Ordinal Statistical Models of Physical Activity Levels from Accelerometer Data

Improvements in accelerometer technology has led to new types of data on which more powerful predictive models can be built to assess physical activity. This paper explains and implements ordinal random forest and partial proportional odds models which both take into account the ordinality of responses given explanatory accelerometer data. The data analyzed comes from 28 adults performing activities of daily living in two visits while wearing accelerometers on the ankle, hip, right and left wrist. The first visit provided training data and the second testing data so that an independent sample, cross-validation approach could be used. We found that ordinal random forest produces similar accuracy rates and better linearly weighted kappa values than random forest. On the testing set, the ankle produced the best accuracy rates (33.3%), followed by the left wrist (34.7%), hip (36.9%) and then the right wrist (37.3%) using the best performing decision model for a four-activity level response. Linearly weighted kappa values indicated substantial agreement. For a two-activity level response, the error rates on the ankle, hip, left wrist and right wrist were 15.5%, 15.9%, 16.5% and 18.8%, respectively. The partial proportional odds model had significant goodness of fit (p < 0.0001) and provided interpretable coefficients (at p = 0.05), but there was significant variability in accuracy. These models can be used on accelerometer data collected during exercise studies and levels of activity can be assessed without direct observation. This work also can lead to theoretical improvements of current modeling techniques that are used for this purpose.