Additional file 1: Supplementary Information on Methods including (in order of appearance): Figure S1. Directed acyclic graph depicting the hypothesised relations between neighbourhood residential density, other environmental attributes, household car ownership, covariates and outcome variables (moderate-to-vigorous physical activity and sedentary time). Detailed description of statistical analyses (generalised additive mixed models and mediation analyses) and hypotheses. Table S1. Outline of regression analyses. Supplementary Results including (in order of appearance): Direct and mediated effects of neighbourhood environmental attributes on MVPA and ST. Table S2. Step 1: Direct effects of neighbourhood residential density on other environmental attributes [pathways 1 in Fig. 1]. Figure S2. Shape of significant nonlinear relationships of residential density with environment attributes (400 m street-network residential buffers). Figure S3. Shape of significant nonlinear relationships of residential density ...