1932

Abstract

Bifactor and other hierarchical models have become central to representing and explaining observations in psychopathology, health, and other areas of clinical science, as well as in the behavioral sciences more broadly. This prominence comes after a relatively rapid period of rediscovery, however, and certain features remain poorly understood. Here, hierarchical models are compared and contrasted with other models of superordinate structure, with a focus on implications for model comparisons and interpretation. Issues pertaining to the specification and estimation of bifactor and other hierarchical models are reviewed in exploratory as well as confirmatory modeling scenarios, as are emerging findings about model fit and selection. Bifactor and other hierarchical models provide a powerful mechanism for parsing shared and unique components of variance, but care is required in specifying and making inferences about them.

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/content/journals/10.1146/annurev-clinpsy-050718-095522
2019-05-07
2024-10-06
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Literature Cited

  1. Abad FJ, Garcia-Garzon E, Garrido LE, Barrada JR 2017. Iteration of partially specified target matrices: application to the bi-factor case. Multivar. Behav. Res. 52:416–29
    [Google Scholar]
  2. Adcock CJ 1964. Higher-order factors. Br. J. Math. Stat. Psychol. 17:153–60
    [Google Scholar]
  3. Aguado J, Luciano JV, Cebolla A, Serrano-Blanco A, Soler J, Garcia-Campayo J 2015. Bifactor analysis and construct validity of the Five Facet Mindfulness Questionnaire (FFMQ) in non-clinical Spanish samples. Front. Psychol. 6:404
    [Google Scholar]
  4. Bauer DJ, Howard AL, Baldasaro RE, Curran PJ, Hussong AM 2013. A trifactor model for integrating ratings across multiple informants. Psychol. Methods 18:475–93
    [Google Scholar]
  5. Beaujean AA 2015. John Carroll's views on intelligence: bi-factor versus higher-order models. J. Intell. 3:121–36
    [Google Scholar]
  6. Bollen KA, Harden JJ, Ray S, Zavisca J 2014. BIC and alternative Bayesian information criteria in the selection of structural equation models. Struct. Equ. Model. 21:1–19
    [Google Scholar]
  7. Bonifay W, Cai L 2017. On the complexity of item response theory models. Multivar. Behav. Res. 52:465–84
    [Google Scholar]
  8. Carroll JB, Schweiker RF 1951. Factor analysis in educational research. Rev. Educ. Res. 21:368–88
    [Google Scholar]
  9. Caspi A, Houts RM, Belsky DW, Goldman-Mellor SJ, Harrington H 2014. The p factor: one general psychopathology factor in the structure of psychiatric disorders?. Clin. Psychol. Sci. 2:119–37
    [Google Scholar]
  10. DeMars CE 2006. Application of the bi-factor multidimensional item response theory model to testlet-based tests. J. Educ. Meas. 43:145–68
    [Google Scholar]
  11. Eid M, Geiser C, Koch T, Heene M 2017. Anomalous results in G-factor models: explanations and alternatives. Psychol. Methods 22:541–62
    [Google Scholar]
  12. Frisby CL, Beaujean AA 2015. Testing Spearman's hypotheses using a bi-factor model with WAIS-IV/WMS-IV standardization data. Intelligence 51:79–97
    [Google Scholar]
  13. Galton F 1883. Inquiries into Human Faculty and its Development London: Macmillan
    [Google Scholar]
  14. Gignac GE 2016. The higher-order model imposes a proportionality constraint: that is why the bifactor model tends to fit better. Intelligence 55:57–68
    [Google Scholar]
  15. Gonzalez O, MacKinnon DP 2018. A bifactor approach to model multifaceted constructs in statistical mediation analysis. Educ. Psychol. Meas. 78:5–31
    [Google Scholar]
  16. Green S, Yang Y 2018. Empirical underidentification with the bifactor model: a case study. Educ. Psychol. Meas. 78:717–36
    [Google Scholar]
  17. Greene AL, Eaton NR 2017. The temporal stability of the bifactor model comorbidity: an examination of moderated continuity pathways. Compr. Psychiatry 72:74–82
    [Google Scholar]
  18. Grunwald PD 2007. The Minimum Description Length Principle Cambridge, MA: MIT Press
    [Google Scholar]
  19. Gu H, Wen Z, Fan X 2017. Examining and controlling for wording effect in a self-report measure: a Monte Carlo simulation study. Struct. Equ. Model. 24:545–55
    [Google Scholar]
  20. Holzinger KJ, Harman HH 1938. Comparison of two factorial analyses. Psychometrika 3:45–60
    [Google Scholar]
  21. Holzinger KJ, Swineford F 1937. The bi-factor method. Psychometrika 2:41–54
    [Google Scholar]
  22. Humphreys LG 1981. The primary mental ability. Intelligence and Learning MP Friedman, JP Das, N O'Connor 87–102 New York: Plenum
    [Google Scholar]
  23. Jennrich RI, Bentler PM 2011. Exploratory bifactor analysis. Psychometrika 76:537–49
    [Google Scholar]
  24. Jennrich RI, Bentler PM 2012. Exploratory bifactor analysis: the oblique case. Psychometrika 77:442–54
    [Google Scholar]
  25. Kim H, Eaton NR 2015. The hierarchical structure of common mental disorders: connecting multiple levels of comorbidity, bifactor models, and predictive validity. J. Abnorm. Psychol. 124:1064–78
    [Google Scholar]
  26. Koch T, Holtmann J, Bohn J, Eid M 2018. Explaining general and specific factors in longitudinal multimethod, and bifactor models: Some caveats and recommendations. Psychol. Methods 23:505–23
    [Google Scholar]
  27. Krueger RF, Markon KE, Patrick CJ, Benning SD, Kramer MD 2007. Linking antisocial behavior, substance use, and personality: an integrative quantitative model of the adult externalizing spectrum. J. Abnorm. Psychol. 116:645–66
    [Google Scholar]
  28. Laceulle OM, Vollebergh WAM, Ormel J 2015. The structure of psychopathology in adolescence: replication of a general psychopathology factor in the TRAILS study. Clin. Psychol. Sci. 3:850–60
    [Google Scholar]
  29. Lahey BB, Applegate B, Hakes JK, Zald DH, Hariri AR, Rathouz PJ 2012. Is there a general factor of prevalent psychopathology during adulthood?. J. Abnorm. Psychol. 121:971–77
    [Google Scholar]
  30. Lv J, Liu JS 2014. Model selection principles in misspecified models. J. R. Statist. Soc. B 76:141–67
    [Google Scholar]
  31. Mansolf M, Reise SP 2016. Exploratory bifactor analysis: the Schmid–Leiman orthogonalization and Jennrich–Bentler rotations. Multivar. Behav. Res. 51:698–717
    [Google Scholar]
  32. Markon KE, Krueger RF 2004. An empirical comparison of information-theoretic selection criteria for multivariate behavior genetic models. Behav. Genet. 34:593–610
    [Google Scholar]
  33. Martel MM, Pan PM, Hoffman MS, Gadelha A, do Rosário MC 2017. A general psychopathology factor (P factor) in children: structural model analysis and external validation through familial risk and child global executive function. J. Abnorm. Psychol. 126:137–48
    [Google Scholar]
  34. McLarnon MJ, Goffin RD, Schneider TJ, Johnston NG 2016. To be or not to be: exploring the nature of positively and negatively keyed personality items in high-stakes testing. J. Personal. Assess. 98:480–90
    [Google Scholar]
  35. Murray AL, Johnson W 2013. The limitations of model fit in comparing the bi-factor versus higher-order models of human cognitive ability structure. Intelligence 41:407–22
    [Google Scholar]
  36. Nalisnick E, Smyth P 2017. Learning approximately objective priors. 33rd Conference on Uncertainty in Artificial Intelligence, Sydney, Australia, 11–15 August 2017 G Elidan, K Kersting 355–64 Red Hook, NY: Assoc. Uncertain. Artif. Intell.
    [Google Scholar]
  37. Naragon-Gainey K, Prenoveau JM, Brown TA, Zinbarg RE 2016. A comparison and integration of structural models of depression and anxiety in a clinical sample: support for and validation of the tri-level model. J. Abnorm. Psychol. 125:853–67
    [Google Scholar]
  38. Patalay P, Fonagy P, Deighton J, Belsky J, Vostanis P, Wolpert M 2015. A general psychopathology factor in early adolescence. Br. J. Psychiatry 207:15–22
    [Google Scholar]
  39. Reise SP 2012. The rediscovery of bifactor measurement models. Multivar. Behav. Res. 47:667–96
    [Google Scholar]
  40. Reise SP, Kim DS, Mansolf M, Widaman KF 2016. Is the bifactor model a better model or is it just better at modeling implausible responses? Application of iteratively reweighted least squares to the Rosenberg Self-Esteem Scale. Multivar. Behav. Res. 51:818–38
    [Google Scholar]
  41. Reise SP, Moore TM, Haviland MG 2010. Bifactor models and rotations: exploring the extent to which multidimensional data yield univocal scale scores. J. Personal. Assess. 92:544–59
    [Google Scholar]
  42. Rissanen J 2003. Complexity of simple nonlogarithmic loss functions. IEEE Trans. Inf. Theory 49:476–84
    [Google Scholar]
  43. Rissanen J 2007. Information and Complexity in Statistical Modeling New York: Springer
    [Google Scholar]
  44. Schmid J, Leiman JM 1957. The development of hierarchical factor solutions. Psychometrika 22:53–61
    [Google Scholar]
  45. Shevlin M, McElroy E, Bentall RP, Reininghaus U, Murphy J 2017. The psychosis continuum: testing a bifactor model of psychosis in a general population sample. Schizophr. Bull. 43:133–41
    [Google Scholar]
  46. Spearman CE 1904a. The proof and measurement of association between two things. Am. J. Psychol. 15:72–101
    [Google Scholar]
  47. Spearman CE 1904b. “General intelligence,” objectively determined and measured. Am. J. Psychol. 15:201–93
    [Google Scholar]
  48. Stochl J, Khandaker GM, Lewis G, Perez J, Goodyer IM 2015. Mood, anxiety, and psychotic phenomena measure a common psychopathological factor. Psychol. Med. 45:1483–93
    [Google Scholar]
  49. Thomson GH 1939. The Factorial Analysis of Human Ability London: Univ. Lond. Press
    [Google Scholar]
  50. Thurstone LL 1944. Second-order factors. Psychometrika 9:71–100
    [Google Scholar]
  51. Tomas JM, Oliver A 1999. Rosenberg's Self-Esteem Scale: two factors or method effects. Struct. Equ. Model. 6:84–98
    [Google Scholar]
  52. Waller NG 2018. Direct Schmid–Leiman transformations and rank-deficient loadings matrices. Psychometrika 83:858–70
    [Google Scholar]
  53. Wherry RJ 1959. Hierarchical factor solutions without rotation. Psychometrika 24:45–51
    [Google Scholar]
  54. Wherry RJ, Winer BJ 1953. A method for factoring large numbers of items. Psychometrika 18:161–79
    [Google Scholar]
  55. White H 1982. Maximum likelihood estimation of misspecified models. Econometrica 50:1–25
    [Google Scholar]
  56. Witthöft M, Fischer S, Jasper F, Rist F, Nater UM 2016. Clarifying the latent structure and correlates of somatic symptom distress: a bifactor model approach. Psychol. Assess. 28:109–15
    [Google Scholar]
  57. Yung Y-F, Thissen D, McLeod LD 1999. On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika 64:113–28
    [Google Scholar]
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