Journal of Official Statistics, Vol.20, No.3, 2004. pp. 481493

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On the Distribution of Random Effects in a Population-based Multi-stage Cluster Sample Survey

Data from surveys are often characterised by clustering of individual level responses within higher level units such as households, enumeration districts or counties. Multilevel modelling is an appropriate method for analysing data from such studies, but an assumption of normality is required if the estimated standard errors are used to make inferences about the parameters. We evaluated the distribution of random effects at the postcode sector and district health authority levels of clustering for 13 health outcomes and lifestyle risk factors using data from the Health Survey for England 1994. Normal plots supported the assumption of normality for eight outcomes. A positive relationship was found between skewness at the individual and cluster levels. The findings of this study suggest that for outcomes with non-normal distributions at the cluster level, the application of a normalising transformation to the individual level residuals may also have a normalising effect at the cluster level.

Multilevel models, hierarchical data, components of variance

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