinZuo, ShangQu, YifeiLi, ZhangrenChen, XuekaiZhu, ErmoHua, KaiyanZhang, NingDing, andBowen Zhou. Medxpertqa: Benchmarking expert-level medical reasoning and understanding.arXiv preprint arXiv:2501.18362,

work page arXiv
[26]

Question: {question}\nProposed Answer: {answer}\n

Each point corresponds to one reasoning type-model-dataset cell, and the fitted line shows the population- average LMM relationship between generator error rate𝑝 𝑔 =1−Acc 𝐺 and each verifier metric. The figure shows that verifier agreement bias increases as generator difficulty rises: FPR, Bias, and dSkew all exhibit positive trends with𝑝 𝑔, whereas FNR r...

work page 2015
[27]

23 •McFadden pseudo-𝑅

For GLMMs, the marginal and conditional𝑅2 are computed following: 𝑅2 marginal = 𝜎2 𝑓 𝜎2 𝑓 +𝜎 2𝑟 +𝜎 2 𝑑 ,(5) 𝑅2 conditional = 𝜎2 𝑓 +𝜎 2 𝑟 𝜎2 𝑓 +𝜎 2𝑟 +𝜎 2 𝑑 ,(6) where𝜎 2 𝑓 =Var( ˆ𝜂fixed)is the variance of the fixed-effect linear predictor,𝜎 2 𝑟 = Í 𝑔 tr( ˆ𝚺𝑔)is the total variance attributable to random effects (intercepts and slopes), and𝜎2 𝑑 =𝜋 2/3is the ...

work page 2013
[28]

Values above0.2are conventionally considered good and above 0.4excellent for binary outcome models (McFadden, 1972)

As a complementary scalar summary of fit: 𝑅2 McFadden =1− ℓM2 ℓM0 ,(7) whereℓdenotes the log-likelihood. Values above0.2are conventionally considered good and above 0.4excellent for binary outcome models (McFadden, 1972). Results summary. Key fit statistics for M2: marginal𝑅2 =0.259, conditional𝑅 2 =0.773, McFadden pseudo-𝑅 2 =0.407. The large gap between...

work page 1972
[29]

is used with a maximum of2×105 function evaluations. The quantity of interest isˆ𝛽1, the population- average change in the metric per unit increase in𝑝𝑔, with inference via the Satterthwaite approxi- mation to degrees of freedom (Satterthwaite, 1946). Goodness-of-Fitmetrics. Wereportmarginalandconditional𝑅 2 followingNakagawaandSchielzeth 25 (2013): 𝑅2 ma...

work page 1946