IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v172y2009i3p659-687.html
   My bibliography  Save this article

Prediction in multilevel generalized linear models

Author

Listed:
  • Anders Skrondal
  • Sophia Rabe‐Hesketh

Abstract

Summary. We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix. For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic random‐intercept models under a range of conditions.

Suggested Citation

  • Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
  • Handle: RePEc:bla:jorssa:v:172:y:2009:i:3:p:659-687
    DOI: 10.1111/j.1467-985X.2009.00587.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-985X.2009.00587.x
    Download Restriction: no

    References listed on IDEAS

    as
    1. David Afshartous & Jan de Leeuw, 2005. "Prediction in Multilevel Models," Journal of Educational and Behavioral Statistics, , vol. 30(2), pages 109-139, June.
    2. David Afshartous & Michael Wolf, 2007. "Avoiding ‘data snooping’ in multilevel and mixed effects models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 1035-1059, October.
    3. Sophia Rabe‐Hesketh & Anders Skrondal, 2006. "Multilevel modelling of complex survey data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 805-827, October.
    4. Robert Tsutakawa & Jane Johnson, 1990. "The effect of uncertainty of item parameter estimation on ability estimates," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 371-390, June.
    5. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    6. Nicholas T. Longford, 2001. "Simulation‐based diagnostics in random‐coefficient models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 259-273.
    7. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
    8. Anders Skrondal & Sophia Rabe-Hesketh, 2007. "Redundant Overdispersion Parameters in Multilevel Models for Categorical Responses," Journal of Educational and Behavioral Statistics, , vol. 32(4), pages 419-430, December.
    9. Duchateau, Luc & Janssen, Paul, 2005. "Understanding Heterogeneity in Generalized Mixed and Frailty Models," The American Statistician, American Statistical Association, vol. 59, pages 143-146, May.
    10. Edward Frees & Jee-Seon Kim, 2006. "Multilevel Model Prediction," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 79-104, March.
    11. Hua-Hua Chang & William Stout, 1993. "The asymptotic posterior normality of the latent trait in an IRT model," Psychometrika, Springer;The Psychometric Society, vol. 58(1), pages 37-52, March.
    12. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
    13. Stephen W. Raudenbush & JDouglas Willms, 1995. "The Estimation of School Effects," Journal of Educational and Behavioral Statistics, , vol. 20(4), pages 307-335, December.
    14. Harvey Goldstein & David J. Spiegelhalter, 1996. "League Tables and Their Limitations: Statistical Issues in Comparisons of Institutional Performance," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 385-409, May.
    15. Robert J. Mislevy, 1986. "Recent Developments in the Factor Analysis of Categorical Variables," Journal of Educational and Behavioral Statistics, , vol. 11(1), pages 3-31, March.
    16. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    17. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
    18. Jiming Jiang & P. Lahiri, 2001. "Empirical Best Prediction for Small Area Inference with Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 217-243, June.
    19. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
    Full references (including those not matched with items on IDEAS)

    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:bla:jorssa:v:172:y:2009:i:3:p:659-687. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/rssssea.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.