Modeling a bivariate residential‐workplace neighborhood effect when estimating the effect of proximity to fast‐food establishments on body mass index

Hierarchical modeling is the preferred approach of modeling neighborhood effects. When both residential and workplace neighborhoods are known, a bivariate (residential-workplace) neighborhood random effect that quantifies the extent that a neighborhood's residential and workplace effects are correlated may be modeled. However, standard statistical software for hierarchical models does not easily allow correlations between the random effects of distinct clustering variables to be incorporated. To overcome this challenge, we develop a Bayesian model and an accompanying estimation procedure that allows for correlated bivariate neighborhood effects and allows individuals to reside or work in multiple neighborhoods, cross-sectional and longitudinal heterogeneity between individuals, and serial correlation between repeated observations over time. Simulation studies that vary key model parameters evaluate how well each aspect of the model is identified by the data. We apply the model to the motivating Framingham Heart Study linked food establishment data to examine whether (i) proximity to fast-food establishments is associated with body mass index, (ii) workplace neighborhood exposure associations are larger than those for residential neighborhood exposure, and (iii) residential neighborhood exposure associations correlate with workplace neighborhood exposure. Comparisons of the full model to models with restricted versions of the covariance structure illustrate the impact of including each feature of the covariance structure.