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Multilevel modelling of complex survey data

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  • Sophia Rabe-Hesketh
  • Anders Skrondal

Abstract

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. Copyright 2006 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series A (Statistics in Society).

Volume (Year): 169 (2006)
Issue (Month): 4 ()
Pages: 805-827

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Handle: RePEc:bla:jorssa:v:169:y:2006:i:4:p:805-827

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  1. 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.
  2. 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.
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Cited by:
  1. Ana Maria Osorio & Catalina Bolancé & Nyovane Madise & Katharina Rathmann, 2013. "Social Determinants of Child Health in Colombia: Can Community Education Moderate the Effect of Family Characteristics?," Working Papers XREAP2013-02, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2013.
  2. Elena Pirani & Silvana Salvini, 2012. "Socioeconomic Inequalities and Self-Rated Health: A Multilevel Study of Italian Elderly," Population Research and Policy Review, Springer, vol. 31(1), pages 97-117, February.
  3. Amini, Chiara & Commander, Simon, 2012. "Educational scores: How does Russia fare?," Journal of Comparative Economics, Elsevier, vol. 40(3), pages 508-527.
  4. Sophia Rabe-Hesketh & Anders Skrondal, 2007. "Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods," Psychometrika, Springer, vol. 72(2), pages 123-140, June.
  5. Yu, Li & Orazem, Peter, 2011. "O-Ring Production on U.S. Hog Farms: Joint Choices of Farm Size, Technology, and Compensation," Staff General Research Papers 12992, Iowa State University, Department of Economics.

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