IDEAS home Printed from https://ideas.repec.org/a/sae/somere/v32y2003i2p208-252.html
   My bibliography  Save this article

Finite Sampling Properties of the Point Estimates and Confidence Intervals of the RMSEA

Author

Listed:
  • Patrick J. Curran
  • Kenneth A. Bollen
  • Feinian Chen
  • Pamela Paxton
  • James B. Kirby

Abstract

A key advantage of the root mean square error of approximation (RMSEA) is that under certain assumptions, the sample estimate has a known sampling distribution that allows for the computation of confidence intervals. However, little is known about the finite sampling behaviors of this measure under violations of these ideal asymptotic conditions. This information is critical for developing optimal criteria for using the RMSEA to evaluate model fit in practice. Using data generated from a computer simulation study, the authors empirically tested a set of theoretically generated research hypotheses about the sampling characteristics of the RMSEA under conditions commonly encountered in applied social science research. The results suggest that both the sample estimates and confidence intervals are accurate for sample sizes of n = 200 and higher, but caution is warranted in the use of these measures at smaller sample sizes, at least for the types of models considered here.

Suggested Citation

  • Patrick J. Curran & Kenneth A. Bollen & Feinian Chen & Pamela Paxton & James B. Kirby, 2003. "Finite Sampling Properties of the Point Estimates and Confidence Intervals of the RMSEA," Sociological Methods & Research, , vol. 32(2), pages 208-252, November.
    • Handle: RePEc:sae:somere:v:32:y:2003:i:2:p:208-252
    DOI: 10.1177/0049124103256130
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0049124103256130
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0049124103256130?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
    ---><---

    References listed on IDEAS

    as
    1. Ledyard Tucker & Charles Lewis, 1973. "A reliability coefficient for maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 1-10, March.
    2. Albert Satorra & Willem Saris, 1985. "Power of the likelihood ratio test in covariance structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 83-90, March.
    3. Roderick McDonald, 1989. "An index of goodness-of-fit based on noncentrality," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 97-103, December.
    4. James Steiger & Alexander Shapiro & Michael Browne, 1985. "On the multivariate asymptotic distribution of sequential Chi-square statistics," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 253-263, September.
    5. Mariano, Roberto S, 1982. "Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous-Equations Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 503-533, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Berger, Ron & Herstein, Ram & Silbiger, Avi & Barnes, Bradley R., 2018. "Is guanxi universal in China? Some evidence of a paradoxical shift," Journal of Business Research, Elsevier, vol. 86(C), pages 344-355.

    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. Randi Hammervold & Ulf Olsson, 2012. "Testing structural equation models: the impact of error variances in the data generating process," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(5), pages 1547-1570, August.
    2. Ogasawara, Haruhiko, 2016. "Bias correction of the Akaike information criterion in factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 144-159.
    3. Ke-Hai Yuan & Peter Bentler, 2006. "Mean Comparison: Manifest Variable Versus Latent Variable," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 139-159, March.
    4. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
    5. Ke-Hai Yuan & Peter M. Bentler & Wei Zhang, 2005. "The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis," Sociological Methods & Research, , vol. 34(2), pages 240-258, November.
    6. Kenneth A. Bollen & James B. Kirby & Patrick J. Curran & Pamela M. Paxton & Feinian Chen, 2007. "Latent Variable Models Under Misspecification: Two-Stage Least Squares (2SLS) and Maximum Likelihood (ML) Estimators," Sociological Methods & Research, , vol. 36(1), pages 48-86, August.
    7. Yuan, Ke-Hai & Hayashi, Kentaro & Bentler, Peter M., 2007. "Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1262-1282, July.
    8. P. M. Bentler & Chih-Ping Chou, 1990. "Model Search With TETRAD II and EQS," Sociological Methods & Research, , vol. 19(1), pages 67-79, August.
    9. Claes Fornell & Youjae Yi, 1992. "Assumptions of the Two-Step Approach to Latent Variable Modeling," Sociological Methods & Research, , vol. 20(3), pages 291-320, February.
    10. Sharma, Subhash & Mukherjee, Soumen & Kumar, Ajith & Dillon, William R., 2005. "A simulation study to investigate the use of cutoff values for assessing model fit in covariance structure models," Journal of Business Research, Elsevier, vol. 58(7), pages 935-943, July.
    11. David W. Gerbing & James C. Anderson, 1992. "Monte Carlo Evaluations of Goodness of Fit Indices for Structural Equation Models," Sociological Methods & Research, , vol. 21(2), pages 132-160, November.
    12. Scholderer, Joachim & Grunert, Klaus G., 2005. "Consumers, food and convenience: The long way from resource constraints to actual consumption patterns," Journal of Economic Psychology, Elsevier, vol. 26(1), pages 105-128, February.
    13. Michael W. Browne & Robert Cudeck, 1992. "Alternative Ways of Assessing Model Fit," Sociological Methods & Research, , vol. 21(2), pages 230-258, November.
    14. Kenneth A. Bollen, 1989. "A New Incremental Fit Index for General Structural Equation Models," Sociological Methods & Research, , vol. 17(3), pages 303-316, February.
    15. Felix T. Mavondo & Mark A. Farrell, 2000. "Measuring Market Orientation: Are There Differences Between Business Marketers and Consumer Marketers?," Australian Journal of Management, Australian School of Business, vol. 25(2), pages 223-244, September.
    16. Haruhiko Ogasawara, 2007. "Higher-order approximations to the distributions of fit indexes under fixed alternatives in structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 227-243, June.
    17. Kenneth A. Bollen & Jersey Liang, 1988. "Some Properties of Hoelter's CN," Sociological Methods & Research, , vol. 16(4), pages 492-503, May.
    18. César Merino-Soto & Gina Chávez-Ventura & Verónica López-Fernández & Guillermo M. Chans & Filiberto Toledano-Toledano, 2022. "Learning Self-Regulation Questionnaire (SRQ-L): Psychometric and Measurement Invariance Evidence in Peruvian Undergraduate Students," Sustainability, MDPI, vol. 14(18), pages 1-17, September.
    19. Julia Grass & Florian Krieger & Philipp Paulus & Samuel Greiff & Anja Strobel & Alexander Strobel, 2019. "Thinking in action: Need for Cognition predicts Self-Control together with Action Orientation," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-20, August.
    20. Fetene B. Tekle & Dereje W. Gudicha & Jeroen K. Vermunt, 2016. "Power analysis for the bootstrap likelihood ratio test for the number of classes in latent class models," 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. 10(2), pages 209-224, June.

    More about this item

    Statistics

    Access and download statistics

    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:sae:somere:v:32:y:2003:i:2:p:208-252. 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: SAGE Publications (email available below). General contact details of provider: .

    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.