Modeling physical activity data using L0‐penalized expectile regression

Abstract
In recent years accelerometers have become widely used to objectively assess physical activity. Usually intensity ranges are assigned to the measured accelerometer counts by simple cut points, disregarding the underlying activity pattern. Under the assumption that physical activity can be seen as distinct sequence of distinguishable activities, the use of hidden Markov models (HMM) has been proposed to improve the modeling of accelerometer data. As further improvement we propose to use expectile regression utilizing a Whittaker smoother with an L0‐penalty to better capture the intensity levels underlying the observed counts. Different expectile asymmetries beyond the mean allow the distinction of monotonous and more variable activities as expectiles effectively model the complete distribution of the counts. This new approach is investigated in a simulation study, where we simulated 1,000 days of accelerometer data with 1 and 5 s epochs, based on collected labeled data to resemble real‐life data as closely as possible. The expectile regression is compared to HMMs and the commonly used cut point method with regard to misclassification rate, number of identified bouts and identified levels as well as the proportion of the estimate being in the range of urn:x-wiley:03233847:media:bimj2015:bimj2015-math-0001 of the true activity level. In summary, expectile regression utilizing a Whittaker smoother with an L0‐penalty outperforms HMMs and the cut point method and is hence a promising approach to model accelerometer data.