A Multilevel Analysis of Neighbourhood, School, Friend and Individual-Level Variation in Primary School Children’s Physical Activity

Physical activity is influenced by individual, inter-personal and environmental factors. In this paper, we explore the variability in children’s moderate-to-vigorous physical activity (MVPA) at different individual, parent, friend, school and neighbourhood levels. Valid accelerometer data were collected for 1077 children aged 9, and 1129 at age 11, and the average minutes of MVPA were derived for weekdays and weekends. We used a multiple-membership, multiple-classification model (MMMC) multilevel model to compare the variation in physical activity outcomes at each of the different levels. There were differences in the proportion of variance attributable to the different levels between genders, for weekdays and weekends, at ages 9 and 11. The largest proportion of variability in MVPA was attributable to individual variation, accounting for half of the total residual variability for boys, and two thirds of the variability for girls. MVPA clustered within friendship groups, with friends influencing peer MVPA. Including covariates at the different levels explained only small amounts (3%–13%) of variability. There is a need to enhance our understanding of individual level influences on children’s physical activity.


Model Specification
The model is a multiple-membership multiple-classification model (MMMC) for social network dependencies [1,2] with children (level 1) belong to multiple clique-2 friendship groups (level 2, multiple-membership) nested within clique-3 (level 3), nested within schools (level 4) and neighbourhoods (level 5, cross-classified). We fit three models, whose specification is given in detail below. We use classification notation [1], which provides a simpler notation than multiple subscript notation and remains readable for more complex non-hierarchical multilevel models.

General Model
Let be the MVPA for individual = 1, … , . The multilevel model consists of fixed and random terms as follows: = fixed + random

Model 1: Variance components
This model describes the percentage of total variation in MVPA at the neighbourhood, school and friendship levels. The fixed effect consists of 0 , an intercept term, and random effects are at the clique-2, clique-3, school and neighbourhood levels. The clique-3 and clique-2 levels are multiple-membership, with clieu-2 nested within clique-3, and schools and cliques are cross-classified with neighbourhood.

Model 2 -Gender random slopes model
This model describes the percentage of total variation in MVPA at the neighbourhood, school and friendship levels separately for boys and girls by adding gender as a fixed effect and as a random coefficient at the neighbourhood, school and clique levels.

Model 3 -full model
The full model includes child, parent, school and neighbourhood characteristics as fixed effects: where , = 1, … , are the variables representing the child, parent, school and neighbourhood characteristics, and are the corresponding coefficients.
The random term is the same as for model 2 above.

MCMC Technical Details Prior Distributions
We used the MLwiN default non-informative prior distributions for all parameters which express a lack of prior knowledge about the parameters before data collection. These are improper uniform priors (p(β) ∝ 1) for the fixed effects, and weakly informative inverse-Wishart distributions for the variance parameters. Further details can be found in Browne 2016, Chapter 1 [3].

MCMC Estimation
While the chain of sampled parameter values will eventually converge to the required distribution, it may take an initial period (the 'burn-in') to converge, and these values are discarded. Additionally, the sampled values are correlated and if this correlation is high, the chain is said to be slow-mixing and more iterations are required to sample adequately from the full distribution. We assessed convergence of the algorithm via trace plots and by exploring different starting values, and used a burn-in of 20,000 samples for all models. Our models exhibited slow-mixing due to small variance parameters at some levels, and so we based estimation on 1,000,000 iterations to ensure adequate mixing and used hierarchical centring at the highest level, a reparameterisation that can improve mixing of MCMC algorithms [3,4].