Computing the DFC/HP and manipulating the functions returned objects

Hassan Roland Nasser

2022-07-23

library(digiRhythm)
data <- digiRhythm::df691b_1 
data <- resample_dgm(data, 15)
data <- remove_activity_outliers(data)
activity = names(data)[3]
head(activity)
#> [1] "Steps"

Degree of functional Coupling and harmonic power

The degree of functional coupling and the harmonic power could be computed using the dfc function as shown below.

The DFC algorithm is a bit complicated. It’s, therefore, needed that we clarify few points about some computing considerations and also about the arguments of the function itself:

The user does not need worry about looping over days, extract the lomb scargle periodogram for every 7 days and then compile the results to obtain the degree of functional coupling. This is done in loop inside the dfc function. However, the is also a function call lomb_scargle_periodogram where the user can investigate the activity a little bit deeper. We preview the lomb_scargle_periodogram function and its output, then we go to the dfc function.

df <- data[1:672, c('datetime', activity)]
my_lsp <- lomb_scargle_periodogram(df, alpha = 0.01, plot = TRUE)
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df, alpha = 0.01, plot = TRUE): This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

In the above plot, we see plenty of information. First, we have the whole periodogram for the dataframe df visualized. Second, we can distinguish between harmonic and non harmonic frequencies. Harmonic frequencies are plotted in blue and tagged with the time period they correspond to. For instance, we can check the power of the 24h cycles, 12h cycles, 6h cycles and so on. Third, we have a dotted horizontal line that makes it easy to visually check which frequencies are considered to originated from noise rather than from a actual signal. Frequency bars that make it above this line are considered to be originated from a real activity. The probability of this event is calculated using the method of Baluev (2008). The plot also shows, as title, the activity time span used for the computation.

Now, to the DFC. The below plot shows the DFC and HP in the same graph. Both variables are percentages.

my_dfc <- dfc(data, activity = activity,  plot = FALSE, verbose = FALSE)
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Warning: Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> Warning: Removed 1 rows containing missing values (geom_hline).
#> Removed 1 rows containing missing values (geom_text).
#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#> v Correct time format: First column has a POSIXct Format 
#> v Number of days: Bigger or equal to 7 
#> v Correct numeric format - Column 2 ==> Steps 
#> The data is digiRhythm friendly
#> Warning in lomb_scargle_periodogram(df_var, alpha = sig, sampling = sampling, : This LSP function is customized to use data with 7 days span only. But, the data contains less or more than 7 days.
#>          A dynamic number of days will be introduced in a later version.

#Setting plot to TRUE will visualize all the LSP plots (like the one above) during each sliding window. Rather used for deeper investigation and debugging.
print(my_dfc)

# Accessing output data and changing the plots using DigiRhythm

The DFC function returns a object of type ggplot:

class(my_dfc)
#> [1] "gg"     "ggplot"

As shown, the class is gg or ggplot. This allows the user to: - Access the data of DFC or HP directly from the returned object. - Add aesthetics layer to the plot as needed.

To access the data, one has to use the data component of the DFC object. We illustrate this in the below code:

head(my_dfc$data)
#>         date       dfc        hp
#> 1 2020-08-25 0.8159025 0.2107367
#> 2 2020-08-26 1.0000000 0.1283563
#> 3 2020-08-27 1.0000000 0.1379133
#> 4 2020-08-28 1.0000000 0.1539973
#> 5 2020-08-29 1.0000000 0.1620310
#> 6 2020-08-30 1.0000000 0.1951330

As shown, we can access a dataframe where the first comlumn is the date and the second two columns are the DFC and HP respectively. This will allow the users to be able to use the returned data in further studies such as modelling.

Users can also change the aesthetics of the plot directly if they wish. This is possible by adding a ggplot layer to the returned DFC object. For instance, this is the original plot returned by the DFC:

print(my_dfc)

As an illustrative example, in the below code we add a new aesthetic layer to the ggplot object. This layer does nothing but increasing the width of the x-axis. Users can add any other aesthetic layer as they wish; the immagination is the only limit.

library(ggplot2)
new_plot <- my_dfc + 
  theme(
    text=element_text(family="Times", size=8), 
    axis.text.y=element_text(size=15, colour="black"))
print(new_plot)