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Multilevel modelling of complex survey data

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  • Sophia Rabe‐Hesketh
  • Anders Skrondal

Abstract

Summary. Multilevel modelling is sometimes used for data from complex surveys involving multistage sampling, unequal sampling probabilities and stratification. We consider generalized linear mixed models and particularly the case of dichotomous responses. A pseudolikelihood approach for accommodating inverse probability weights in multilevel models with an arbitrary number of levels is implemented by using adaptive quadrature. A sandwich estimator is used to obtain standard errors that account for stratification and clustering. When level 1 weights are used that vary between elementary units in clusters, the scaling of the weights becomes important. We point out that not only variance components but also regression coefficients can be severely biased when the response is dichotomous. The pseudolikelihood methodology is applied to complex survey data on reading proficiency from the American sample of the ‘Program for international student assessment’ 2000 study, using the Stata program gllamm which can estimate a wide range of multilevel and latent variable models. Performance of pseudo‐maximum‐likelihood with different methods for handling level 1 weights is investigated in a Monte Carlo experiment. Pseudo‐maximum‐likelihood estimators of (conditional) regression coefficients perform well for large cluster sizes but are biased for small cluster sizes. In contrast, estimators of marginal effects perform well in both situations. We conclude that caution must be exercised in pseudo‐maximum‐likelihood estimation for small cluster sizes when level 1 weights are used.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssa:v:169:y:2006:i:4:p:805-827
    DOI: 10.1111/j.1467-985X.2006.00426.x
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    References listed on IDEAS

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    1. S. Rabe-Hesketh & A. Skrondal, 2001. "Parameterization of Multivariate Random Effects Models for Categorical Data," Biometrics, The International Biometric Society, vol. 57(4), pages 1256-1263, December.
    2. Ganzeboom, H.B.G. & de Graaf, P.M. & Treiman, D.J. & de Leeuw, J., 1992. "A standard international socio-economic index of occupational status," WORC Paper 92.01.001/1, Tilburg University, Work and Organization Research Centre.
    3. 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.
    4. Germán Rodríguez & Noreen Goldman, 2001. "Improved estimation procedures for multilevel models with binary response: a case‐study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 339-355.
    5. Germáan Rodríguez & Noreen Goldman, 1995. "An Assessment of Estimation Procedures for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(1), pages 73-89, January.
    6. Anders Skrondal & Sophia Rabe-Hesketh, 2003. "Multilevel logistic regression for polytomous data and rankings," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 267-287, June.
    7. Edward L. Korn & Barry I. Graubard, 2003. "Estimating variance components by using survey data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 175-190, February.
    8. 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.
    9. 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.
    10. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
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