Modeling of ordinal longitudinal accelerometer data

Abstract

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 implements an ordinal random forest model with recursive forecasting to take into account the ordinal, longitudinal nature of responses. The data 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 indepen- dent sample, cross-validation approach could be used. For this type of data, prior responses are not available at the testing stage or in practice. However, recursive forecasts can be made with prior predictions in place of lagging responses on models which were built to use lagging responses as explanatory variables. Models are fit to account for multiple time series, with different time series for each participant in the study. We found that ordinal random forest, when the time series is taken into account, produces better accuracy rates and better linearly weighted kappa values than both ordinary ordinal forest and random forest. On the testing set, the lowest error rates were produced by the ankle (28.0%), followed by the left wrist (28.7%), hip (28.9%) and then the right wrist (30.2%) using the best performing decision model for a four-activity level response. In addition, linearly weighted kappa values indicated substantial agreement. The approach of this work can be adapted to other types of longitudinal ordinal models for improvements in modeling techniques.