Variance estimation in the analysis of clustered longitudinal survey data

We investigate the impact of cluster sampling on standard errors in the analysis of longitudinal survey data. We consider a widely used class of regression models for longitudinal data and a standard class of point estimators of a generalized least squares type. We argue theoretically that the impact of ignoring clustering in standard error estimation will tend to increase with the number of waves in the analysis, under some patterns of clustering which are realistic for many social surveys. The implication is that it is, in general, at least as important to allow for clustering in standard errors for longitudinal analyses as for crosssectional analyses. We illustrate this theoretical argument with empirical evidence from a regression analysis of longitudinal data on gender role attitudes from the British Household Panel Survey. We also compare two approaches to variance estimation in the analysis of longitudinal survey data: a survey sampling approach based upon linearization and a multilevel modelling approach. We conclude that the impact of clustering can be seriously underestimated if it is simply handled by including an additive random effect to represent the clustering in a multilevel model.