Advertisement

Quality & Quantity

, Volume 47, Issue 3, pp 1413–1427 | Cite as

Double serial correlation for multilevel growth curve models

  • Dickson Nkafu Anumendem
  • Geert Verbeke
  • Bieke De Fraine
  • Patrick Onghena
  • Jan Van Damme
Article

Abstract

Multilevel growth curve models for repeated measures data have become increasingly popular and stand as a flexible tool for investigating longitudinal change in students’ outcome variables. In addition, these models allow the estimation of school effects on students’ outcomes though making strong assumptions about the serial independence of level-1 residuals. This paper introduces a method which takes into account the serial correlation of level-1 residuals and also introduces such serial correlation at level-2 in a complex double serial correlation (DSC) multilevel growth curve model. The results of this study from both real and simulated data show a great improvement in school effects estimates compared to those that have previously been found using multilevel growth curve models without correcting for DSC for both the students’ status and growth criteria.

Keywords

Multilevel growth curve model Double serial correlation Student growth School effects 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anumendem, D.N., De Fraine, B., Onghena, P., Van Damme, J.: The impact of coding time on the estimation of school effects. Qual. Quant. (2011). doi: 10.1007/s11135-011-9581-3
  2. Bauer D.J., Cai L.: Consequences of unmodeled nonlinear effects in multilevel models. J. Educ. Behav. Stat. 34, 97–114 (2009)CrossRefGoogle Scholar
  3. Box, G.P., Jenkins, G.M.: Time Series Analysis—Forecasting and Control, revised edn. Holden-Day, San Francisco, CA (1970)Google Scholar
  4. Cleveland W.S., Devlin S.J.: Locally weighted regression: an approach to regression analysis by local fitting. J. Am. Stat. Assoc. 83, 596–610 (1988)CrossRefGoogle Scholar
  5. Diggle P.J.: An approach to the analysis of repeated measures. Biometrics 44, 959–971 (1988)CrossRefGoogle Scholar
  6. Diggle P.J.: Time Series: A Biostatistical Introduction. Oxford University Press, Oxford (1990)Google Scholar
  7. Diggle P.J., Liang K.-Y., Zeger S.L.: Analysis of Longitudinal Data. Clarendon Press, Oxford (1994)Google Scholar
  8. Ferron J., Dailey R., Yi Q.: Effects of misspecifying the first-level error structure in two-level models of change. Multivar. Behav. Res. 37, 379–403 (2002)CrossRefGoogle Scholar
  9. Fitzmaurice G.M., Laird N.M., Ware J.H.: Applied Longitudinal Analysis. Wiley, New Jersey (2004)Google Scholar
  10. Goldstein H., Healy M.J.R., Rasbash J.: Multilevel time series models with applications to repeated measures data. Stat. Med. 13, 1643–1655 (1994)CrossRefGoogle Scholar
  11. Harring J.R.: A nonlinear mixed effects model for latent variables. J. Educ. Behav. Stat. 34, 293–318 (2009)CrossRefGoogle Scholar
  12. Lesaffre E., Asefa M., Verbeke G.: Assessing the goodness-of-fit of the Laird and Ware model: an example: the Jimma infant survival differential study. Stat. Med. 18, 835–854 (1999)CrossRefGoogle Scholar
  13. Morrell C.H., Pearson J.D., Carter H.B., Brant L.J.: Estimating unknown transition times using a piecewise nonlinear mixed-effects model in men with prostate cancer. J. Am. Stat. Assoc. 90, 45–53 (1995)CrossRefGoogle Scholar
  14. Rasbash J., Browne W., Goldstein H., Yang M.: A User’s Guide to MLwiN. Institute of Education, London (2000)Google Scholar
  15. Raudenbush S.W., Willms J.D.: The estimation of school effects. J. Educ. Behav. Stat. 20, 307–335 (1995)Google Scholar
  16. Rowan, B., Denk, C.E.: Modelling the Academic Performance of Schools Using Longitudinal Data: An Analysis of School Effectiveness Measures and School and Principal Effects on School-Level Achievement. Far West Laboratory for Educational Research and Development, San Francisco (1982)Google Scholar
  17. SAS Institute Inc.: SAS User’s Guide: Statistics, 9th edn. SAS Institute Inc., Cary (2003)Google Scholar
  18. Scheerens J., Bosker R.J.: The Foundations of Educational Effectiveness. Pergamon, Oxford (1997)Google Scholar
  19. Singer J.D.: Using SAS proc mixed to fit multilevel models, hierarchical models, and individual growth models. J. Educ. Behav. Stat. 24, 323–355 (1998)Google Scholar
  20. Teddlie C., Reynolds D.: The International Handbook of School Effectiveness Research. Falmer Press, London (2000)Google Scholar
  21. Van Damme, J., Opdenakker, M.-C., Van Landeghem, G., De Fraine, B., Pustjens, H., Vande gaer, E.: Educational effectiveness: An introduction to international and flemish research on schools, teachers, and classes. Acco, Leuven (2006)Google Scholar
  22. Verbeke G., Lesaffre E.: The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Comput. Stat. Data. Anal. 23, 541–556 (1997)CrossRefGoogle Scholar
  23. Verbeke, G., Molenberghs, G.: Linear Mixed Models for Longitudinal Data. Springer Series in Statistics. Springer, New York (2000)Google Scholar
  24. Verbeke G., Lesaffre E., Brant L.J.: The detection of residual serial correlation in linear mixed models. Stat. Med. 17, 1391–1402 (1998)CrossRefGoogle Scholar
  25. Willms J.D., Raudenbush S.W.: A longitudinal hierarchical linear model for estimating school effects and their stability. J. Educ. Meas. 26, 209–232 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Dickson Nkafu Anumendem
    • 1
  • Geert Verbeke
    • 2
  • Bieke De Fraine
    • 1
  • Patrick Onghena
    • 3
  • Jan Van Damme
    • 1
  1. 1.Centre for Educational Effectiveness and EvaluationKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Interuniversity Institute for Biostatistics and statistical BioinformaticsKatholieke Universiteit LeuvenLeuvenBelgium
  3. 3.Centre for Methodology in Educational SciencesKatholieke Universiteit LeuvenLeuvenBelgium

Personalised recommendations