Thresholding method for identifying anomalies in wellbeing time series data

Abstrakt

Identifying atypical patterns in digital behavior, physiological responses, and wellbeing metrics is essential for advancing psychometric research and intervention strategies. Anomaly detection techniques play a crucial role in (1) detecting deviations in digital behavior that may indicate excessive usage, social withdrawal, or digital addiction, (2) analyzing physiological and psychological responses, such as heart rate variability and stress indicators, to identify abnormal patterns related to technology use, and (3) monitoring responses to wellbeing interventions using digital technology by detecting atypical reactions that may require personalized approaches. To address these challenges, our research introduces an effective thresholding method for anomaly detection in multivariate data drawn from a normal distribution - a common model for many psychometric and mental health variables, as well as the distribution of residuals in various statistical models (e.g. regression models or models for time series). The proposed method provides a theoretically grounded threshold that is asymptotically optimal, ensuring that the number of misidentified anomalies approaches zero as the sample size increases. Our approach is compared to other common thresholding methods through simulation, and its performance is further demonstrated using real data.