Motif Probability: A Novel Metric to Advance Temporal Physical Behavior Sequence Analysis Beyond Total Volume and Complexity

Few traditional physical behavior estimates capture accumulation patterns. This study introduces and applies motif probability, a novel metric quantifying the occurrence of a specific sequence of bouts (“motif”), enhancing physical behavior pattern analysis. Motif probability is calculated using a forward algorithm with learned parameters from the hidden semi-Markov model, segmenting accelerometer data into physical behavior sequences. Accelerometer data from 517 participants were processed using hidden semi-Markov models to derive physical behavior states and construct transition matrices, using these parameters to calculate motif probability. In addition, traditional volume-based estimates (e.g., daily average acceleration and time spent in specific intensities) and complexity metrics were calculated. Clustering analysis grouped participants with similar physical behavior sequences, volume-based estimates, complexity metrics, sex, and body mass index z -score. We identified influential estimates with principal component analysis and assessed associations with body mass index z -score and sex with linear and logistic regression, respectively. Five behavioral clusters emerged, characterized by: (a and b) low average acceleration and complexity, (c) highest volume-based estimates, (d) highest complexity, and (e) lowest physical activity and highest sedentary behavior motif probabilities, despite similar volume-based estimates to Cluster 3. Four main components explained 67.4% of the variance: (a) motif probability, (b) volume-based estimates, (c) sedentary behavior and physical activity motif probabilities with complexity, and (d) sedentary behavior estimates. Motif probabilities correlated moderately with complexity and weakly with volume-based estimates, thus capturing complementary aspects of physical behaviors. Motifs were significantly associated with sex but not body mass index z -score. Motif probability captures the occurrence of specific temporal physical behavior sequences, adding temporal detail beyond traditional metrics.