cut_off_point_method: Cut-Off Point Method for Assigning Physical Activity Patterns

In HMMpa: Analysing Accelerometer Data Using Hidden Markov Models

Cut-Off Point Method for Assigning Physical Activity Patterns

Description

This function assigns an activity range to each observation of a time-series, such as for a sequence of impulse counts recorded by an accelerometer. The activity ranges are defined by thresholds called “cut-off points”. Furthermore, bout periods are analysed (see Details for further informations).

Usage

cut_off_point_method(
  x,
  cut_points,
  names_activity_ranges = NA,
  hidden_PA_levels = NA,
  bout_lengths = NULL,
  plotting = 0
)

Arguments

x	a vector object of length T containing non-negative observations of a time-series, such as a sequence of accelerometer impulse counts.
cut_points	a vector object containing cut-off points to separate activity ranges. For instance, the vector c(7,15,23) separates the four activity ranges [0,7);[7,15);[15,23);[23,Inf).
names_activity_ranges	an optional character string vector to name the activity ranges induced by the cut-points. This vector must contain one element more than the vector cut_points.
hidden_PA_levels	an optional vector object of length T containing a sequence of the estimated hidden physical activity levels (i.e. means) underlying the time-series of accelerometer counts. Such a sequence can be extracted by decoding a trained hidden Markov model. The cut-point method classifies then each count by its level in the hidden Markov chain that generates the physical activity counts, and does not use the observed count value (see HMM_based_method for further details). Default is NA (for the traditional cut-point method).
bout_lengths	a vector object (with even number of elemets) to define the range of the bout intervals (see Details for the definition of bouts). For instance, bout_lengths = c(1,1,2,2,3,10,11,20,1,20) defines the five bout intervals [1,1] (1 count); [2,2] (2 counts); [3,10] (3-10 counts); [11,20] (11-20 counts); [1,20] (1-20 counts - overlapping with other bout intervalls is possible). Default value is bout_lengths=NULL.
plotting	a numeric value between 0 and 5 (generates different outputs). NA suppresses graphical output. Default value is 0. 0: output 1-5 1: summary of all results 2: time series of activity counts, classified into activity ranges 3: time series of bouts (and, if available, the sequence of the estimated hidden physical activity levels, extracted by decoding a trained HMM, in green color) 4: barplots of absolute and relative frequencies of time spent in different activity ranges 5: barplots of absolute frequencies of different bout intervals (overall and by activity ranges )

Details

A bout is defined as a period of time spending a defined intensity of physical activities in a specified physical activity range, without switching to activity intensities in a different activity range.

Value

cut_off_point_method returns a list containing the extracted sequence of activity ranges and plots key figures.

activity_ranges

an array object containing the cut-off intervals that indicate the activity ranges.

classification

an integer vector containing the sequence of activity ranges that were assigned to the observed time-series of accelerometer counts. If hidden_PA_levels=NA, then classification is the output of the traditional cut-point method, meaning that an activity range has been assigned to each accelerometer count over its observed value actual position. In case when hidden_PA_levels is available, classification is the output of the extendend cut-point method using hidden Markov models (see HMM_based_method for further details).

classification_per_activity_range

a pairlist object containing the classification of the observed counts by the assigned activity range.

freq_acitvity_range

table object containing the absolute frequencies of classifications into activity ranges.

rel_freq_acitvity_range

table object containing the relative frequencies of classifications into activity ranges.

quantity_of_bouts

overall number of bouts.

bout_periods

an array including the bout length assigned to acitiy ranges.

abs_freq_bouts_el

a pairlist object containing the absolute frequency of bout length per epoch length (aggregated).

Author(s)

Vitali Witowski (2013)

See Also

HMM_based_method

Examples

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) 
  
# 1) Traditional cut point method -----------------------
# Assigning activity ranges to activity counts using 
# fictitious cut-off points that produce the four activity 
# ranges "sedentary"", "light"", "moderate"", and "vigorous". 

  solution_of_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(1,1,2,2,3,3,4,4,5,5,6,12,13,40,41,265,1,265), 
                           plotting = 0)
 print(solution_of_traditional_cut_off_point_method)
 
 
# 2) Extension of the traditional cut_point method 
#     using HMMs                                     
# The following three steps define an extension of the 
# traditional cut-off method by first extracting the hidden 
# physical activity pattern behind the accelerometer counts 
# using a HMM (those three steps are basically combined in 
# the function HMM_based_method, see HMM_based_method for 
# further details and references): 

# Step 1 ---
# Train hidden Markov model for different number of 
# states m=2,...,6 and select the model with the most 
# plausible m
 
m_trained_HMM <- 
  HMM_training(x = x, 
               min_m = 2, 
               max_m = 6, BW_print=FALSE,
               distribution_class = "pois")$trained_HMM_with_selected_m
 
 
 # Step 2 ---
 # Decode the trained HMM (by using the 
 # Viterbi algorithm (global decoding)) to get the estimated 
 # sequence of hidden physical activity levels 
 # underlying the the accelerometer counts 
 
 # You have to compute 'm_trained_HMM' first (see Step 1)
 
   global_decoding <- 
     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$distribution_theta,
                  decoding_method = "global")
  hidden_PA_levels <- global_decoding$decoding_distr_means
  
  
  # Step 3 ---
  # Assigning activity ranges to activity counts using the 
  # information extracted by decoding the HMM for the counts 
  # (PA-levels) and fictitious cut-off points that produce 
  # four so-called activity ranges:"sedentary", "light", 
  # "moderate" and "vigorous":
  
  # You have to compute 'm_trained_HMM' and 'hidden_PA_levels' first (see above)
  
    solution_of_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(1,1,2,2,3,3,4,4,5,5,6,12,13,40,41,265,1,265), 
                             plotting=1)
 

HMMpa documentation built on April 3, 2025, 10:29 p.m.