HMMpa-package: Analysing Accelerometer Data Using Hidden Markov Models

Description

This package provides functions for analyzing accelerometer output data (known as a time-series of (impulse)-counts) to quantify length and intensity of physical activity.

Arguments

Author

Maintainer: Foraita Ronja foraita@leibniz-bips.de (ORCID)

Authors:

Vitali Witowski

Details

Usually, so called activity ranges are used to classify an activity as "sedentary", "moderate" and so on. Activity ranges are separated by certain thresholds (cut-off points). The choice of these cut-off points depends on different components like the subjects' age or the type of accelerometer device.

Cut-off point values and defined activity ranges are important input values of the following analyzing tools provided by this package:

1. Cut-off point method: Assigns an activity range to a count based on its total magnitude independently of other counts.

2. HMM-based method: Assigns an activity range to a count using a stochastic hidden Markov model (HMM), which identifies the physical activity states underlying the given time-series.

The HMM procedure for analyzing accelerometer data can be summarized as follows:

1. Train an HMM to estimate the number of hidden physical activity states (m) and model parameters (delta, gamma, distribution_theta).

2. Decode the trained HMM to classify accelerometer counts into m states.

3. Assign activity ranges based on the total magnitudes of the corresponding states.

References

Witowski, V., Foraita, R., Pitsiladis, Y., Pigeot, I., Wirsik, N. (2014) Using hidden Markov models to improve quantifying physical activity in accelerometer data - A simulation study. PLOS ONE. 9(12), e114089. tools:::Rd_expr_doi("10.1371/journal.pone.0114089")

Examples

Run this code

x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,
  14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,
  5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,
  9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,
  37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,
  11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,
  7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,
  11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,
  2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,
  36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,
  40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,
  5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,
  10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1) 
  
# \donttest{  
# Traditional Cut-off-point method ------------------------
traditional_cut_off_point_method <- 
   cut_off_point_method(
               x = x,
               cut_points = c(5,15,23), 
               names_activity_ranges = c("SED","LIG","MOD","VIG"), 
               bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
               plotting = 1)
               # }
                
# HMM-based Cut-off-point method --------------------------  
# Use a (m = 4 state) hidden Markov model based on the 
# generalized poisson distribution to assign an 
# activity range to the counts. 

# In this example three activity ranges
# (named as "light", "moderate" and "vigorous" physical activity) 
# are separated by the two cut-points 15 and 23.

# \donttest{
HMM_based_cut_off_point_method <- 
   HMM_based_method(
               x = x, 
               cut_points = c(15,23), 
               min_m = 4, 
               max_m = 4, 
               names_activity_ranges = c("LIG","MOD","VIG"), 
               distribution_class = "genpois", 
               training_method = "numerical",
               DNM_limit_accuracy = 0.05,
               DNM_max_iter = 10,
               bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
               plotting = 1)
               # }       
                
# The HMM-based approach can be split into three steps ---------
# 1) Training of a HMM for given time-series of accelerometer counts 
#    Here: A poisson distribution is trained based on a HMM for
#          m = 2,..., 6 states. 
#          Select the HMM with the most plausibel m. 
# \donttest{
      m_trained_HMM <- HMM_training(x = x, 
                                min_m = 2, 
                                max_m = 6, 
               distribution_class = "pois")$trained_HMM_with_selected_m  
 # }              

# 2) Decoding the trained HMM to extract hidden physical
#    activity (PA) levels
# \donttest{
hidden_PA_levels <- HMM_decoding(x = x, 
                                 m = m_trained_HMM$m, 
                             delta = m_trained_HMM$delta, 
                             gamma = m_trained_HMM$gamma, 
                distribution_class = m_trained_HMM$distribution_class, 
                distribution_theta = m_trained_HMM$distribution_theta)
 hidden_PA_levels <- hidden_PA_levels$decoding_distr_means
 # }
 
# 3) Assigning user-specified activity ranges to the accelerometer
#    counts via the total magnitudes of their corresponding 
#    hidden PA-level
#    Here: 4 activity levels ("sedentary", "light", "moderate" and 
#         "vigorous" physical activity) are separated by 
#          3 cut-point (5, 15, 23)
# \donttest{
 HMM_based_cut_off_point_method <- 
    cut_off_point_method(x = x, 
          hidden_PA_levels = hidden_PA_levels, 
                cut_points = c(5,15,23), 
     names_activity_ranges = c("SED","LIG","MOD","VIG"), 
              bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
                  plotting = 1)  
# }

               
# Simulate data of a large time-series of highly scattered counts ----
x <- HMM_simulation(size = 1500, 
                    m = 10,
                    gamma = 0.93 * diag(10) + rep(0.07 / 10, times = 10),
                    distribution_class = "norm", 
                    distribution_theta = list(mean = c(10, 100, 200, 300, 450, 
                       600, 700, 900, 1100, 1300, 1500), 
                    sd = c(rep(100,times=10))),
                    obs_round=TRUE, 
                    obs_non_neg=TRUE,
                    plotting=5)$observations                   
                    
# Compare results of the tradional cut-point method   
# and the (6-state-normal-)HMM based method
# \donttest{	
traditional_cut_off_point_method <- 
   cut_off_point_method(x = x, 
                        cut_points = c(200,500,1000), 
                        names_activity_ranges = c("SED","LIG","MOD","VIG"),
                        bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
                        plotting = 1)
                        
HMM_based_cut_off_point_method <- 
   HMM_based_method(x = x,
                    max_scaled_x = 200, 
                    cut_points = c(200,500,1000), 
                    min_m = 6, 
                    max_m = 6,
                    BW_limit_accuracy = 0.5, 
                    BW_max_iter = 10,
                    names_activity_ranges = c("SED","LIG","MOD","VIG"), 
                     distribution_class = "norm", 
                     bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
                     plotting = 1)
# }