IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v81y2002i1p47-66.html
   My bibliography  Save this article

Asymptotic Expansions and Bootstrap Approximations in Factor Analysis

Author

Listed:
  • Ichikawa, Masanori
  • Konishi, Sadanori

Abstract

We derive asymptotic expansions for the distributions of the normal theory maximum likelihood estimators of unique variances and uniquenesses (standardized unique variances) in the factor analysis model. Asymptotic expansions are given for the distributions of non-Studentized and also Studentized statistics to construct accurate confidence intervals. In the case of Studentized statistics, we investigate the accuracy of the asymptotic approximations to the exact distributions that are determined by Monte Carlo simulations. The results show that, compared with normal approximations, the asymptotic expansions generally improve the accuracy of the approximations in the tail area except for the cases of the uniqueness estimators whose true values are close to their upper bounds unity. We also compare three types of confidence intervals that are based on the distributions of the Studentized statistics; each of which employs normal approximation, asymptotic expansion of the percentile points of the Studentized statistic, and further modification using the bootstrap. The results show that while the first type of confidence intervals were far from equal-tailed, the latter two achieved better balance in both sides.

Suggested Citation

  • Ichikawa, Masanori & Konishi, Sadanori, 2002. "Asymptotic Expansions and Bootstrap Approximations in Factor Analysis," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 47-66, April.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:1:p:47-66
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(01)91991-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Otto Driel, 1978. "On various causes of improper solutions in maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 225-243, June.
    2. Robert Jennrich & Dorothy Thayer, 1973. "A note on Lawley's formulas for standard errors in maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 571-580, December.
    3. Masanori Ichikawa & Sadanori Konishi, 1995. "Application of the bootstrap methods in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 60(1), pages 77-93, March.
    4. Fujikoshi, Yasunori, 1985. "Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria," Journal of Multivariate Analysis, Elsevier, vol. 17(1), pages 27-37, August.
    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. Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
    2. Weihua Fan & Gregory R. Hancock, 2012. "Robust Means Modeling," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 137-156, February.
    3. Alban Mbina Mbina & Guy Martial Nkiet & Fulgence Eyi Obiang, 2019. "Variable selection in discriminant analysis for mixed continuous-binary variables and several groups," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 773-795, September.
    4. Roderick McDonald, 1986. "Describing the elephant: Structure and function in multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 513-534, December.
    5. Ke-Hai Yuan & Yubin Tian & Hirokazu Yanagihara, 2015. "Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 379-405, June.
    6. David Ory & Patricia Mokhtarian, 2010. "The impact of non-normality, sample size and estimation technique on goodness-of-fit measures in structural equation modeling: evidence from ten empirical models of travel behavior," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(3), pages 427-445, April.
    7. Leland Wilkinson, 1989. "A Cautionary Note on the Use of Factor Analysis:," Sociological Methods & Research, , vol. 17(4), pages 449-459, May.
    8. Nkiet, Guy Martial, 2012. "Direct variable selection for discrimination among several groups," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 151-163.
    9. Kevin M Cummins & Eileen V Pitpitan & Ty Brumback & Tyler M Moore & Ryan S Trim & Duncan B Clark & Sandra A Brown & Susan F Tapert, 2022. "Comparison of factor analysis models applied to the NCANDA neuropsychological test battery," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-22, February.
    10. Kohei Adachi, 2013. "Factor Analysis with EM Algorithm Never Gives Improper Solutions when Sample Covariance and Initial Parameter Matrices Are Proper," Psychometrika, Springer;The Psychometric Society, vol. 78(2), pages 380-394, April.
    11. Feinian Chen & Kenneth A. Bollen & Pamela Paxton & Patrick J. Curran & James B. Kirby, 2001. "Improper Solutions in Structural Equation Models," Sociological Methods & Research, , vol. 29(4), pages 468-508, May.
    12. Ory, David T, 2007. "Structural Equation Modeling of Relative Desired Travel Amounts," Institute of Transportation Studies, Working Paper Series qt8mj659fp, Institute of Transportation Studies, UC Davis.
    13. Masanori Ichikawa & Sadanori Konishi, 1995. "Application of the bootstrap methods in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 60(1), pages 77-93, March.
    14. Hao, Jian & Krishnamoorthy, K., 2001. "Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 62-82, July.
    15. Jonas Månsson & Josefin Dahlander, 2011. "Social interaction impact on attitudes – Native Swedes’ attitudes towards labour immigrants and guest workers after hurricane Gudrun," Baltic Journal of Economics, Baltic International Centre for Economic Policy Studies, vol. 11(1), pages 51-64, July.
    16. Guangjian Zhang & Minami Hattori & Lauren A. Trichtinger, 2023. "Rotating Factors to Simplify Their Structural Paths," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 865-887, September.
    17. Siotani, Minoru & Wakaki, Hirofumi, 2006. "Contributions to multivariate analysis by Professor Yasunori Fujikoshi," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1914-1926, October.
    18. Nakagawa, Tomoyuki & Watanabe, Hiroki & Hyodo, Masashi, 2021. "Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    19. Kenneth A. Bollen, 1987. "Outliers and Improper Solutions," Sociological Methods & Research, , vol. 15(4), pages 375-384, May.
    20. Bryan, Victoria M. & Mayer, John D., 2020. "A meta-analysis of the correlations among broad intelligences: Understanding their relations," Intelligence, Elsevier, vol. 81(C).

    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:jmvana:v:81:y:2002:i:1:p:47-66. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.