Estimation of Exercise Energy Expenditure Using a Wrist-Worn Accelerometer: A Linear Mixed Model Approach with Fixed-Effect Variable Selection

This article presents an approach to estimating exercise energy expenditure based on acceleration measurements from a wrist-worn biaxial sensor. The method uses the linear mixed model that makes it possible to model both between-subject and within-subject variation in energy expenditure. More precisely, a random-intercepts model is used. The variance and mean of the acceleration signals at 15-second intervals as well as subject demographics (height, weight, body mass index, age and VO₂max) are used. Energy expenditure is modelled in four different activities: walking, running, Nordic walking and bicycling. This study introduces an effective backward model selection procedure for selecting the fixed-effect variables in the model. The procedure uses leave-one-out cross-validation to be able to effectively exploit the available data set and to ensure the robustness of the model. Estimation accuracy in test sets is used as a criterion of model performance. The model selection procedure proposed notably improves estimation accuracy. In walking, running, Nordic walking and bicycling, average estimation errors of 3.9, 3.6, 1.9 and 13.5 percent are reached. The respective Person correlations for these activities are 0.91, 0.98, 0.97, and 0.81. These results are also compared to the performance of the general linear model. It is discovered that the linear mixed model outperforms the model that does not take the individual levels of energy expenditure of the subjects into account.