Hierarchical Distributed-Lag Models: Exploring Varying Geographic Scale and Magnitude in Associations Between the Built Environment and Health.

It is well known that associations between features of the built environment and health depend on the geographic scale used to construct environmental attributes. In the built environment literature, it has long been argued that geographic scales may vary across study locations. However, this hypothesized variation has not been systematically examined due to a lack of available statistical methods. We propose a hierarchical distributed-lag model (HDLM) for estimating the underlying overall shape of food environment-health associations as a function of distance from locations of interest. This method enables indirect assessment of relevant geographic scales and captures area-level heterogeneity in the magnitudes of associations, along with relevant distances within areas. The proposed model was used to systematically examine area-level variation in the association between availability of convenience stores around schools and children's weights. For this case study, body mass index (weight kg)/height (m)2) z scores (BMIz) for 7th grade children collected via California's 2001-2009 FitnessGram testing program were linked to a commercial database that contained locations of food outlets statewide. Findings suggested that convenience store availability may influence BMIz only in some places and at varying distances from schools. Future research should examine localized environmental or policy differences that may explain the heterogeneity in convenience store-BMIz associations.