We show results on the Avon longitudinal study of parents and children (ALSPAC) using a new approach for modelling the relationship between health outcomes and physical activity assessed by accelerometers. The key feature of the model is that it uses the histogram of physical activity counts as a predictor function, rather than scalar summary measures such as average daily moderate to vigorous physical activity (MVPA). Three models are fitted: (1a) A regression of fat mass at age 12 (N = 4164) onto the histogram of accelerometer counts at age 12; (1b) A regression of fat mass at age 14 (N = 2403) onto the histogram of accelerometer counts at age 12 and (1c) a regression of fat mass at age 14 (N = 2413) onto the accelerometer counts at age 14. All three models significantly improve on models including MVPA instead of the histogram and improve the goodness of fit of models (2a), (2b) and (2c) from R(2) = 0.267, 0.248 and 0.230 to R(2) = 0.292, 0.263 and 0.258 for models (1a), (1b) and (1c) respectively. The proportion of time spent in sedentary and very light activity (corresponding to slow walking and similar activities) has a positive contribution towards fat mass and time spent in moderate to vigorous activity has a negative contribution towards fat mass.