IDEAS home Printed from https://ideas.repec.org/a/eee/jbrese/v139y2022icp1026-1043.html
   My bibliography  Save this article

How many factors in factor analysis? New insights about parallel analysis with confidence intervals

Author

Listed:
  • Iacobucci, Dawn
  • Ruvio, Ayalla
  • Román, Sergio
  • Moon, Sangkil
  • Herr, Paul M.

Abstract

Factor analysis is an extremely popular model for scale development prior to other modeling in much research in business and the social sciences. A central question in factor analysis remains the determination of the number of factors to extract and retain to explain as much of the data as possible, and do so parsimoniously. Parallel analysis can be helpful, but there is some confusion surrounding this technique, which may lead to incorrect conclusions. This research seeks first to clarify and correct these confusions. Second, we offer R, SAS, and SPSS programs to conduct parallel analysis in factor analysis. Third, we incorporate inferential statistics, enabling hypothesis testing and confidence intervals. Finally, we discuss how parallel analysis can help scholars in ongoing debates about individual differences scales, construct and measure dimensionality, and the utility of multi-item scales. Hopefully, the recurrent question, “How many factors?” can be answered more definitively.

Suggested Citation

  • Iacobucci, Dawn & Ruvio, Ayalla & Román, Sergio & Moon, Sangkil & Herr, Paul M., 2022. "How many factors in factor analysis? New insights about parallel analysis with confidence intervals," Journal of Business Research, Elsevier, vol. 139(C), pages 1026-1043.
    • Handle: RePEc:eee:jbrese:v:139:y:2022:i:c:p:1026-1043
    DOI: 10.1016/j.jbusres.2021.09.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0148296321006603
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jbusres.2021.09.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richard Montanelli & Lloyd Humphreys, 1976. "Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study," Psychometrika, Springer;The Psychometric Society, vol. 41(3), pages 341-348, September.
    2. John Horn, 1965. "A rationale and test for the number of factors in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 30(2), pages 179-185, June.
    3. Louis Guttman, 1954. "Some necessary conditions for common-factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 19(2), pages 149-161, June.
    4. Peter Bentler & Ke-Hai Yuan, 1998. "Tests for linear trend in the smallest eigenvalues of the correlation matrix," Psychometrika, Springer;The Psychometric Society, vol. 63(2), pages 131-144, June.
    5. Patil, Vivek H. & Singh, Surendra N. & Mishra, Sanjay & Todd Donavan, D., 2008. "Efficient theory development and factor retention criteria: Abandon the `eigenvalue greater than one' criterion," Journal of Business Research, Elsevier, vol. 61(2), pages 162-170, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexis Dinno, 2009. "Implementing Horn’s parallel analysis for principal component analysis and factor analysis," Stata Journal, StataCorp LP, vol. 9(2), pages 291-298, June.
    2. Agyeman, Stephen & Cheng, Lin, 2020. "Analysis of barriers to perceived service quality in Ghana: Students’ perspectives on bus mobility attributes," Transport Policy, Elsevier, vol. 99(C), pages 63-85.
    3. Yoo, Sun-Young & Vonk, M. Elizabeth, 2012. "The development and initial validation of the Immigrant Parental Stress Inventory (IPSI) in a sample of Korean immigrant parents," Children and Youth Services Review, Elsevier, vol. 34(5), pages 989-998.
    4. Joanna Radomska & Aleksandra Szpulak & Przemysław Wołczek, 2023. "A multi-item scale for open strategy measurement," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 50(1), pages 51-71, March.
    5. James Heckman & Rodrigo Pinto & Peter Savelyev, 2013. "Understanding the Mechanisms through Which an Influential Early Childhood Program Boosted Adult Outcomes," American Economic Review, American Economic Association, vol. 103(6), pages 2052-2086, October.
    6. Andrea Zammitti & Isabella Valbusa & Sara Santilli & Maria Cristina Ginevra & Salvatore Soresi & Laura Nota, 2023. "Development and Validation of the Decent Work for Inclusive and Sustainable Future Construction Scale in Italy," Sustainability, MDPI, vol. 15(15), pages 1-19, July.
    7. Mohieddine Rahmouni, 2014. "Perception des obstacles aux activités d'innovation dans les entreprises tunisiennes," Revue d’économie du développement, De Boeck Université, vol. 22(3), pages 69-98.
    8. James J. Heckman & Rodrigo Pinto, 2015. "Econometric Mediation Analyses: Identifying the Sources of Treatment Effects from Experimentally Estimated Production Technologies with Unmeasured and Mismeasured Inputs," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 6-31, February.
    9. Peres-Neto, Pedro R. & Jackson, Donald A. & Somers, Keith M., 2005. "How many principal components? stopping rules for determining the number of non-trivial axes revisited," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 974-997, June.
    10. Alexander K. Koch & Julia Nafziger, 2019. "Correlates of Narrow Bracketing," Scandinavian Journal of Economics, Wiley Blackwell, vol. 121(4), pages 1441-1472, October.
    11. Ard H. J. den Reijer & Pieter W. Otter & Jan P. A. M. Jacobs, 2024. "An heuristic scree plot criterion for the number of factors," Statistical Papers, Springer, vol. 65(6), pages 3991-4000, August.
    12. Yinqiu He & Zi Wang & Gongjun Xu, 2021. "A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 442-463, June.
    13. Edoardo Saccenti & Marieke E. Timmerman, 2017. "Considering Horn’s Parallel Analysis from a Random Matrix Theory Point of View," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 186-209, March.
    14. Salim Moussa, 2016. "A Comment on the Estimation of the Reliability of Multidimensional Marketing Constructs: A Store Personality Scale Application," Global Business Review, International Management Institute, vol. 17(5), pages 1125-1144, October.
    15. Godfred O Boateng & Shalean M Collins & Patrick Mbullo & Pauline Wekesa & Maricianah Onono & Torsten B Neilands & Sera L Young, 2018. "A novel household water insecurity scale: Procedures and psychometric analysis among postpartum women in western Kenya," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-28, June.
    16. A. Oumlil & Joseph Balloun, 1994. "Some simple structure significance tests for exploratory component analysis with market survey data," Quality & Quantity: International Journal of Methodology, Springer, vol. 28(4), pages 371-381, November.
    17. Sofie Kragh Pedersen & Alexander K. Koch & Julia Nafziger, 2014. "Who Wants Paternalism?," Bulletin of Economic Research, Wiley Blackwell, vol. 66(S1), pages 147-166, December.
    18. Stefan Schulenberg & Amanda Melton, 2010. "A Confirmatory Factor-Analytic Evaluation of the Purpose in Life Test: Preliminary Psychometric Support for a Replicable Two-Factor Model," Journal of Happiness Studies, Springer, vol. 11(1), pages 95-111, March.
    19. Hudson F Golino & Sacha Epskamp, 2017. "Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-26, June.
    20. Ting Dai & Adam Davey, 2023. "Determining Dimensionality with Dichotomous Variables: A Monte Carlo Simulation Study and Applications to Missing Data in Longitudinal Research," Mathematics, MDPI, vol. 11(6), pages 1-25, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jbrese:v:139:y:2022:i:c:p:1026-1043. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jbusres .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.