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 semiMarkov 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, volumebased 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 ...