IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v39y2014i5p394-422.html
   My bibliography  Save this article

Multilevel Factor Analysis by Model Segregation

Author

Listed:
  • Jonathan Schweig

Abstract

Measures of classroom environments have become central to policy efforts that assess school and teacher quality. This has sparked a wide interest in using multilevel factor analysis to test measurement hypotheses about classroom-level variables. One approach partitions the total covariance matrix and tests models separately on the between-classroom and within-classroom levels. This article shows that when using this approach, robust test statistics, including rescaled and residual-based test statistics provide better inferences about the classroom-level measurement structure than the widely used likelihood ratio test statistic even when the number of classrooms is large, and there is no excess kurtosis in the observed variables. This article then presents an empirical example and a simulation study to demonstrate how item intraclass correlations and within-group sample sizes influence test statistic performance. The results have implications for the study of classroom environments.

Suggested Citation

  • Jonathan Schweig, 2014. "Multilevel Factor Analysis by Model Segregation," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 394-422, October.
    • Handle: RePEc:sae:jedbes:v:39:y:2014:i:5:p:394-422
    DOI: 10.3102/1076998614544784
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998614544784
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998614544784?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. Yuan, Ke-Hai & Bentler, Peter M., 2003. "Eight test statistics for multilevel structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 89-107, October.
    2. Yuan, Ke-Hai & Bentler, Peter M., 2006. "Asymptotic robustness of standard errors in multilevel structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1121-1141, May.
    3. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    4. N. Longford & B. Muthén, 1992. "Factor analysis for clustered observations," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 581-597, December.
    5. Ke-Hai Yuan & Peter Bentler, 2002. "On normal theory based inference for multilevel models with distributional violations," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 539-561, December.
    6. Jiajuan Liang & Peter Bentler, 2004. "An EM algorithm for fitting two-level structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 101-122, March.
    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. Ke-Hai Yuan & Kentaro Hayashi, 2005. "On muthén’s maximum likelihood for two-level covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 147-167, March.
    2. Ke-Hai Yuan & Peter Bentler, 2004. "On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 437-457, September.
    3. Yuan, Ke-Hai & Bentler, Peter M., 2006. "Asymptotic robustness of standard errors in multilevel structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1121-1141, May.
    4. 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.
    5. Yuan, Ke-Hai & Bentler, Peter M., 2005. "Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 328-343, June.
    6. Peter M. Bentler, 2016. "Covariate-free and Covariate-dependent Reliability," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 907-920, December.
    7. Yuan, Ke-Hai & Bentler, Peter M., 2003. "Eight test statistics for multilevel structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 89-107, October.
    8. Jean Jacod & Michael Sørensen, 2018. "A review of asymptotic theory of estimating functions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 415-434, July.
    9. Ron Mittelhammer & George Judge, 2009. "A Minimum Power Divergence Class of CDFs and Estimators for the Binary Choice Model," International Econometric Review (IER), Econometric Research Association, vol. 1(1), pages 33-49, April.
    10. R. M. Balan & Ioana Schiopu-Kratina, 2004. "Asymptotic Results with Generalized Estimating Equations for Longitudinal data II," RePAd Working Paper Series lrsp-TRS398, Département des sciences administratives, UQO.
    11. Majid Ghasemy & Isabel Maria Rosa-Díaz & James Eric Gaskin, 2021. "The Roles of Supervisory Support and Involvement in Influencing Scientists’ Job Satisfaction to Ensure the Achievement of SDGs in Academic Organizations," SAGE Open, , vol. 11(3), pages 21582440211, July.
    12. Benjamin Agbo & Hussain Al-Aqrabi & Richard Hill & Tariq Alsboui, 2022. "Missing Data Imputation in the Internet of Things Sensor Networks," Future Internet, MDPI, vol. 14(5), pages 1-16, May.
    13. Boik, Robert J., 2008. "An implicit function approach to constrained optimization with applications to asymptotic expansions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 465-489, March.
    14. Steven Boker & Michael Neale & Hermine Maes & Michael Wilde & Michael Spiegel & Timothy Brick & Jeffrey Spies & Ryne Estabrook & Sarah Kenny & Timothy Bates & Paras Mehta & John Fox, 2011. "OpenMx: An Open Source Extended Structural Equation Modeling Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 306-317, April.
    15. Ke-Hai Yuan & Wai Chan & Yubin Tian, 2016. "Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 329-351, April.
    16. Wai-Yin Poon & Hai-Bin Wang, 2010. "Analysis of a Two-Level Structural Equation Model With Missing Data," Sociological Methods & Research, , vol. 39(1), pages 25-55, August.
    17. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    18. Bengt O. Muthã‰N, 1994. "Multilevel Covariance Structure Analysis," Sociological Methods & Research, , vol. 22(3), pages 376-398, February.
    19. Soyoung Kim & Jae-Kwang Kim & Kwang Woo Ahn, 2022. "A calibrated Bayesian method for the stratified proportional hazards model with missing covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 169-193, April.
    20. Michon, Richard & Chebat, Jean-Charles & Turley, L. W., 2005. "Mall atmospherics: the interaction effects of the mall environment on shopping behavior," Journal of Business Research, Elsevier, vol. 58(5), pages 576-583, May.

    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:jedbes:v:39:y:2014:i:5:p:394-422. 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.