Jouni Kuha (London School of Economics)

Sample group means in multilevel models: Sampling error as measurement error

Research questions for models for clustered data often concern the effects of cluster-level averages of individual-level variables.  For example, data from a social survey might characterise neigborhoods in
terms of average income, ethnic composition etc. of people within each neighbourhood. Unless the true values of such averages are known from some other source, they are typically estimated by within-cluster
sample estimates, using data on the subjects in the observed data. This incurs a measurement error bias when these estimates are used as explanatory variables in subsequent modelling, even if the individual observations are measured without error. The measurement error variance can, however, be estimated from within-cluster variation, using knowledge of the sampling design within each cluster, and we can then apply relatively standard measurement error methods to adjust for the error. This talk considers such estimation for generalised linear mixed models, comparing common measurement error adjustments to naive analysis with no adjustment.