Skip to main content
SpringerLink
Log in
Book cover

Handbook of Multilevel Analysis pp 401–433Cite as

Resampling Multilevel Models

  • Chapter

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • M. K. Andersson and S. Karlsson. Bootstrapping error component models. Computational Statistics, 16:221–231, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  • J. G. Bagaka's. Two Level Nested Hierarchical Linear Model with Random Intercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com)

    Google Scholar 

  • L. Bellmann, J. Breitung, and J. Wagner. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14:329–342, 1989.

    Article  Google Scholar 

  • J. Booth. Bootstrap methods for generalized linear mixed models with applications to small area estimation. In G. U. H. Seeber, B. J. Francis, R. Hatzinger, and G. Steckel-Berger, editors, Statistical Modelling: Proceedings of the 10th International Workshop on Statistical Modelling, Innsbruck, Austria, 10–14 July, 1995, pages 43–51. Springer, New York, 1995.

    Google Scholar 

  • N. E. Breslow and X. Lin. Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82:81–91, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  • T. S. Breusch. Useful invariance results for generalized regression models. Journal of Econometrics, 13:327–340, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  • F. M. T. A. Busing. Distribution characteristics of variance estimates in two-level models: A Monte Carlo study. Technical Report PRM 93-04, Leiden University, Department of Psychology, Leiden, 1993.

    Google Scholar 

  • F. M. T. A. Busing, E. Meijer, and R. Van der Leeden. MLA: Software for multilevel analysis of data with two levels. User's guide for version 1.0b. Technical Report PRM 94-01, Leiden University, Department of Psychology, Leiden, 1994.

    Google Scholar 

  • F. M. T. A. Busing, E. Meijer, and R. Van der Leeden. The MLA program for two-level analysis with resampling options. In T. A. B. Snijders, B. Engel, J. C. Van Houwelingen, A. Keen, G. J. Stemerdink, and M. Verbeek, editors, SSS'95: Toeval zit Overal, pages 37–58. iec ProGAMMA, Groningen, 1995.

    Google Scholar 

  • F. M. T. A. Busing, E. Meijer, and R. Van der Leeden. Delete-m jackknife for unequal m. Statistics and Computing, 9:3–8, 1999.

    Article  Google Scholar 

  • F. M. T. A. Busing, E. Meijer, and R. Van der Leeden. MLA: Software for MultiLevel Analysis of Data with Two Levels. User's Guide for Version 4.1. Leiden University, Department of Psychology, Leiden, 2005.

    Google Scholar 

  • F. M. T. A. Busing, R. Van der Leeden, and E. Meijer. MLA: Software for two-level analysis with resampling options. Multilevel Modelling Newsletter, 7(3):11–13, 1995.

    Google Scholar 

  • J. Carpenter, H. Goldstein, and J. Rasbash. A non-parametric bootstrap for multilevel models. Multilevel Modelling Newsletter, 11(1):2–5, 1999.

    Google Scholar 

  • A. C. Davison and D. V. Hinkley. Bootstrap Methods and their Application. Cambridge University Press, Cambridge, UK, 1997.

    MATH  Google Scholar 

  • J. de Leeuw and E. Meijer. Introduction to multilevel analysis. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • D. Draper. Bayesian multilevel analysis and MCMC. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • S. H. C. lowercaseDu Toit and M. lowercaseDu Toit. Multilevel structural equation modeling. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • B. Efron. The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia, 1982.

    Google Scholar 

  • B. Efron. Better bootstrap confidence intervals. Journal of the American Statistical Association, 82:171–200, 1987. (with discussion).

    Article  MATH  MathSciNet  Google Scholar 

  • B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap. Chapman & Hall, New York, 1993.

    MATH  Google Scholar 

  • C. C. Frangos and W. R. Schucany. Jackknife estimation of the bootstrap acceleration constant. Computational Statistics & Data Analysis, 9:271–282, 1990.

    Article  MATH  Google Scholar 

  • D. A. Freedman. Bootstrapping regression models. The Annals of Statistics, 9:1218–1228, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  • W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors. Markov Chain Monte Carlo in Practice. Chapman & Hall, London, 1996.

    Google Scholar 

  • H. Goldstein. Consistent estimators for multilevel generalised linear models using an iterated bootstrap. Multilevel Modelling Newsletter, (1):3–6, 1996.

    Google Scholar 

  • H. Goldstein. Bootstrapping for multilevel models. Working paper, Multilevel Models Project, London, 1998.

    Google Scholar 

  • H. Goldstein. Multilevel Statistical Models, 3rd edition. Edward Arnold, London, 2003.

    MATH  Google Scholar 

  • C. Gouri'eroux and A. Monfort. Simulation-Based Econometric Methods. Oxford University Press, Oxford, UK, 1996.

    Google Scholar 

  • P. Hall. The Bootstrap and Edgeworth Expansion. Springer, New York, 1992.

    Google Scholar 

  • D. Hedeker. Multilevel models for ordinal and nominal variables. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • D. V. Hinkley. Bootstrap methods. Journal of the Royal Statistical Society, Series B, 50:321–337, 1988.

    MATH  MathSciNet  Google Scholar 

  • I. G. G. Kreft, J. de Leeuw, and R. Van der Leeden. Review of five multilevel analysis programs: BMDP-5V, GENMOD, HLM, ML3, VARCL. The American Statistician, 48:324–335, 1994.

    Article  Google Scholar 

  • A. Y. C. Kuk. Asymptotically unbiased estimation in generalized linear models with random effects. Journal of the Royal Statistical Society, Series B, 57:395–407, 1995.

    MATH  MathSciNet  Google Scholar 

  • N. M. Laird and T. A. Louis. Empirical Bayes confidence intervals based on bootstrap samples. Journal of the American Statistical Association, 82:739–757, 1987. (with discussion)

    Article  MATH  MathSciNet  Google Scholar 

  • N. M. Laird and T. A. Louis. Empirical Bayes confidence intervals for a series of related experiments. Biometrics, 45:481–495, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  • W. Langer. Mehrebenenanalyse: eine Einführung für Forschung und Praxis. VS Verlag für Sozialwissenschaften, Wiesbaden, Germany, 2004.

    Google Scholar 

  • D. J. LeBlond. Methodology for Predicting Batch Manufacturing Risk. Master's thesis, Colorado State University, Fort Collins, 2005.

    Google Scholar 

  • S.-Y. Lee. Multilevel analysis of structural equation models. Biometrika, 77:763–772, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  • N. T. Longford. VARCL. Software for Variance Component Analysis of Data with Nested Random Effects (Maximum Likelihood). Educational Testing Service, Princeton, NJ, 1990.

    Google Scholar 

  • N. T. Longford. Missing data. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • J. R. Magnus. Maximum likelihood estimation of the GLSmodel with unknown parameters in the disturbance covariance matrix. Journal of Econometrics, 7:281–312, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  • B. D. McCullough and H. D. Vinod. Implementing the double bootstrap. Computational Economics, 12:79–95, 1998.

    Article  MATH  Google Scholar 

  • E. Meijer, F. M. T. A. Busing, and R. Van der Leeden. Estimating bootstrap confidence intervals for two-level models. In J. J. Hox and E. D. de Leeuw, editors, Assumptions, Robustness, and Estimation Methods in Multivariate Modeling, pages 35–47. TT Publicaties, Amsterdam, 1998.

    Google Scholar 

  • E. Meijer, R. Van der Leeden, and F. M. T. A. Busing. Implementing the bootstrap for multilevel models. Multilevel Modelling Newsletter, 7(2):7–11, 1995.

    Google Scholar 

  • A. M. Mood, F. A. Graybill, and D. C. Boes. Introduction to the Theory of Statistics, 3rd edition. McGraw-Hill, Singapore, 1974.

    MATH  Google Scholar 

  • L. H. Moulton and S. L. Zeger. Analyzing repeated measures on generalized linear models via the bootstrap. Biometrics, 45:381–394, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  • B. O. Muth'en. Multilevel covariance structure analysis. Sociological Methods & Research, 22:376–398, 1994.

    Article  Google Scholar 

  • H. Putter. Consistency of Resampling Methods. PhD thesis, Leiden University, Leiden, 1994.

    Google Scholar 

  • M. H. Quenouille. Approximate tests of correlation in time series. Journal of the Royal Statistical Society, Series B, 11:68–84, 1949.

    MATH  MathSciNet  Google Scholar 

  • M. H. Quenouille. Notes on bias in estimation. Biometrika, 43:353–360, 1956.

    MATH  MathSciNet  Google Scholar 

  • J. Rasbash and W. Browne. Non-hierarchical multilevel models. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • J. Rasbash, F. Steele, W. J. Browne, and B. Prosser. A User's Guide to MLwiN. Version 2.0. Centre for Multilevel Modelling, University of Bristol, Bristol, UK, 2005.

    Google Scholar 

  • S. W. Raudenbush. Many small groups. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • S. W. Raudenbush, A. S. Bryk, Y. F. Cheong, and R. Congdon. HLM 6: Hierarchical Linear and Nonlinear Modeling. Scientific Software International, Chicago, 2004.

    Google Scholar 

  • G. Rodr'guez. Multilevel generalized linear models. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • W. R. Schucany, H. L. Gray, and D. B. Owen. On bias reduction in estimation. Journal of the American Statistical Association, 66:524–533, 1971.

    Article  MATH  Google Scholar 

  • S. R. Searle, G. Casella, and C. E. McCulloch. Variance Components. Wiley, New York, 1992.

    MATH  Google Scholar 

  • J. Shao and D. Tu. The Jackknife and Bootstrap. Springer, New York, 1995.

    MATH  Google Scholar 

  • A. Skrondal and S. Rabe-Hesketh. Multilevel and related models for longitudinal data. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 7. Springer, New York, 2008. (this volume)

    Google Scholar 

  • T. A. B. Snijders. Analysis of longitudinal data using the hierarchical linear model. Quality & Quantity, 30:405–426, 1996.

    Article  Google Scholar 

  • T. A. B. Snijders and J. Berkhof. Diagnostic checks for multilevel models. In J. de Leeuw and E. Meijer, editors, Handbook of Multilevel Analysis, Chapter 1. Springer, New York, 2008. (this volume).

    Google Scholar 

  • S. Stern. Simulation-based estimation. Journal of Economic Literature, 35:2006–2039, 1997.

    Google Scholar 

  • J. M. F. Ten Berge, W. P. Krijnen, T. Wansbeek, and A. Shapiro. Some new results on correlation-preserving factor scores prediction methods. Linear Algebra and its Applications, 289:311–318, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  • K. E. Train. Discrete Choice Methods with Simulation. Cambridge University Press, Cambridge, UK, 2003.

    MATH  Google Scholar 

  • D. Tu and L. Zhang. Jackknife approximations for some nonparametric confidence intervals of functional parameters based on normalizing transformations. Computational Statistics, 7:3–15, 1992.

    MATH  Google Scholar 

  • J. W. Tukey. Bias and confidence in not-quite large samples. The Annals of Mathematical Statistics, 29:614, 1958.

    Article  Google Scholar 

  • R. Van der Leeden. Multilevel analysis of repeated measures data. Quality & Quantity, 32:15–29, 1998.

    Article  Google Scholar 

  • R. Van der Leeden and F. M. T. A. Busing. First iteration versus final IGLS/RIGLS estimates in two-level models: A Monte Carlo study with ML3. Technical Report PRM 02-94, Leiden University, Department of Psychology, Leiden, 1994.

    Google Scholar 

  • R. Van der Leeden, F. M. T. A. Busing, and E. Meijer. Bootstrap methods for two-level models. Technical Report PRM 97-04, Leiden University, Department of Psychology, Leiden, 1997.

    Google Scholar 

  • G. Verbeke and E. Lesaffre. Large sample properties of the maximum likelihood estimators in linear mixed models with misspecified random-effects distributions. Technical Report 1996.1, Catholic University of Leuven, Biostatistical Centre for Clinical Trials, Leuven, 1996.

    Google Scholar 

  • G. Verbeke and E. Lesaffre. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Computational Statistics & Data Analysis, 23:541–556, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  • H. White. Maximum likelihood estimation of misspecified models. Econometrica, 50:1–25, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  • K. M. Wolter. Introduction to Variance Estimation. Springer, New York, 1985.

    MATH  Google Scholar 

  • C. F. J. Wu. Jackknife, bootstrap and other resampling methods in regression analysis. The Annals of Statistics, 14:1261–1350, 1986. (with discussion).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Psychology, Leiden University, PO Box 9555, Los Angeles, 2300RB Leiden, The Netherlands

    Rien van der Leeden & Frank M.T.A. Busing

  2. University of Groningen, Faculty of Economics, and RAND Corporation, PO Box 2138, 1776 Main St, Santa Monica CA 90407-2138, USA

    Erik Meijer

Authors
  1. Rien van der Leeden
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Meijer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Frank M.T.A. Busing
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistics, University of California at Los Angeles, Los Angeles, CA 90095-1554, USA

    Jan de Leeuw

  2. RAND Corporation, 1776 Main St, PO Box 2138, Santa Monica, CA 90407-2138, USA

    Erik Meijer

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Leeden, R.v., Meijer, E., Busing, F.M. (2008). Resampling Multilevel Models. In: Leeuw, J.d., Meijer, E. (eds) Handbook of Multilevel Analysis. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73186-5_11

Download citation

Publish with us

Policies and ethics

Search

Navigation