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REVIEW 5 major objections 6 minor 21 references

Euclidean Ideal Point Estimation From Roll-Call Data via Distance-Based Bipartite Network Models

T0 review · 5 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The paper claims that replacing the squared-distance and Gaussian utility functions of standard ideal point models with Euclidean distance in a shared legislator–bill space restores metric structure and recovers factional and coalition stru

desk verdict The metric argument is correct, but the paper's comparative evidence is confounded by extra legislator intercepts and a placeholder replication link; the application is suggestive, not demonstrative. read the letter →

arxiv 2512.11610 v2 pith:B4AUFTMF submitted 2025-12-12 stat.AP

Seungju Lee , In Kyun Kim , Jong Hee Park , Ick Hoon Jin This is my paper · ORCID
classification stat.AP MSC 62H3062P25
keywords idealpointestimationroll-callvotingEuclideandistancemetricspacestriangleinequalitybipartitenetworkslatentspaceitemresponsemodelcoalitionstructure
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

This paper argues that standard ideal point estimators such as NOMINATE and Bayesian IRT build on squared or Gaussian utility functions that fail the triangle inequality, so the distances they produce are not true distances. When researchers use those coordinates to measure party cohesion or identify factions, the geometry can misrepresent actual voting coalitions: in simulated four-faction legislatures, both methods collapse factions into two party blobs. The authors propose Euclidean LSIRM, which embeds legislators and bills together in a Euclidean space and makes vote probability decline with straight-line distance, restoring metric properties. In simulations and in the 118th U.S. House, the model separates factions, improves vote prediction (accuracy 0.80 versus 0.72; error-reduction metric 0.45 versus 0.23), and lets bill locations act as anchors that explain the meaning of the dimensions. The paper therefore aims to show that metric structure is a precondition for valid clustering and spatial interpretation of roll-call data.

What carries the argument

The central object is the Euclidean-distance bipartite latent space model (Euclidean LSIRM): a joint embedding of legislators and bills as nodes in a bipartite network, with voting probability governed by logit(P(y = 1)) = theta_i + beta_j − gamma||z_i − w_j||. The key identity doing the work is that the L2 norm satisfies the triangle inequality via Cauchy–Schwarz, whereas the quadratic and Gaussian utility functions of BIRT and NOMINATE do not. This single property converts estimated positions into a genuine metric space, making distances, ratios, and cluster silhouettes interpretable.

What would settle it

Generate roll-call data from the quadratic/BIRT utility process with known faction structure and compare recovery: if Euclidean LSIRM does not match or beat BIRT's silhouette scores on data generated from BIRT's own mechanism, then the reported cluster-recovery advantage is specific to the Euclidean data-generating assumption, not a general property of metric distances.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the choice between squared distance and Euclidean distance determines whether ideal point estimates can support distance-based inference. The model specifies logit(P(y_ij = 1)) = theta_i + beta_j − gamma||z_i − w_j||, with legislators z_i and bills w_j embedded in a common K-dimensional Euclidean space. Because Euclidean distance satisfies the triangle inequality, distances become cardinally interpretable and clustering statistics are valid; the simulations and application show that factions invisible to non-metric methods become spatially distinct. The paper also finds that jointly embedding bills, rather than reducing them to uninterp

Load-bearing premise

The paper's central claim depends on the assumption that actual roll-call voting probabilities are a monotone decreasing function of Euclidean distance in a shared latent space (Eq. 3)—the very process used in its simulations—so if the true response mechanism is squared-distance or otherwise non-Euclidean, the claimed advantages would not follow.

Editorial extensions

If this is right

  • Clustering and faction-identification from roll-call coordinates become valid because the triangle inequality prevents intransitive proximity artifacts.
  • Party cohesion and polarization comparisons across parties and dimensions become meaningful because Euclidean distances are on a common, cardinal scale.
  • Joint legislator–bill embedding gives a direct way to interpret latent dimensions by reading the bills that anchor each region of the space.
  • Predictive performance improves on close votes, suggesting that metric structure carries signal that non-metric scaling misses.
  • Euclidean distance can represent certain homophilous structures with lower latent dimensionality than inner-product models, yielding more parsimonious embeddings.

Reading between the lines

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

  • The critique generalizes: any study that clusters points using squared distances—network embeddings, preference maps, similarity scales—faces the same triangle-inequality distortion, so the argument is a concrete instance of a broader measurement principle.
  • The simulation evidence should be read with care: data were generated from the same Euclidean-distance process the model assumes, so the cluster-recovery results demonstrate internal consistency more than external validity against real legislative behavior.
  • A testable extension: if metric structure is the operative advantage, the gap in faction recovery between Euclidean LSIRM and non-metric estimators should widen as intra-party factionalism increases; this could be checked across multiple Congresses or assemblies.
  • The bill-anchor interpretation could be quantified by validating whether bills supported by both far-left and far-right factions cluster together out-of-sample, as the establishment–outsider reading of the second dimension predicts.
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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

5 major / 6 minor

Summary. The paper proposes a Euclidean-distance latent space item response model (LSIRM) for roll-call voting, treating legislators and bills as nodes in a bipartite network embedded in a common metric space. The central claim is that conventional ideal point methods (BIRT, NOMINATE) rely on quadratic or Gaussian utility functions that violate the triangle inequality, generating non-metric 'distances' that distort coalition/cluster recovery, whereas Euclidean LSIRM restores metric structure and improves both cluster recovery and vote prediction. The paper presents a metric-property proof for Euclidean distance, three simulation studies comparing LSIRM with BIRT, and an application to the 118th U.S. House reporting higher classification accuracy and APRE, plus bill embeddings that reveal an establishment–outsider cleavage.

Significance. If the claims were fully supported, the paper would offer a useful alternative to standard ideal point estimators, particularly for researchers interested in coalition structure and interpretable bill locations. The joint embedding of legislators and bills in a shared Euclidean space is a sensible extension of existing latent space models, and the geometric interpretation of bills as anchors is a genuine strength. The metric proof itself is correct, though standard. However, the current evidence is not sufficient to establish the paper's central claims: the theoretical argument conflates utility functions with distances, the model comparison is confounded by extra legislator intercepts, the empirical evaluation is in-sample, and the simulation DGP is under-specified. These issues are load-bearing because they bear directly on the claim that Euclidean distance—rather than more flexible parameterization—explains the reported gains.

major comments (5)
  1. [Section 2.2, Eqs. (1)–(3)] The theoretical motivation conflates utility functions with distances. In Eq. (1), proximity voting is defined as U_i(y) = -d(x_i,y) + ε, where d is explicitly a metric. Conventional BIRT and NOMINATE use squared or Gaussian transforms of Euclidean distance as utility functions; the latent positions of legislators and bills still live in a Euclidean space, and the Euclidean distances between those positions satisfy the triangle inequality. The demonstration that dQ(x,y)=(x-y)^2 or a Gaussian 'similarity' violates the triangle inequality applies to the transformed utility, not to the distance between ideal points. The paper's conclusion that 'when distances lack metric validity' (Section 2.2) or that BIRT/NOMINATE produce 'non-metric distances' is therefore not established. This is a load-bearing issue because the paper's title and main claim are about 'restoring metric structure.'
  2. [Section 3.2 vs. Section 2.2; Section 5.2] The model comparison is confounded. LSIRM in Eq. (3) includes legislator-specific intercepts θ_i, bill intercepts β_j, a logit link, and Euclidean distance. The BIRT comparator in Section 2.2 is P(y=1)=Φ(β_j^T x_i - α_j), which has no legislator intercept and uses a probit link. LSIRM therefore has N additional free parameters (the θ_i) as well as a different link function. The reported improvements—silhouette 0.861 vs. 0.778 (Section 4.2), accuracy 0.80 vs. 0.72 and APRE 0.45 vs. 0.23 (Section 5.2)—may be due to this added flexibility rather than to the Euclidean distance specification. A fair comparison would estimate a Euclidean-distance model without θ_i, or add legislator intercepts to the BIRT comparator, or otherwise isolate the distance specification.
  3. [Section 5.2] The empirical predictive metrics are in-sample. The paper reports classification accuracy and APRE for the 118th House but does not describe any train/test split, cross-validation, or posterior predictive checking. In-sample fit is expected to favor the more parameterized model, so the reported gains do not constitute evidence of superior predictive performance. The authors should provide out-of-sample evaluation (e.g., holdout roll calls or cross-validated posterior prediction).
  4. [Section 4] The simulation DGP is under-specified, preventing assessment of circularity. The text says, e.g., 'Targeted clusters vote Yea with probability p; non-targeted clusters vote Yea with probability q' (Section 4.2) and 'legislators who vote Yea with probability p rather than following their bloc' (Section 4.1), but it never states the full generative model. If data were generated from Eq. (3) with known latent positions, then LSIRM's cluster recovery is partly a self-consistency check. If data were generated from a simpler block model, the mechanism linking that DGP to LSIRM's distance structure is unclear. Exact generative equations, including the role of γ and the latent positions, must be provided.
  5. [Data Availability Statement] The data availability statement contains a placeholder URL ('https://doi.org/link', p. 18), which is not acceptable for a journal submission. The replication archive and code must be made available at a valid DOI or repository.
minor comments (6)
  1. [Section 3.3] The conditional distributions are garbled. For example, π(θ_i) is written as proportional to a product over all i and j, and the notation 'NY' is ambiguous. The sentence 'This posterior kernel cannot be expressed with standard distribution...' is confusing. The full conditionals should be rewritten clearly with proper indices and normalizing constants.
  2. [Sections 1 and 4] The abstract and introduction claim that 'NOMINATE and BIRT compress factions' (silhouette 0.778), but the simulation comparisons in Section 4 only report BIRT results; NOMINATE appears only in Figure 1. It should be made clear which methods are included in each quantitative comparison.
  3. [Section 6] The discussion of 'dimensional efficiency' (citing Nakis et al. 2025) and 'balanced influence' is not directly connected to the simulations or empirical application. Either connect these claims to concrete results or move them to a clearly labeled speculation paragraph.
  4. [Section 5.2] The interpretation of the second dimension's variance (SD = 0.74 for LSIRM vs. 0.18 for BIRT) is based on point estimates without uncertainty intervals. Posterior credible intervals for the variance of the second dimension would strengthen the claim that factional structure is genuinely recovered.
  5. [References] Duck-Mayr and Montgomery (2023a) and (2023b) appear to be the same work; the duplicated reference should be merged. Several other references (e.g., Nakis et al. 2025) are cited in ways that suggest they may be preprints; the version and availability should be indicated.
  6. [Figures] In Figures 6, 7, and 9, the text refers to 'grey triangle' markers for bridge bills or bill positions, but the captions use 'gray markers' without specifying which color/shape corresponds to which bill type. The figure legends need to be fully self-explanatory.

Circularity Check

1 steps flagged · score 3.0 of 10

No derivation-chain circularity; one in-sample 'prediction' reported as predictive evidence.

  1. fitted input called prediction [Section 5.2, 'Legislator Positions and Faction Recovery'; cf. Abstract and Introduction]
    "Classification accuracy reaches 0.80 for Euclidean LSIRM versus 0.72 for BIRT, indicating the Euclidean embedding better predicts individual votes. The Aggregate Proportional Reduction in Error (APRE), which accounts for vote margins by comparing errors to baseline minority-vote predictions, reaches 0.45 for Euclidean LSIRM versus 0.23 for BIRT"

    These accuracy/APRE values are computed on the same 1,225 roll-calls used to fit the model; no train/test split, cross-validation, or other out-of-sample procedure is described. The claim that LSIRM 'better predicts individual votes' is thus a restatement of its in-sample fit, not an independent prediction. The fitted probabilities are exactly the quantity being summarized as 'predictive performance,' so this empirical support reduces to a fit diagnostic rather than evidence of predictive superiority. In addition, Eq. (3) gives LSIRM legislator-specific intercepts θ_i absent from the BIRT comparator, so the accuracy gap is not identified as evidence for the Euclidean metric per se.

full rationale

The paper's central derivation—that squared/Gaussian utilities violate the triangle inequality while Euclidean distance satisfies it—is a self-contained mathematical argument and is not circular. The proposed model is explicitly adapted from Jeon et al. (2021), a self-citation involving co-author Jin, but the paper does not lean on that citation as proof of its legislative claims; it supplies its own MCMC algorithm, fresh simulations, and a real-data application. The simulations in the main text are described as blockmodel-style generative processes (targeted groups vote 'Yea' with probability p, others with q), not as draws from Eq. (3), so the cluster-recovery results are not the model merely reproducing its own DGP by construction. The main circularity-adjacent issue is the in-sample accuracy/APRE being labeled as 'predictive performance' without out-of-sample validation. There is also a real confound between the Euclidean-distance specification and the added legislator intercepts θ_i in comparisons against BIRT, but that is a validity threat to the causal attribution, not a circularity of the derivation chain. Overall, the core metric argument stands independently; the reported predictive evidence is weaker than presented.

Assumptions & free parameters 6 free parameters · 4 assumptions · 2 invented entities

The central claim rests on a domain assumption (Euclidean-distance homophily), an arbitrary scaling choice, and a constellation of fitted parameters. No new physical entities are introduced; the invented entities are the latent space and the proximity parameter, neither of which has a falsifiable handle outside the paper's own model.

free parameters (6)
  • Latent dimension K = 2 (chosen by analyst)
    The paper uses two-dimensional embeddings but does not perform model selection or report sensitivity to K.
  • γ (proximity strength) = estimated (e.g., ~3.18, ~3.21 in simulations)
    Estimated from data; central to the distance-based voting probability.
  • Legislator positions z_i = posterior means
    The main output; 451 × 2 coordinates for the 118th House.
  • Bill positions w_j = posterior means
    1225 × 2 coordinates; used as interpretive anchors.
  • Baseline propensities θ_i, β_j = estimated
    Additive intercepts separating baseline voting rates from spatial proximity.
  • Prior hyperparameters (aσ, bσ, μγ, σγ) = not specified numerically in text
    Chosen without sensitivity analysis; values not reported.
assumptions (4)
  • standard math Euclidean distance satisfies the triangle inequality (via Cauchy-Schwarz)
    Used to justify metric claims; correct.
  • domain assumption Roll-call voting probability is a monotone decreasing function of Euclidean distance in a shared latent space (Eq. 3)
    Load-bearing assumption; if the true response process is e.g. quadratic or projective, the model is misspecified.
  • domain assumption Abstentions and non-votes are ignorable missing data
    The analysis excludes abstentions without modeling the missingness mechanism.
  • ad hoc to paper The unit scale of each latent dimension is comparable (via N(0, I_K) prior)
    Cardinal comparability of distances across dimensions depends on this arbitrary scaling choice.
invented entities (2)
  • Two-dimensional Euclidean latent space for legislators and bills
    purpose: Represents ideological positions and policy locations; enables distance-based clustering and bill anchors.
    The space is a modeling construct with no direct external observable; its only handle is through vote predictions, and the paper does not provide out-of-sample validation.
  • Proximity strength γ
    purpose: Quantifies how strongly voting depends on spatial distance vs. baseline propensities.
    A model parameter with no independent measurement; interpretation depends on the model being correct.

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Cite this review

Pith. "Pith review of Euclidean Ideal Point Estimation From Roll-Call Data via Distance-Based Bipartite Network Models." pith.science (2026). https://pith.science/paper/B4AUFTMF

@misc{pith2026251211610,
  author       = {Pith},
  title        = {Pith review of: Euclidean Ideal Point Estimation From Roll-Call Data via Distance-Based Bipartite Network Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B4AUFTMF}},
  note         = {Machine review of arXiv:2512.11610}
}
read the original abstract

Conventional ideal point models rely on Gaussian or quadratic utility functions that violate the triangle inequality, producing non-metric distances that complicate geometric interpretation and undermine clustering and dispersion-based analyses. We introduce a distance-based alternative that adapts the Latent Space Item Response Model (LSIRM) to roll-call data, treating legislators and bills as nodes in a bipartite network jointly embedded in a Euclidean metric space. Through controlled simulations, Euclidean LSIRM consistently recovers latent coalition structure with superior cluster separation relative to existing methods. Applied to the 118th U.S. House, the model provides competitive predictive performance while yielding bill embeddings that clarify cross-cutting issue alignments. The results show that restoring metric structure to ideal point estimation provides a clearer and more coherent inference about party cohesion, factional divisions, and multidimensional legislative behavior.

Figures

Figures reproduced from arXiv: 2512.11610 by the authors.

Figure 1
Figure 1. Coalition-cluster distortion in non-metric ideal point methods. Ground truth: four distinct coalitions (marked by colors and shapes)—Party A majority (70, blue squares) and minority (10, purple triangles); Party B majority (70, red circles) and minority (10, pink crosses). The 400-bill agenda includes 200 partisan bills (party-line division) and 200 faction￾specific bills (50 per faction). Despite this clear structu… view at source ↗
Figure 2
Figure 2. Euclidean LSIRM latent positions for Simulation 1. Each panel shows ideal point estimates for 10 legislative groups organized into two blocs (red filled markers vs. blue open markers). Columns vary independent voter proportion; rows vary “Yea” probability p [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Cluster recovery under moderate noise (p = 0.80, q = 0.20). Left and center columns show representative latent maps; colors denote ground-truth cluster membership. Right column shows silhouette distributions over 100 replications (Euclidean LSIRM: black triangles; BIRT: green circles). 4.3.2 Noise Sweep Each party contains two factions (80 legislators total). We fixed the agenda and varied voting noise: targeted fac… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Faction recovery under shifting legislative agendas. Colors and markers denote six true factions. Silhouette distributions: Euclidean LSIRM (black triangles), BIRT (green circles). 4.3.3 Cross-Party Coalitions We introduced unequal faction sizes (70 vs. 10 legislators …
Figure 5
Figure 5. Figure 5: Faction recovery under varying noise levels. Euclidean LSIRM maps include bill positions (gray markers). Silhouette distributions: Euclidean LSIRM (black triangles), BIRT (green circles). (a) BIRT (b) Euclidean LSIRM [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Majority consensus scenario. Legislators colored by party; shaped by faction (L1: blue squares, L2: purple triangles, C1: red circles, C2: pink crosses). Euclidean LSIRM draws allied majority factions (L1, C1) closer together, with Bridge-A bills (grey triangle) positi…
Figure 7
Figure 7. Figure 7: Ends-against-the-middle scenario. Euclidean LSIRM draws minority factions (L2, C2) toward each other, with Bridge-B bills (grey triangle) near this pairing. structures. 5. Application: 118th U.S. House of Representatives 5.1 Data and Context We apply Euclidean LSIRM to…
Figure 8
Figure 8. Figure 8: Two-dimensional ideal point estimates for the 118th U.S. House. Legislators are plotted by party and factional affiliation: Mainstream Democrats (blue squares), “Squad” Democrats (purple triangles), Mainstream Republicans (red circles), and Freedom Caucus Republicans (…
Figure 9
Figure 9. Figure 9: Two-dimensional ideal point estimates for the 118th U.S. House. Legislators are plotted by party and factional affiliation: Mainstream Democrats (blue squares), “Squad” Democrats (purple triangles), Mainstream Republicans (red circles), and Freedom Caucus Republicans (…

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Reference graph

Works this paper leans on

21 extracted references · 5 canonical work pages

  1. [3]

    ISSN: 1573-1375

    A mixture model for random graphs.Statistics and Computing 18 (2): 173–183. ISSN: 1573-1375. https://doi.org/10.1007/s11222-007-9046-7. https://doi.org/10.1007/s11222-007-9046-7. Davis, Otto A, Melvin J Hinich, and Peter C Ordeshook

    doi:10.1007/s11222-007-9046-7

  2. [7]

    Holland, Paul W., Kathryn Blackmond Laskey, and Samuel Leinhardt

    https://www.jstor.org/stable/26997946. Holland, Paul W., Kathryn Blackmond Laskey, and Samuel Leinhardt

    arXiv

  3. [8]

    Jackman, Simon

    https://www.sciencedirect.com/science/article/pii/0378873383900217. Jackman, Simon

    arXiv

  4. [10]

    Journal of Statistical Software 24 (5)

    Fitting position latent cluster models for social networks with latentnet. Journal of Statistical Software 24 (5). https://doi.org/10.18637/jss.v024.i05. Lei, Rayleigh, and Abel Rodriguez

    doi:10.18637/jss.v024.i05

  5. [11]

    Lewis, Jeffrey B., Keith Poole, Howard Rosenthal, Adam Boche, Aaron Rudkin, and Luke Sonnet

    A novel class of unfolding models for binary preference data.Political Analysis 33 (1): 32–48. Lewis, Jeffrey B., Keith Poole, Howard Rosenthal, Adam Boche, Aaron Rudkin, and Luke Sonnet. 2025.V oteview: congressional roll-call votes database. Data retrieved from V oteview.com. https://voteview.com. Li, Wu-Jun, Dit-Yan Y eung, and Zhihua Zhang

    2025

  6. [12]

    arXiv preprint arXiv:2305.05833

    A statistical model of bipartite networks: application to cosponsorship in the united states senate. arXiv preprint arXiv:2305.05833. Marble, William, and Matthew Tyler

    arXiv

  7. [13]

    https://www.cambridge.org/core/ product/identif ier/S0898588X16000110/type/journal_article

    https://doi.org/10.1017/S0898588X16000110. https://www.cambridge.org/core/ product/identif ier/S0898588X16000110/type/journal_article. 20 Seungju Lee et al. Miller, Kurt, Michael Jordan, and Thomas Griffiths

    work page doi:10.1017/s0898588x16000110

  8. [15]

    In 2011 ieee international workshop on machine learning for signal processing, 1–6

    Infinite multiple membership relational modeling for complex networks. In 2011 ieee international workshop on machine learning for signal processing, 1–6. https://doi.org/10. 1109/MLSP.2011.6064546. Moser, Scott, Abel Rodríguez, and Chelsea L Lofland

    arXiv 2011

Show all 21 references
  1. [16]

    arXiv preprint arXiv:2503.01723

    How low can you go? searching for the intrinsic dimensionality of complex networks using metric node embeddings. arXiv preprint arXiv:2503.01723. Nowicki, Krzysztof, and Tom A. B. Snijders

    arXiv

  2. [17]

    org/stable/2670253

    https://www.jstor. org/stable/2670253. Palla, Konstantina, David A. Knowles, and Zoubin Ghahramani

  3. [22]

    https://proceedings.neurips.cc/paper_f iles/paper/2009/f ile/437d7d1d97917cd627a34a6a 0f b41136-Paper.pdf

    Curran Associates, Inc. https://proceedings.neurips.cc/paper_f iles/paper/2009/f ile/437d7d1d97917cd627a34a6a 0f b41136-Paper.pdf . Mørup, Morten, Mikkel N. Schmidt, and Lars Kai Hansen

    2009

  4. [1957]

    Harper & Row

    An economic theory of democracy. Harper & Row. Duck-Mayr, JBrandon, and Jacob Montgomery. 2023a. Ends against the middle: measuring latent traits when opposites respond the same way for antithetical reasons. Political Analysis 31 (4): 606–625. https://doi.org/10.1017/pan.2022....

    2022 doi

  5. [2007]

    In Algorithms and Models for the W eb-Graph,edited by Anthony Bonato and Fan R

    Random dot product graph models for social networks [in en]. In Algorithms and Models for the W eb-Graph,edited by Anthony Bonato and Fan R. K. Chung, 138–149. Berlin, Heidelberg: Springer. ISBN: 978-3-540-77004-6. https://doi.org/10.1007/978-3-540-77004-6\_11. Zhou, Mingyuan

    doi

  6. [2008]

    Journal of Machine Learning Research 9 (65): 1981–2014

    Mixed membership stochastic blockmodels. Journal of Machine Learning Research 9 (65): 1981–2014. ISSN: 1533-7928, accessed September 1,

    1981

  7. [2011]

    Stochastic blockmodels and community structure in networks.Phys. Rev. E 83 (1): 016107. https://doi.org/10.1103/PhysRevE.83.016107. https://link.aps.org/doi/10.1103/PhysRevE.83.016107. Kemp, Charles, Joshua B. Tenenbaum, Thomas L. Griffiths, Takeshi Yamada, and Naonori Ueda

    doi

  8. [2012]

    In Proceedings of the 29th international coference on international conference on machine learning,395–402

    An infinite latent attribute model for network data. In Proceedings of the 29th international coference on international conference on machine learning,395–402. ICML’12. Edinburgh, Scotland: Omnipress. ISBN: 9781450312851. Poole, Keith T., and Howard Rosenthal. 2007.Ideology a...

    2007

  9. [2013]

    https://doi.org/10.1214/12-AOAS617

    Model-based clustering of large networks.The Annals of Applied Statistics 7 (2): 1010–1039. https://doi.org/10.1214/12-AOAS617. https://doi.org/10.1214/12-AOAS617. Y oung, Stephen J., and Edward R. Scheinerman

    doi

  10. [2020]

    American Journal of Political Science 64 (3): 452–470

    Party sub-brands and american party factions. American Journal of Political Science 64 (3): 452–470. https://doi.org/https://doi.org/10.1111/ajps.12504. eprint: https://onlinelibrary.wiley.com/doi/pdf /10.1111/ajps.12504. https://onlinelibrary.wiley.com/doi/abs/10.1111/ajps.12...

    doi

  11. [2023]

    https://doi.org/10.1086/723805

    The bipartisan path to effective lawmaking.The Journal of Politics 85:1048–1063. https://doi.org/10.1086/723805. Hoff, P., A. Raftery, and M. S. Handcock

    doi

  12. [2024]

    Journal of the American Statistical Association 120 (550): 631–644

    l1-based bayesian ideal point model for multidimensional politics. Journal of the American Statistical Association 120 (550): 631–644. https://doi.org/10.1080/01621459.2024.2425461. eprint: https://doi.org/10.1080/01621459.2024.2425461. https://doi.org/10.1080/01621459.2024.24...

    2024

  13. [2025]

    https://doi.org/10.1007/s10588-008-9040-4

    https://doi.org/10.1007/s10588-008-9040-4. https://doi.org/10.1007/s10588-008-9040-4

    doi

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Reviewed August 3, 2026 · model on record in the stance chip above.