Pith. sign in

REVIEW 3 major objections 6 minor 42 references

The Correlation Thresholding Algorithm for Exploratory Factor Analysis

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The Correlation Thresholding algorithm recovers factor structure with average F1 0.901 and stays competitive when its assumptions are violated.

desk verdict Solid sensitivity analysis of CT for EFA; the low-dimensional claims hold up, but the high-dimensional robustness conclusion rests on oracle selection and is overstated as written. read the letter →

arxiv 2505.21100 v1 pith:YPOFLGED submitted 2025-05-27 stat.ME

Dale S. Kim , Audrey Lu , Qing Zhou This is my paper
classification stat.ME MSC 62H25
keywords exploratoryfactoranalysiscorrelationthresholdinggraphscliquesstructurelearningthresholdabilityuniquechildconditionmodelselection
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 the Correlation Thresholding (CT) algorithm, originally developed under two strong assumptions, is robust enough to be a practical tool for exploratory factor analysis. The algorithm solves the three classical EFA problems—number of factors, zero-loading constraints, and rotational choice—at once by thresholding the correlation matrix and reading structure off the graph's maximal cliques. Its two assumptions are thresholdability, meaning within-factor correlations dominate between-factor correlations, and the unique child condition, meaning each latent factor has at least one uniquely-loading indicator. Through simulations that deliberately violate these assumptions, the paper claims average F1 of 0.901 in low-dimensional settings, graceful degradation as violations worsen, and recovery of a hypothesized five-factor model in the ABCD youth UPPS-P data with F1 0.974 after checking only 24 candidate models. The practical upshot is that CT can replace the sequential, computationally heavy EFA pipeline with one graph-based procedure.

What carries the argument

The central object is the thresholded correlation graph G(X, E(τ)), whose edge set contains pairs with |ρ_ij| > τ. Under thresholdability, a suitable τ separates within-factor from between-factor correlations; the independent maximal cliques of this graph then correspond one-to-one to the latent factors' child sets, provided the unique child condition holds. The algorithm searches over all distinct sample correlations as candidate thresholds, proposes a structure for each threshold, estimates each structure by MLE, and selects the final model with BIC.

What would settle it

Re-running the CT algorithm on datasets where thresholdability fails through a mechanism not captured by α or β, such as correlated residuals or strongly non-Gaussian ordinal items while the factor structure is known, and observing a large drop in F1 score would falsify the robustness claim. A direct check is to compare CT's recovered structure against the known model in such data; if average F1 falls materially below the reported 0.901 range, the claim is not general.

Watch

Extended reading notes

Core claim

The central claim is that the CT algorithm—which thresholds a sample correlation matrix at all distinct values, extracts independent maximal cliques, and uses those cliques to propose factor structures—recovers the true loading support and factor count accurately even when thresholdability and the unique child condition are violated. In the paper's simulations, violations induced by increasing factor correlation through α and by adding random cross-loadings through β degrade performance gradually: structural accuracy stays high until α equals 1, and it remains moderate when up to half the latent variables lose their unique child. On the real ABCD UPPS-P data, CT is claimed to be the only method that recovers the hypothesized five-factor structure, with F1 0.974, while evaluating 24 models versus 1350 for EFA-MCP.

Load-bearing premise

The load-bearing premise is that the simulation design—Gaussian data, loadings and factor correlations in [0.6, 0.8], and violations induced only through the α and β parameters—is representative of how real factor analysis data depart from the algorithm's assumptions.

Editorial extensions

If this is right

  • If the simulations are right, practitioners can recover the number of factors and loading support in one step instead of combining separate eigenvalue, thresholding, and rotation decisions.
  • Average F1 of 0.901 across low-dimensional conditions means CT tends to outperform EFA, EFA-LASSO, and EFA-MCP in structural accuracy.
  • Accuracy remains high unless thresholdability fails strongly (α close to 1), so mild violations are not fatal.
  • With up to half of latent variables violating the unique child condition, CT stays competitive with the penalized alternatives, though it tends to over-extract factors.
  • In high-dimensional settings where n is less than p, CT remains a practical structure-learning option where penalized EFA is computationally prohibitive.

Reading between the lines

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

  • The paper defines sortability as a continuous measure of how separable within- and between-factor correlations are; an extension it does not develop is to estimate sortability on real data as a pre-hoc diagnostic, so users can know when CT's output should be trusted.
  • Because CT only needs a correlation matrix for structure learning, it could be applied to ordinal or non-linear items by replacing Pearson correlations with polychoric correlations; the paper mentions this as future work, implying the robustness findings might transfer to item-response-theory settings, though this is not tested.
  • The factor-splitting pattern when the unique child condition fails suggests a practical warning sign: if CT selects more factors than theory expects, checking whether the estimated maximal cliques are much smaller than the theoretical child-set size could indicate over-extraction rather than true structure.
  • The computational comparison counts models evaluated, not the cost of clique enumeration; in very large p settings the real bottleneck may shift to the threshold search and clique extraction, so the advantage over penalized EFA could be smaller than the model count alone suggests.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This paper evaluates the Correlation Thresholding (CT) algorithm of Kim and Zhou (2023) for exploratory factor analysis, which simultaneously determines the number of factors, loading constraints, and rotational identifiability from thresholded correlation graphs. The authors review the two key assumptions (thresholdability and the unique child condition), discuss their implications, and report simulation studies in low-dimensional settings (d = 2-5, n = 250, 500, 1000) and high-dimensional settings (n < p), along with an ABCD UPPS-P real-data example. CT is compared with standard EFA, EFA-LASSO, and EFA-MCP. The main claims are that CT shows reasonable robustness to assumption violations, competitive or superior structural accuracy and fit, and high-dimensional viability while evaluating far fewer candidate models than penalized alternatives.

Significance. If the claims hold, the paper provides a practically valuable validation of a unified EFA procedure that avoids separate steps for factor-count determination, loading-sparsity learning, and rotation selection. The low-dimensional simulation design is thorough (100 datasets per condition, multiple d and n), with a sensible 'sortability' diagnostic, and the real-data example is instructive. The paper also ships reproducible code and supplementary materials, which strengthens its contribution. The significance is tempered by the fact that the high-dimensional results are based on oracle selection of the best candidate structure rather than the algorithm's full model-selection step, so the paper's strongest general claim is not yet fully supported.

major comments (3)
  1. [Section 4.4 and Figure 10] The high-dimensional results are oracle quantities. The text states 'we focused on only studying the structural accuracy of the CT algorithm. We did this by running the CT algorithm except for the estimation and model selection steps. Doing this yields a set of proposed structures, from which we examined the structure closest to the true structure.' Hence the reported F1, HD, and d_hat values do not describe the model that Algorithm 1's Step 10 (BIC) would return, and the Section 6 claim that 'The CT algorithm also showed viability as a structure learning method in high-dimensional settings' is not backed by an end-to-end run in n < p. This is especially concerning because Section 4.3 already documents cases in which BIC selects a worse structure than available candidates; if BIC behaves similarly in high dimensions, the oracle-best F1 could overstate practical accuracy. The authors should either run the full algorithm in high dimensions (possibly with a coarser threshold grid and a scalable estimation/selection procedure) or explicitly reclassify the high-dimensional results as an upper bound on structural accuracy.
  2. [Sections 4.2-4.3 and Abstract] The robustness conclusions are specific to a narrow perturbation family. Thresholdability violations are induced only by scaling factor correlations (alpha) and unique-child violations only by adding random cross-loadings (beta), all on Gaussian data with loadings and factor correlations in [0.6, 0.8]. Real EFA settings also involve ordinal/non-Gaussian items, correlated residuals, and structural misspecifications that are not spanned by alpha and beta. The abstract's blanket statement that the CT algorithm 'shows reasonable robustness against violating these assumptions' should be qualified to the simulated violation space, or additional simulations covering these other violation types should be added.
  3. [Section 4.3] The paper reports that 'the candidate set of structures included solutions with d and F1 scores closer to the true model than the one selected by BIC' when the unique child condition is violated. Since Step 10 of Algorithm 1 is an integral part of the CT procedure, the finding that BIC sometimes selects a worse model is load-bearing for the algorithm's practical recommendation. The manuscript would be stronger if it (i) examined alternative selection criteria (e.g., cross-validation or stability selection) and (ii) reported how often BIC misses the best candidate in the simulation conditions.
minor comments (6)
  1. [Equation (B1)] The function h in the Hamming distance definition is not defined; please define h(A,B) as the cardinality of the symmetric difference.
  2. [Section 2.1, Equation (5) area] The non-redundant elements of eSigma contain typos; for example, the (1,1) entry shows eomega_1^2 (and elsewhere eomega_i^2) although eOmega is a diagonal matrix with entries eomega_i, so the diagonal of eSigma should be elambda^2 + eomega_i. In addition, the (5,2) entry appears to read elambda_21 elambda_45 phi_12 but should likely be elambda_21 elambda_52 phi_12.
  3. [Table 1 caption] The word 'threshsoldable' should be 'thresholdable'.
  4. [Section 4.1] The counting convention for the number of models for the EFA variants is briefly stated but could be clearer; in particular, it should state explicitly whether the same thresholds are applied to each EFA method or whether the unique structures/d values are pooled.
  5. [Sections 4.2 and 4.3] The phrase 'we will only examine the results for the n=1000 case' is repeated without a summary of the n=250/500 patterns in the main text; please add a brief description of how those results differ, either in the main text or in the supplement.
  6. [Section 4.4] The high-dimensional threshold grid uses 50 equidistant values, whereas the low-dimensional grid uses all unique sample correlations; the possible effect of this different granularity on the high-dimensional results should be discussed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the CT robustness claims are evaluated on independently simulated data and an external real-data benchmark, not derived from the algorithm's own fitted inputs.

full rationale

This paper is an empirical sensitivity analysis of an existing algorithm. The CT algorithm and its theoretical guarantees are cited from Kim and Zhou (2023), but the simulations are generated independently of that theory: data are drawn from Gaussian factor models with known loading matrices, factor correlations, and error variances, and the recovered structure is compared to the true support (Section 4). No parameter is fitted to the target outcome and then renamed a prediction; the reported F1, Hamming distance, BIC, TLI, and RMSEA values come from actual runs of the specified procedures or from the explicitly stated oracle-best candidate in the high-dimensional setting. The self-citations to Kim and Zhou (2023) supply the algorithm and its assumptions, but the paper does not use those citations to force the empirical conclusion. The only caveat worth noting is the Section 4.4 high-dimensional protocol ('we examined the structure closest to the true structure' rather than the BIC-selected output); this is an oracle evaluation and limits the strength of the n<p viability claim, but it is a methodological limitation, not a circular reduction, since the reported F1 and HD values are still scored against an external true structure. Overall, the derivation chain is self-contained with respect to the empirical claims, and no equation or fitted quantity is equivalent to its own input by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim is an empirical robustness claim; it does not introduce new theoretical entities. The main ledger items are the simulation design constants (alpha, beta, loading range, threshold grid) and the inherited assumptions from Kim and Zhou (2023) that frame the study.

free parameters (4)
  • Threshold grid tau = low-dimensional: all unique |r_ij|; high-dimensional: 50 equidistant points in [0,1]
    The candidate structures and hence the final model depend on the set of thresholds; the paper chooses them by implementation convenience, not by a principled selection rule (Section 2.1, Section 4.1).
  • Loadings and factor correlation range = [0.6, 0.8]
    All non-zero lambda_ij and off-diagonal Phi entries are drawn from [0.6, 0.8] (Appendix B.1); this range affects how often thresholdability holds and how easy structure recovery is.
  • Factor correlation scaling alpha = 0, 0.25, 0.5, 0.75, 1
    Chosen by the authors to control the severity of thresholdability violations; the robustness conclusions are conditional on this mechanism (Section 4.2).
  • Unique child violation proportion beta = 0 to 1 by available fraction of latent variables
    Chosen to vary the number of latent variables without unique indicators; the conclusion of moderate robustness depends on the range studied (Section 4.3).
assumptions (5)
  • domain assumption The factor analysis model X = Lambda L + epsilon with L ~ N(0, Phi), epsilon ~ N(0, Omega) diagonal, and d < p.
    Used throughout Equation 1 and in all simulations; if the true generative model is non-Gaussian or has correlated residuals, the simulation evidence may not apply. Located in Section 2, Equation 1.
  • domain assumption Thresholdability and the unique child condition are sufficient for consistency of the CT algorithm.
    The paper inherits these from Kim and Zhou (2023) and uses them to frame the simulations; the robustness claims are about relaxing them, not about removing the need for a well-posed factor model. Introduced as Assumption 2.1 and Assumption 3.1.
  • standard math MLE and BIC are consistent for the candidate factor models.
    Step 8 assumes consistent parameter estimation and Step 10 assumes a consistent model selection criterion; the paper states this is 'easily satisfied by using MLE and BIC model selection' (Section 2.2).
  • standard math Independent maximal cliques can be extracted in polynomial time and correspond to child sets when the unique child condition holds.
    Algorithm 1 relies on this graph-theoretic machinery from Eppstein et al. and Kim and Zhou (2023); it is not proven in this paper.
  • domain assumption The Watts et al. (2020) five-factor model is the true structure of the youth UPPS-P scale.
    The real data F1 score treats the hypothesized model as ground truth (Section 5).

how reviews work

0 comments
Cite this review

Pith. "Pith review of The Correlation Thresholding Algorithm for Exploratory Factor Analysis." pith.science (2026). https://pith.science/paper/YPOFLGED

@misc{pith2026250521100,
  author       = {Pith},
  title        = {Pith review of: The Correlation Thresholding Algorithm for Exploratory Factor Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YPOFLGED}},
  note         = {Machine review of arXiv:2505.21100}
}
read the original abstract

Exploratory factor analysis is often used in the social sciences to estimate potential measurement models. To do this, several important issues need to be addressed: (1) determining the number of factors, (2) learning constraints in the factor loadings, and (3) selecting a solution amongst rotationally equivalent choices. Traditionally, these issues are treated separately. This work examines the Correlation Thresholding (CT) algorithm, which uses a graph-theoretic perspective to solve all three simultaneously, from a unified framework. Despite this advantage, it relies on several assumptions that may not hold in practice. We discuss the implications of these assumptions and assess the sensitivity of the CT algorithm to them for practical use in exploratory factor analysis. This is examined over a series of simulation studies, as well as a real data example. The CT algorithm shows reasonable robustness against violating these assumptions and very competitive performance in comparison to other methods.

Figures

Figures reproduced from arXiv: 2505.21100 by the authors.

Figure 1
Figure 1. An example graph for illustrating cliques. The vertex set {X1, X2, X4} is a clique, but not a maximal clique, since X5 can be added to the set and it would remain a clique. The set {X1, X2, X4, X5} is a maximal clique, since there is no vertex that can be added to it and have the set remain a clique. example. Consider the following parameters: Λ =e        λe11 λe21 λe31 λe32 λe42 λe52        , Φ =  1 … view at source ↗
Figure 2
Figure 2. (a) The factor analysis model described in Equation 5; (b) The graph G(X, E0). this correspondence by using these graphs to gain insight into the structure of the factor analysis model. If indeed the between-factor correlations have a lower magnitude than the within￾factor correlations, then there will exist a threshold τ0 such that the correlations corresponding to E0 and Ec 0 can be separated. If a set of paramete… view at source ↗
Figure 3
Figure 3. A high-level diagram of the CT algorithm. A set of candidate thresholds τk each suggest a candidate factor analysis structure through clique analysis. Each of these structures is then estimated and compared through model selection. and parameter estimates will hold so long as a consistent parameter estimation method is used in Step 8, and a consistent model selection procedure is used in Step 10. This is easily sati… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Three structures that yield the same thresholded correlation graph. it is not maximal since L2 yields {3, 4, 5}. In this case, L3 will not be identified as a latent variable, since its clique is subsumed by the one yielded by L2. Therefore, the unique child condition i…
Figure 5
Figure 5. Figure 5: Average structural accuracy statistics for the low-dimensional simulation, as a function of α. While there does seem to be a slightly curved relationship between fit and α, this is attributable to several outliers downardly influencing the average at lower α. These can…
Figure 6
Figure 6. Figure 6: Average model fit and computational efficiency statistics for the low-dimensional simulation, as a function of α. For the fit statistics in d = 2, we note that CT and EFA are largely overlapping, and LA and MCP are largely overlapping. all their children would be given…
Figure 7
Figure 7. Figure 7: Average structural accuracy statistics for the low-dimensional simulation, as a function of β. For d = 2, we note that CT and EFA are largely overlapping on dˆ, and LA and MCP are largely overlapping on all three metrics. We can see that the ratio starts at about 1 whe…
Figure 8
Figure 8. Figure 8: Average model fit and computational efficiency statistics for the low-dimensional simulation, as a function of β [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Ratios between the average maximal clique size of the estimated model’s graph (|Cck|) and the true model’s graph (|Ck|), calculated per d and β. of the CT algorithm on data with a large number of latent factors d ∈ {25, 50, 100}. Computing the MLE when n < p with large…
Figure 10
Figure 10. Figure 10: Average structural accuracy and computational efficiency statistics for the high-dimensional sim￾ulation, as a function of α and β. a set of proposed structures, from which we examined the structure closest to the true structure. As with the low-dimensional settings, …
Figure 11
Figure 11. Figure 11: Path diagram of the youth UPPS-P scale. structure learning methods. We also provided a comparison of methods in a real data example. We showed that the CT algorithm performed well when its assumptions were met, and showed good robustness to violations of thresholdabil…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

42 extracted references · 37 canonical work pages

  1. [1]

    \ Gerbing, D W

    Anderson1988 APACrefauthors Anderson, J C. \ Gerbing, D W. APACrefauthors \ 1988 . Structural equation modeling in practice: A review and recommended two-step approach Structural equation modeling in practice: A review and recommended two-step approach . Psychological Bulletin 103 3 411--423

    work page 1988

  2. [2]

    \ Moshagen, M

    Auerswald2019 APACrefauthors Auerswald, M. \ Moshagen, M. APACrefauthors \ 2019 . How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic ...

    work page 2019

  3. [3]

    \ Lennox, R

    Bollen1991 APACrefauthors Bollen, K. \ Lennox, R. APACrefauthors \ 1991 . Conventional wisdom on measurement: A structural equation perspective Conventional wisdom on measurement: A structural equation perspective . Psychological Bulletin 110 2 305–314 . APACrefDOI doi:10.1037/0033-2909.110.2.305 APACrefDOI

    doi:10.1037/0033-2909.110.2.305 1991

  4. [4]

    APACrefauthors \ 1968

    Browne1968 APACrefauthors Browne, M W. APACrefauthors \ 1968 . A comparison of factor analytic techniques A comparison of factor analytic techniques . Psychometrika 33 3 1968

    work page 1968

  5. [5]

    APACrefauthors \ 2001

    Browne2001 APACrefauthors Browne, M W. APACrefauthors \ 2001 . An overview of analytic rotation in exploratory factor analysis An overview of analytic rotation in exploratory factor analysis . Multivariate Behavioral Research 36 1 111--150

    work page 2001

  6. [6]

    APACrefauthors \ 1966

    Cattell1966 APACrefauthors Cattell, R B. APACrefauthors \ 1966 . The Scree Test for the number of factors The Scree Test for the number of factors . Multivariate Behavioral Research 1 2 245--276

    work page 1966

  7. [7]

    , Fisher, C B

    Clark2018 APACrefauthors Clark, D B. , Fisher, C B. , Bookheimer, S. , Brown, S A. , Evans, J H. , Hopfer, C. Yurgelun-Todd, D. APACrefauthors \ 2018 . Biomedical ethics and clinical oversight in multisite observational neuroimaging studies with children and adolescents: The ABCD experience Biomedical ethics and clinical oversight in multisite observation...

    work page 2018

  8. [8]

    , L \" o ffler, M

    Eppstein2010 APACrefauthors Eppstein, D. , L \" o ffler, M. \ Strash, D. APACrefauthors \ 2010 . Listing all maximal cliques in sparse graphs in near-optimal time Listing all maximal cliques in sparse graphs in near-optimal time . International S ymposium on A lgorithms and C omputation International S ymposium on A lgorithms and C omputation \ ( \ 403--414)

    work page 2010

Show all 42 references
  1. [9]

    , MacCallum, R C

    Ford1986 APACrefauthors Ford, J K. , MacCallum, R C. \ Tait, M. APACrefauthors \ 1986 . The application of exploratory factor analysis in applied psychology: A critical review and analysis The application of exploratory factor analysis in applied psychology: A critical review ...

    1986

  2. [10]

    APACrefauthors \ 1995

    Glorfeld1995 APACrefauthors Glorfeld, L W. APACrefauthors \ 1995 . An improvement on Horn's parallel analysis methodology for selecting the correct number of factors to retain An improvement on Horn's parallel analysis methodology for selecting the correct number of factors to...

    1995

  3. [11]

    APACrefauthors \ 2006

    Graham2006 APACrefauthors Graham, J M. APACrefauthors \ 2006 . Congeneric and (essentially) tau-equivalent estimates of score reliability: What they are and how to use them Congeneric and (essentially) tau-equivalent estimates of score reliability: What they are and how to use...

    2006 doi

  4. [12]

    APACrefauthors \ 1954

    Guttman1954 APACrefauthors Guttman, L. APACrefauthors \ 1954 . Some necessary conditions for common-factor analysis Some necessary conditions for common-factor analysis . Psychometrika 19 2 149--161

    1954

  5. [13]

    \ Kaiser, H F

    Harris1964 APACrefauthors Harris, C W. \ Kaiser, H F. APACrefauthors \ 1964 . Oblique factor analytic solutions by orthogonal transformations Oblique factor analytic solutions by orthogonal transformations . Psychometrika 29 4 347--362

    1964

  6. [14]

    APACrefauthors \ 1985

    Hattie1985 APACrefauthors Hattie, J. APACrefauthors \ 1985 . Methodology review: Assessing unidimensionality of tests and items Methodology review: Assessing unidimensionality of tests and items . Applied Psychological Measurement 9 2 139--164

    1985

  7. [15]

    \ Yamamoto, M

    Hirose2014b APACrefauthors Hirose, K. \ Yamamoto, M. APACrefauthors \ 2014 1 . Estimation of an oblique structure via penalized likelihood factor analysis Estimation of an oblique structure via penalized likelihood factor analysis . Computational Statistics and Data Analysis 7...

    2014

  8. [16]

    \ Yamamoto, M

    Hirose2014a APACrefauthors Hirose, K. \ Yamamoto, M. APACrefauthors \ 2014 2 . Sparse estimation via nonconcave penalized likelihood in factor analysis model Sparse estimation via nonconcave penalized likelihood in factor analysis model . Statistics and Computing 25 5 863--875

    2014

  9. [17]

    APACrefauthors \ 1965

    Horn1965 APACrefauthors Horn, J L. APACrefauthors \ 1965 . A rationale and test for the number of factors in factor analysis A rationale and test for the number of factors in factor analysis . Psychometrika 30 2 179--185

    1965

  10. [18]

    APACrefauthors \ 2016

    Howard2016 APACrefauthors Howard, M C. APACrefauthors \ 2016 . A review of exploratory factor analysis decisions and overview of current practices: What we are doing and how can we improve? A review of exploratory factor analysis decisions and overview of current practices: Wh...

    2016

  11. [19]

    APACrefauthors \ 2001

    Jennrich2001 APACrefauthors Jennrich, R I. APACrefauthors \ 2001 . A simple general procedure for orthogonal rotation A simple general procedure for orthogonal rotation . Psychometrika 66 2 289--306

    2001

  12. [20]

    APACrefauthors \ 2006

    Jennrich2006 APACrefauthors Jennrich, R I. APACrefauthors \ 2006 . Rotation to simple loadings using component loss functions: The oblique Case Rotation to simple loadings using component loss functions: The oblique Case . Psychometrika 71 1 173--191

    2006

  13. [21]

    APACrefauthors \ 1960

    Kaiser1960 APACrefauthors Kaiser, H F. APACrefauthors \ 1960 . The application of electronic computers to factor analysis The application of electronic computers to factor analysis . Educational and Psychological Measurement 20 1 141--151

    1960

  14. [22]

    \ Zhou, Q

    Kim2023 APACrefauthors Kim, D S. \ Zhou, Q. APACrefauthors \ 2023 . Structure learning of latent factors via clique search on correlation thresholded graphs Structure learning of latent factors via clique search on correlation thresholded graphs . Proceedings of the 40th I nte...

    2023

  15. [23]

    \ Ramsey, J

    Kummerfeld2016 APACrefauthors Kummerfeld, E. \ Ramsey, J. APACrefauthors \ 2016 Aug . Causal clustering for 1-factor measurement models Causal clustering for 1-factor measurement models . Proceedings of the 22nd ACM SIGKDD I nternational C onference on K nowledge D iscovery an...

    2016

  16. [24]

    \ Bühlmann, P

    Meinshausen_2010 APACrefauthors Meinshausen, N. \ Bühlmann, P. APACrefauthors \ 2010 . Stability selection Stability selection . Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 4 417–473 . APACrefDOI doi:10.1111/j.1467-9868.2010.00740.x APACrefDOI

    2010

  17. [25]

    , Hunter, M D

    Neale2016 APACrefauthors Neale, M C. , Hunter, M D. , Pritikin, J N. , Zahery, M. , Brick, T R. , Kirkpatrick, R M. Boker, S M. APACrefauthors \ 2016 . OpenMx 2.0: Extended structural equation and statistical modeling Openmx 2.0: Extended structural equation and statistical mo...

    2016 doi

  18. [26]

    , Zhang, G

    Preacher2013 APACrefauthors Preacher, K J. , Zhang, G. , Kim, C. \ Mels, G. APACrefauthors \ 2013 . Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective Choosing the optimal number of factors in exploratory factor analysis: A mod...

    2013

  19. [27]

    APACrefauthors \ 2023

    R2023 APACrefauthors R Core Team . APACrefauthors \ 2023 . R: A Language and Environment for Statistical Computing R: A language and environment for statistical computing \ [ ]. Vienna, Austria . APACrefURL https://www.R-project.org/ APACrefURL

    2023

  20. [28]

    , Walls, T A

    Raiche2013 APACrefauthors Ra \^ i che, G. , Walls, T A. , Magis, D. , Riopel, M. \ Blais, J G. APACrefauthors \ 2013 . Non-graphical solutions for Cattell's Scree Test Non-graphical solutions for Cattell's Scree Test . Methodology 9 1 23--29

    2013

  21. [29]

    \ Nestler, S

    Scharf2019 APACrefauthors Scharf, F. \ Nestler, S. APACrefauthors \ 2019 . Should regularization replace simple structure rotation in exploratory factor analysis? Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeli...

    2019

  22. [30]

    , Spirtes, P

    Scheines1998 APACrefauthors Scheines, R. , Spirtes, P. , Glymour, C. , Meek, C. \ Richardson, T. APACrefauthors \ 1998 . The TETRAD project: Constraint based aids to causal model specification The TETRAD project: Constraint based aids to causal model specification . Multivaria...

    1998

  23. [31]

    , Hoyer, P O

    Shimizu2009 APACrefauthors Shimizu, S. , Hoyer, P O. \ Hyvärinen, A. APACrefauthors \ 2009 . Estimation of linear non-Gaussian acyclic models for latent factors Estimation of linear non-gaussian acyclic models for latent factors . Neurocomputing 72 7–9 2024-–2027 . APACrefDOI ...

    2009 doi

  24. [32]

    , Scheines, R

    Silva2006 APACrefauthors Silva, R. , Scheines, R. , Glymour, C. \ Spirtes, P. APACrefauthors \ 2006 . Learning the structure of linear latent variable models Learning the structure of linear latent variable models . Journal of Machine Learning Research 7 191--246

    2006

  25. [33]

    \ Lind, J C

    Steiger1980 APACrefauthors Steiger, J H. \ Lind, J C. APACrefauthors \ 1980 . Statistically based tests for the number of common factors Statistically based tests for the number of common factors . Meeting of the P sychometric S ociety. Meeting of the P sychometric S ociety. I...

    1980

  26. [34]

    APACrefauthors \ 1996

    Tibshirani1996 APACrefauthors Tibshirani, R. APACrefauthors \ 1996 . Regression shrinkage and selection via the Lasso Regression shrinkage and selection via the Lasso . Journal of the Royal Statistical Society: Series B 58 1 267--288

    1996

  27. [35]

    \ Lewis, C

    Tucker1973 APACrefauthors Tucker, L R. \ Lewis, C. APACrefauthors \ 1973 . A reliability coefficient for maximum likelihood factor analysis A reliability coefficient for maximum likelihood factor analysis . Psychometrika 38 1 1–10

    1973

  28. [36]

    \ Jackson, D N

    Velicer1990 APACrefauthors Velicer, W F. \ Jackson, D N. APACrefauthors \ 1990 . Component analysis versus common factor analysis: Some issues in selecting an appropriate procedure Component analysis versus common factor analysis: Some issues in selecting an appropriate proced...

    1990

  29. [37]

    , Koob, G F

    Volkow2018 APACrefauthors Volkow, N D. , Koob, G F. , Croyle, R T. , Bianchi, D W. , Gordon, J A. , Koroshetz, W J. Weiss, S R. APACrefauthors \ 2018 . The conception of the ABCD study: From substance use to a broad NIH collaboration The conception of the ABCD study: From subs...

    2018 doi

  30. [38]

    , Smith, G T

    Watts2020 APACrefauthors Watts, A L. , Smith, G T. , Barch, D M. \ Sher, K J. APACrefauthors \ 2020 . Factor structure, measurement and structural invariance, and external validity of an abbreviated youth version of the UPPS-P Impulsive Behavior Scale Factor structure, measure...

    2020 doi

  31. [39]

    APACrefauthors \ 1983

    Whitely1983 APACrefauthors Whitely, S E. APACrefauthors \ 1983 . Construct validity: Construct representation versus nomothetic span Construct validity: Construct representation versus nomothetic span . Psychological Bulletin 93 1 179--197

    1983

  32. [40]

    \ Lynam, D R

    Whiteside2001 APACrefauthors Whiteside, S P. \ Lynam, D R. APACrefauthors \ 2001 . The Five Factor Model and impulsivity: Using a structural model of personality to understand impulsivity The five factor model and impulsivity: Using a structural model of personality to underst...

    2001 doi

  33. [41]

    APACrefauthors \ 2010

    Zhang2010 APACrefauthors Zhang, C H. APACrefauthors \ 2010 . Nearly unbiased variable selection under minimax concave penalty Nearly unbiased variable selection under minimax concave penalty . Annals of Statistics 38 2 894--942

    2010

  34. [42]

    \ Velicer, W F

    Zwick1986 APACrefauthors Zwick, W R. \ Velicer, W F. APACrefauthors \ 1986 . Comparison of five rules for determining the number of components to retain Comparison of five rules for determining the number of components to retain . Psychological Bulletin 99 432--442

    1986

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.