Two distinct subscales emerged to describe independent mobility in this population. They represent the frequency that children report being permitted to go to destinations unsupervised by an adult locally (Local-IM) and in the wider neighbourhood (Area-IM). As would be expected both boys and girls had higher scores for Local-IM than Area-IM indicating that parents were more willing to let them visit 'local' destinations i.e. friends house, park, local shops and school unsupervised compared to those which were assumed to be further away. Both Local-IM and Area-IM were higher in boys compared to girls. This is consistent with other studies [1, 30] where parents appear more willing to let boys visit places outside the home unsupervised compared to girls.
Children who reported being allowed to visit destinations unsupervised locally (Local-IM) and in the wider (Area-IM) neighbourhood had higher levels of weekday physical activity compared to those who reported lower levels of Local-IM and Area-IM. This positive association with objectively measured physical activity for weekdays remained even after adjustment for a range of potential confounders (BMI, IMD, pubertal status and minutes of daylight from 3 pm until sunset). For weekend physical activity, only Local-IM in girls was significantly related to average weekend physical activity. The lack of significant association between Area-IM and weekend physical activity may indicate that at this age young people get the majority of their physical activity at weekends 'locally'. Logically however you would expect that young people have more time to visit destinations further afield at weekends. It may be that children at this age spend more time supervised by parents on weekend visits and as Area-IM scores are hypothesised to only reflect 'unsupervised' visits, Area-IM is not associated with weekend physical activity. It is possible that Area-IM may relate to physical activity at weekends later in adolescence as distance travelled and range of destinations visited unsupervised increases . Variability in Area-IM scores is also less than that for Local-IM so could have affected power to detect significant relationships in analyses.
The assumption that Local-IM reflects destinations accessible to young people unsupervised and that Area-IM reflects destinations further away from where children live needs to be confirmed. Objective measures such as Geographical Information Systems could be used alongside self-reported independent mobility to ascertain the location of destinations visited unsupervised.
Physical activity and factors such as independent mobility are likely to be influenced by the type of neighbourhood (housing density, land use mix, available green space) as well as perceptions of that neighbourhood. For example, a parent may be much more likely to allow independent mobility if they perceive their environment to be safe and traffic density to be low and vice versa. Although the current study includes a wide range of participants from a single city, the variability in types of neighbourhood within a city could be smaller than that between different cities. These findings therefore should be confirmed in other geographical locations. The inclusion of minutes of daylight after school (3 pm) is relatively unusual in the literature, but these data confirm that minutes of daylight are positively related to both independent mobility and physical activity so should be considered as a potential confounder in future work. Available daylight is particularly relevant when investigating independent mobility as darkness has been reported as a barrier to parents allowing their children to play outside unsupervised . Studies where the measurement period is restricted to only winter or summer may not therefore be generalisable to other seasons.
Our limited knowledge with respect to independent mobility and physical activity may be a result of measurement challenges and lack of a coherent theoretical framework. Many studies including this one have relied on self-reported perceptions of independent mobility by either the child or the parent. Where direct measures such as detailed observation have been used, samples are usually relatively small and often in restricted situations (e.g. close to home or in the school playground). New equipment taking advantage of developments in satellite technology (e.g. portable Global Positioning Satellite (GPS) receivers) offer the potential for novel objective measures of children's movement within their neighbourhood. If combined with accelerometry data and information on level of supervision they offer a potentially more robust approach to measuring independent mobility in relation to physical activity. Examples of this integration of measures are slowly emerging in the literature . Data presented are to date based on small, homogeneous samples from a narrow range of neighbourhoods and reliability and validity of output generated by GPS and accelerometry has rarely been fully described . Larger more diverse studies are required that can document movement within the environment for a broad range of children and neighbourhoods.
We know very little about the factors which determine level of independent mobility in young people. Johansson  compared the characteristics of parents whose attitudes favour car use compared to those who favour independent travel. They found that parents with a favourable attitude towards independent travel were more likely to express a strong trust in the environment and road users and felt less need to protect their children. We also know that older children and males experience more independent mobility than females and younger children and that the reasons for decisions related to independent mobility in young people are a complex interaction between the child, the family and the environment .
This complexity can only be addressed by a coherent theoretical framework where independent mobility is combined with other more established physical, social-environmental and personal determinants of physical activity . A limitation of this paper is its lack of theoretical direction. Although a rationale for investigating independent mobility in relation to physical activity has been presented the independent mobility constructs developed have not been systematically linked to other determinants of physical activity.
Other constructs that relate to independent mobility can be found within existing theoretical frameworks. Examples of these constructs include autonomous motivation embedded in the Self Determination Theory [36, 37] and habits and norm directed behaviour in relation to humans and the environment [38–40]. However there has been limited theoretical work focussed specifically on the concept of independent mobility and physical activity. A greater emphasis on IM is consistent with the shift in recent years to focus on changing the environment as well as the individual as part of the public health agenda . However the cross-sectional nature of this study means we cannot determine whether higher levels of independent mobility are causally linked to higher levels of physical activity or vice versa. Longitudinal data are required to establish whether change in independent mobility is associated with a concomitant change in physical activity.
The main limitations of this study are the reliance on self-reported independent mobility and the cross-sectional design. The strengths of this study include the development of a specific measure of independent mobility, the use of an objective measure of physical activity in a relatively large sample and the measurement of and adjustment for a range of confounders in the analyses.