Negative binomial mixed effects location-scale models for intensive longitudinal count-type physical activity data provided by wearable devices.

In recent years, the use of wearable devices, for example, accelerometers, have become increasingly prevalent. Wearable devices enable more accurate real-time tracking of a subject's physical activity (PA) level, such as steps, number of activity bouts, or time in moderate-to-vigorous intensity PA (MVPA), which are important general health markers and can often be represented as counts. These intensive within-subject count data provided by wearable devices, for example, minutes in MVPA summarized per hour across days and even months, allow the possibility for modeling not only the mean PA level, but also the dispersion level for each subject. Especially in the context of daily PA, subjects' dispersion levels are potentially informative in reflecting their exercise patterns: some subjects might exhibit consistent PA across time and can be considered "less dispersed" subjects; while others might have a large amount of PA at a particular time point, while being sedentary for most of the day, and can be considered "more dispersed" subjects. Thus, we propose a negative binomial mixed effects location-scale model to model these intensive longitudinal PA counts and to account for the heterogeneity in both the mean and dispersion level across subjects. Further, to handle the issue of inflated numbers of zeros in the PA data, we also propose a hurdle/zero-inflated version which additionally includes the modeling of the probability of having $>$0 PA levels.