Analysis of household effects on longitudinal health outcomes using a joint mean-correlation multilevel model with grouped random effects

Previous cross-sectional research has found correlation in the health outcomes of coresident adults. However, the study of household effects in longitudinal data is challenging due to the complex association structure arising from changes in household membership over time. We propose a ‘grouped’ multilevel model where the groups (called ‘superhouseholds’) are specified to capture changes in household structure. Correlated household random effects are used to capture correlations between households sharing an individual(s), and correlations between household pairs can depend on covariates that describe their relationship. We develop a constrained MCMC procedure for model estimation that ensures the group-specific correlation matrices (where dimensions can vary across groups) are positive definite, and implement it as an R package. The performance and robustness of our models is evaluated in a simulation study and then applied in analyses of household and area effects on self-rated physical and mental health in the UK using data from a national household panel survey.