1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Clinical Psychology
  4. Volume 10, 2014
  5. Article

Annual Review of Clinical Psychology

Volume 10, 2014

Exploratory Structural Equation Modeling: An Integration of the Best Features of Exploratory and Confirmatory Factor Analysis

Abstract

Exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), path analysis, and structural equation modeling (SEM) have long histories in clinical research. Although CFA has largely superseded EFA, CFAs of multidimensional constructs typically fail to meet standards of good measurement: goodness of fit, measurement invariance, lack of differential item functioning, and well-differentiated factors in support of discriminant validity. Part of the problem is undue reliance on overly restrictive CFAs in which each item loads on only one factor. Exploratory SEM (ESEM), an overarching integration of the best aspects of CFA/SEM and traditional EFA, provides confirmatory tests of a priori factor structures, relations between latent factors and multigroup/multioccasion tests of full (mean structure) measurement invariance. It incorporates all combinations of CFA factors, ESEM factors, covariates, grouping/multiple-indicator multiple-cause (MIMIC) variables, latent growth, and complex structures that typically have required CFA/SEM. ESEM has broad applicability to clinical studies that are not appropriately addressed either by traditional EFA or CFA/SEM.

Keyword(s): bifactor models, exploratory and confirmatory factor analysis, exploratory structural equation model within confirmatory factor analysis, exploratory structural equation models, multiple-indicator multiple-cause (MIMIC) models, multitrait-multimethod models
Loading

Article metrics loading...

/content/journals/10.1146/annurev-clinpsy-032813-153700
2014-03-28
2024-04-23
Loading full text...

Full text loading...

/deliver/fulltext/clinpsy/10/1/annurev-clinpsy-032813-153700.html?itemId=/content/journals/10.1146/annurev-clinpsy-032813-153700&mimeType=html&fmt=ahah

Literature Cited

  1. Asparouhov T, Muthén B. 2009. Exploratory structural equation modeling. Struct. Equ. Model. 16:397–438Presents mathematical/statistical basis of ESEM. [Google Scholar]
  2. Bandalos DL. 2008. Is parceling really necessary? A comparison of results from item parceling and categorical variable methodology. Struct. Equ. Model. 15:211–40 [Google Scholar]
  3. Bollen KA. 1989. Structural Equations with Latent Variables New York: Wiley
  4. Bollen KA. 2002. Latent variables in psychology and the social sciences. Annu. Rev. Psychol. 53:605–34 [Google Scholar]
  5. Brown TA. 2006. Confirmatory Factor Analysis for Applied Research New York: Guilford
  6. Browne MW. 2001. An overview of analytic rotation in exploratory factor analysis. Multivar. Behav. Res. 36:111–50 [Google Scholar]
  7. Burns GL, Walsh JA, Servera M, Lorenzo-Seva U, Cardo E, Rodríguez-Fornells A. 2013. Construct validity of ADHD/ODD rating scales: recommendations for the evaluation of forthcoming DSM-V ADHD/ODD scales. J. Abnorm. Child. Psychol. 41:15–26Applies ESEM to derive a latent MTMM matrix; overcomes many objections to the Campbell-Fiske criteria. [Google Scholar]
  8. Byrne BM. 2011. Structural Equation Modeling with Mplus: Basic Concepts, Applications, and Programming Mahwah, NJ: Routledge
  9. Byrne BM, Shavelson RJ, Muthén B. 1989. Testing for the equivalence of factor covariance and mean structures: the issue of partial measurement invariance. Psychol. Bull. 105:456–66 [Google Scholar]
  10. Campbell DT, Fiske DW. 1959. Convergent and discriminant validation by the multitrait- multimethod matrix. Psychol. Bull. 56:81–105 [Google Scholar]
  11. Campbell DT, O'Connell EJ. 1967. Methods factors in multitrait-multimethod matrices: multiplicative rather than additive?. Multivar. Behav. Res. 2:409–26 [Google Scholar]
  12. Carroll JB. 1953. An analytical solution for approximating simple structure in factor analysis. Psychometrika 18:123–38 [Google Scholar]
  13. Caspi A, Roberts BW, Shiner RL. 2005. Personality development: stability and change. Annu. Rev. Psychol. 56:453–84 [Google Scholar]
  14. Cattell RB. 1949. A note on factor invariance and the identification of factors. Br. J. Psychol. 2:134–39 [Google Scholar]
  15. Church AT, Burke PJ. 1994. Exploratory and confirmatory tests of the Big 5 and Tellegens three- and four-dimensional models. J. Personal. Soc. Psychol. 66:93–114 [Google Scholar]
  16. Cohen J. 1968. Multiple regression as a general data-analytic system. Psychol. Bull. 70:426–43 [Google Scholar]
  17. Comrey AL. 1984. Comparison of two methods to identify major personality factors. Appl. Psychol. Meas. 8:397–408 [Google Scholar]
  18. Costa PT Jr, McCrae RR. 1994. “Set like plaster”? Evidence for the stability of adult personality. Can Personality Change? T Heatherton, J Weinberger 21–40 Washington, DC: Am. Psychol. Assoc. [Google Scholar]
  19. Cudeck R, MacCallum RC. 2007. Factor Analysis at 100: Historical Developments and Future Directions Mahwah, NJ: Erlbaum
  20. De Winter JCF, Dodou D, Wieringa PA. 2009. Exploratory factor analysis with small sample sizes. Multivar. Behav. Res. 44:147–81 [Google Scholar]
  21. Dolan CV, Oort FJ, Stoel RD, Wichterts JM. 2009. Testing measurement invariance in the target rotated multigroup exploratory factor model. Struct. Equ. Model. 16:295–314 [Google Scholar]
  22. Furnham A, Guenole N, Levine SZ, Chamorro-Premuzic T. 2013. The NEO Personality Inventory–Revised: factor structure and gender invariance from exploratory structural equation modeling analyses in a high-stakes setting. Assessment 20:114–23 [Google Scholar]
  23. Gallucci M, Perugini M. 2007. The marker index: a new method of selection of marker variables in factor analysis. TPM Test. Psychom. Methodol. Appl. Psychol. 14:3–25 [Google Scholar]
  24. Howarth E. 1972. A factor analysis of selected markers for objective personality factors. Multivariate Behav. Res. 7:451–76 [Google Scholar]
  25. Jöreskog KG. 1969. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika 34:183–202 [Google Scholar]
  26. Jöreskog KG. 1979. Statistical estimation of structural models in longitudinal investigations. Longitudinal Research in the Study of Behavior and Development JR Nesselroade, B Baltes 303–51 New York: Academic [Google Scholar]
  27. Jöreskog KG, Sörbom D. 1979. Advances in Factor Analysis and Structural Equation Models New York: Univ. Press Am.
  28. Jöreskog K, Sörbom D. 1993. LISREL 8: Structural Equation Modeling with the SIMPLIS Command Language Chicago, IL: Sci. Softw. Intl.
  29. Kushner MG, Maurer EW, Thuras P, Donahue C, Frye B. et al. 2013. Hybrid cognitive behavioral therapy versus relaxation training for co-occurring anxiety and alcohol disorder: a randomized clinical trial. J. Consult. Clin. Psychol. 81:429–42RCT clinical intervention that demonstrates usefulness of ESEM in delineating symptoms of co-occurring anxiety and alcohol disorders. [Google Scholar]
  30. Lang FR, John D, Lüdtke O, Schupp J, Wagner GG. 2011. Short assessment of the Big Five: robust across survey methods except telephone interviewing. Behav. Res. Methods 43:548–67Applies ESEM to evaluate results of an RCT study. [Google Scholar]
  31. Little TD, Cunningham WA, Shahar G, Widaman KF. 2002. To parcel or not to parcel: exploring the question and weighing the merits. Struct. Equ. Model. 9151–73
  32. MacCallum RC, Zhang S, Preacher KJ, Rucker DD. 2002. On the practice of dichotomization of quantitative variables. Psychol. Methods 7:19–40 [Google Scholar]
  33. Maïano C, Morin AJ, Lafranchi MC, Therme P. 2013. The Eating Attitudes Test-26 revisited using exploratory structural equation modeling. J. Abnorm. Child Psychol. 41:775–88 [Google Scholar]
  34. Marsh HW. 1988. Multitrait multimethod analysis. Educational Research Methodology, Measurement and Evaluation: An International Handbook JP Keeves 570–80 Oxford, UK: Pergamon [Google Scholar]
  35. Marsh HW. 1993. Multitrait-multimethod analyses: inferring each trait/method combination with multiple indicators. Appl. Meas. Educ. 6:49–81 [Google Scholar]
  36. Marsh HW. 1994. Confirmatory factor analysis models of factorial invariance: a multifaceted approach. Struct. Equ. Model. 1:5–34 [Google Scholar]
  37. Marsh HW. 1995. The analysis of multitrait multimethod data. International Encyclopedia of Education TH Husen, TN Postlethwaite 5125–28 Oxford, UK: Pergamon, 2nd ed.. [Google Scholar]
  38. Marsh HW. 2007. Application of confirmatory factor analysis and structural equation modeling in sport/exercise psychology. Handbook of Sport Psychology G Tenenbaum, RC Eklund 774–98 New York: Wiley, 3rd ed.. [Google Scholar]
  39. Marsh HW, Grayson D. 1994. Longitudinal stability of latent means and individual differences: a unified approach. Struct. Equ. Model. 1:317–59 [Google Scholar]
  40. Marsh HW, Grayson D. 1995. Latent variable models of multitrait-multimethod data. Structural Equation Modeling: Concepts, Issues, and Applications RH Hoyle 177–98 Thousand Oaks, CA: Sage [Google Scholar]
  41. Marsh HW, Hau K-T. 1996. Assessing goodness of fit: Is parsimony always desirable?. J. Exp. Educ. 64:364–90 [Google Scholar]
  42. Marsh HW, Hau K-T, Grayson D. 2005. Goodness of fit evaluation in structural equation modeling. Psychometrics: A Festschrift to Roderick P. McDonald A Maydeu-Olivares, J McArdle 275–340 Hillsdale, NJ: Erlbaum [Google Scholar]
  43. Marsh HW, Hau K-T, Balla JR, Grayson D. 1998. Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivar. Behav. Res. 33:181–220 [Google Scholar]
  44. Marsh HW, Hocevar D. 1988. A new, more powerful approach to multitrait-multimethod analyses: application of second-order confirmatory factor analysis. J. Appl. Psychol. 73:107–11 [Google Scholar]
  45. Marsh HW, Hocevar D. 1991. The multidimensionality of students' evaluations of teaching effectiveness: the generality of factor structures across academic discipline, instructor level, and course level. Teach. Teach. Educ. 7:9–18 [Google Scholar]
  46. Marsh HW, Liem GAD, Martin AJ, Morin AJS, Nagengast B. 2011a. Methodological- measurement fruitfulness of exploratory structural equation modeling (ESEM): new approaches to key substantive issues in motivation and engagement. J. Psychoeduc. Assess. 29:322–46 [Google Scholar]
  47. Marsh HW, Lüdtke O, Muthén BO, Asparouhov T, Morin AJS, Trautwein U. 2010. A new look at the Big Five factor structure through exploratory structural equation modeling. Psychol. Assess. 22:471–91Resolves longstanding debate about the appropriateness of EFA and CFA for the NEO-FFI Big Five personality inventory. [Google Scholar]
  48. Marsh HW, Lüdtke O, Nagengast B, Morin AJS, Von Davier M. 2013a. Why item parcels are (almost) never appropriate: Two wrongs do not make a right—camouflaging misspecification with item parcels in CFA models. Psychol. Methods 18:257–84Demonstrates inappropriateness of item parcels with real/simulated data unless ICM-CFAs at item level fit, as well as ESEMs. [Google Scholar]
  49. Marsh HW, Muthén B, Asparouhov T, Lüdtke O, Robitzsch A. et al. 2009. Exploratory structural equation modeling, integrating CFA and EFA: application to students' evaluations of university teaching. Struct. Equ. Model. 16:439–76Empirically demonstrates ESEM; introduces 13-model taxonomy of ESEM invariance over multiple groups and occasions as well as application of ESEM MIMIC. [Google Scholar]
  50. Marsh HW, Nagengast B, Morin AJS. 2013b. Measurement invariance of Big Five factors over the life span: ESEM tests of gender, age, plasticity, maturity, and la dolce vita effects. Dev. Psychol. 491194–218Introduces EwC; extends the hybrid integration of MIMIC and multigroup approaches to invariance; posits the la dolce vita effect of personality change in old age.
  51. Marsh HW, Nagengast B, Morin AJS, Parada RH, Craven RG, Hamilton LR. 2011b. Construct validity of the multidimensional structure of bullying and victimization: an application of exploratory structural equation modeling. J. Educ. Psychol. 103:701–32 [Google Scholar]
  52. Marsh HW, O'Neill R. 1984. Self Description Questionnaire III: the construct validity of multidimensional self-concept ratings by late adolescents. J. Educ. Meas. 21:2153–74 [Google Scholar]
  53. Marsh HW, Tracey DK, Craven RG. 2006. Multidimensional self-concept structure for preadolescents with mild intellectual disabilities: a hybrid multigroup-MIMIC approach to factorial invariance and latent mean differences. Educ. Psychol. Meas. 66:795–818 [Google Scholar]
  54. Marsh HW, Vallerand RJ, Lafrenière M-AK, Parker P, Morin AJS. et al. 2013c. Passion: Does one scale fit all? Construct validity of two-factor passion scale and psychometric invariance over different activities and languages. Psychol. Assess. 25:796–809 [Google Scholar]
  55. McCrae RR, Costa Jr PT. 1997. Personality trait structure as a human universal. Am. Psychol. 52:509–16 [Google Scholar]
  56. McCrae RR, Zonderman AB, Costa PT Jr, Bond MH, Paunonen S. 1996. Evaluating the replicability of factors in the revised NEO Personality Inventory: confirmatory factor analysis versus Procrustes rotation. J. Personal. Soc. Psychol. 70:552–66 [Google Scholar]
  57. McDonald RP. 1985. Factor Analysis and Related Methods Hillsdale, NJ: Erlbaum
  58. Meleddu M, Guicciardi M, Scalas LF, Fadda D. 2012. Validation of an Italian version of the Oxford Happiness Inventory in adolescence. J. Personal. Assess. 94:175–85 [Google Scholar]
  59. Meredith W. 1964. Rotation to achieve factorial invariance. Psychometrika 29:187–206 [Google Scholar]
  60. Meredith W. 1993. Measurement invariance, factor analysis and factorial invariance. Psychometrika 58:525–43 [Google Scholar]
  61. Millsap RE. 2011. Statistical Approaches to Measurement Invariance New York: Routledge
  62. Mora PA, Berkowitz A, Contrada RJ, Wisnivesky J, Horne R. et al. 2011. Factor structure and longitudinal invariance of the Medical Adherence Report Scale–Asthma. Psychol. Health 26:6713–27 [Google Scholar]
  63. Morin AJS, Maïano C. 2011. Cross-validation of the short form of the physical self-inventory (PSI-S) using exploratory structural equation modeling (ESEM). Psychol. Sport Exerc. 12:540–54 [Google Scholar]
  64. Morin AJS, Marsh HW, Nagengast B. 2013. Exploratory structural equation modeling: an introduction. Structural Equation Modeling: A Second Course, ed. GR Hancock, RO Mueller 395–436 Greenwich, CT: IAP, 2nd ed..Provides a comprehensive overview of ESEM and subsequent extensions (e.g., EwC) with examples (including Mplus syntax) based on simulated data. [Google Scholar]
  65. Muthén B, Asparouhov T. 2012. Bayesian structural equation modeling: a more flexible representation of substantive theory. Psychol. Methods 17:313–35 [Google Scholar]
  66. Muthén BO. 2002. Beyond SEM: general latent variable modeling. Behaviormetrika 29:81–117 [Google Scholar]
  67. Muthén LK, Muthén BO. 2009. Mplus short courses. Topic 1: Exploratory factor analysis, confirmatory factor analysis, and structural equation modeling for continuous outcomes. Los Angeles, CA: Muthén & Muthén http://www.statmodel.com/course_materials.shtml
  68. Myers ND, Chase MA, Pierce SW, Martin E. 2011. Coaching efficacy and exploratory structural equation modeling: a substantive-methodological synergy. J. Sport Exerc. Psychol. 33:779–806 [Google Scholar]
  69. Olson JF, Martin MO, Mullis IVS. 2008. TIMSS 2007 Technical Report Chestnut Hill, MA: TIMSS, PIRLS Intl. Study Cent.
  70. Organ. Econ. Coop. Dev 2007. PISA 2006: Science Competencies for Tomorrow's World. Paris: Organ. Econ. Coop. Dev.
  71. Overall JE. 1974. Marker variable factor analysis: a regional principal axes solution. Multivar. Behav. Res. 9:149–64 [Google Scholar]
  72. Pettersson E, Turkheimer E, Horn E, Menatti AR. 2012. The general factor of personality and evaluation. Eur. J. Personal. 26:292–302Provides the first published application of the ESEM bifactor model, with target rotation as an alternative to higher-order factor models. [Google Scholar]
  73. Reise SP. 2012. The rediscovery of bifactor measurement models. Multivar. Behav. Res. 47:667–96 [Google Scholar]
  74. Sass DA, Schmitt TA. 2010. A comparative investigation of rotation criteria within exploratory factor analysis. Multivar. Behav. Res. 45:1–33 [Google Scholar]
  75. Sass DA, Smith PL. 2006. The effects of parceling unidimensional scales on structural parameter estimates in structural equation modeling. Struct. Equ. Model. 13:566–86 [Google Scholar]
  76. Schmitt TA, Sass DA. 2011. Rotation criteria and hypothesis testing for exploratory factor analysis: implications for factor pattern loadings and interfactor correlations. Educ. Psychol. Meas. 71:95–113 [Google Scholar]
  77. Skrondal A, Rabe-Hesketh S. 2004. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models New York: Chapman & Hall/CRC
  78. Strauss ME, Smith GT. 2009. Construct validity: advances in theory and methodology. Annu. Rev. Clin. Psychol. 5:1–25 [Google Scholar]
  79. Thurstone LL. 1947. Multiple Factor Analysis Chicago: Univ. Chicago Press
  80. Toland MD, De Ayala RJ. 2005. A multilevel factor analysis of students' evaluations of teaching. Educ. Psychol. Meas. 65:272–96 [Google Scholar]
  81. Tomarken AJ, Waller NG. 2005. Structural equation modeling: strengths, limitations, and misconceptions. Annu. Rev. Clin. Psychol. 1:31–65 [Google Scholar]
  82. Vandenberg RJ, Lance CE. 2000. A review and synthesis of the measurement invariance literature: suggestions, practices, and recommendations for organizational research. Organ. Res. Methods 3:4–70 [Google Scholar]
  83. Vassend O, Skrondal A. 1997. Validation of the NEO Personality Inventory and the five-factor model. Can findings from exploratory and confirmatory factor analysis be reconciled?. Eur. J. Personal. 11:147–66 [Google Scholar]
  84. Velicer WF, Fava JL. 1998. The effects of variable and subject sampling on factor pattern recovery. Psychol. Methods 3:231–51 [Google Scholar]
  85. Williams LJ, O'Boyle EH Jr. 2008. Measurement models for linking latent variables and indicators: a review of human resource management research using parcels. Hum. Resour. Manag. Rev. 18:233–42 [Google Scholar]
/content/journals/10.1146/annurev-clinpsy-032813-153700
Loading
Exploratory Structural Equation Modeling: An Integration of the Best Features of Exploratory and Confirmatory Factor Analysis
Annual Review of Clinical Psychology 10, 85 (2014); https://doi.org/10.1146/annurev-clinpsy-032813-153700
/content/journals/10.1146/annurev-clinpsy-032813-153700
/content/journals/10.1146/annurev-clinpsy-032813-153700
Loading

Data & Media loading...

Supplemental Material

Supplementary Data

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error