Modelling correlations among grouped random effects in multilevel models with an application to the estimation of household effects on longitudinal health outcomes

Summary

A standard assumption of multilevel models is that all the random effects at a given level in the data structure are independent for different units. We develop multilevel models for grouped data structures where correlations are allowed between pairs of random effects for units in the same group, and within-group random effect correlations may depend on covariates that characterise the relationship between pairs of units. Constrained MCMC estimation is used to ensure that the group-specific correlation matrices are positive definite. The research is motivated by the study of household effects in longitudinal studies where household membership may change over time. Household random effects are allowed to be correlated within clusters of households that share individuals over time, with correlations depending on covariates that describe the connections between household pairs. The proposed model is applied in analyses of household and area effects on self-rated health in the UK.