03 - Kernel Density Plots

Kernel density plots are effective way to visualize the distribution of variable (in this case, time). Thus, kernel plots can be considered as plots of smoothed histograms.

Here we’ll work with two R packages: activity and overlap. We also will load two sample time datasets along with the packages to perform the activty test.

#Loading required packages
library("overlap")
library ("activity")
#Loading two activity datasets (time)
act_x<-read.table("./data/act_x.txt", header= T)
act_y<-read.table("./data/act_y.txt", header= T)

But before plotting the kernels, we must transform time data to radians using the following formula:

\[ rad=time*2*{\pi} \]

rad_x<-act_x$Time_2*2*pi
rad_y<-act_y$Time_2*2*pi

And one more step before the fun start… we must compute fitted data. In this example, we will use only one condition (A) of the two conditions available in the dataset (A and B).

fitact_a <-fitact(rad_x[act_x$Condition=="A"])
fitact_b <-fitact(rad_y[act_y$Condition=="A"])

Density plots

Now we will plot kernel density functions for our two datasets separately.

#Density plot for dataset A
plot(fitact_a, yunit="dens", las=1, dline=list(col="lightblue"), tline=list(col="blue"), main="Data X", ylim=c(0,0.17))

#Density plot for dataset B
plot(fitact_b, yunit="dens", las=1, dline=list(col="pink"), tline=list(col="red"), main = "Data Y")

And we also are able to depict both kernels in one plot:

plot(fitact_a, yunit="dens", las=1, dline=list(col="lightblue"), tline=list(col="blue"), ylim=c(0,0.17))
     plot(fitact_b, yunit="dens", add=TRUE, dline=list(col="pink"), tline=list(col="red"))
     legend("topright", inset = c(0,0), title = "Data", c("X", "Y"), lty= c(1,1), col = c("lightblue", "pink"), bty = "n")

It is very nice, isn’t it?

Overlap coefficient dhat5

The overlap coefficient of is the area under a density curve.This index is merely descriptive. On the other hand, the function CompareCkern of the package activity, is a probability test that assess if two datasets come from the same activity distribution. In addition, this test calculate overlap index dhat5 for two fitted distributions (with function fitact).

Below we compare datasets X and Y, and test if they come or not from the same activity distribution:

compareCkern(fitact_a, fitact_b, reps = 100)

##        obs       null     seNull      pNull 
## 0.94528569 0.96108573 0.01154511 0.10000000

Overlap assessment

Before plotting overlaps we must extracti data for condition = A…

act_a <- rad_x[act_x$Condition=="A"]
act_b <- rad_y[act_y$Condition=="A"]

And now we will graph the Density Plots!

#Density plot for A
densityPlot(act_a, xscale = 24, xcenter = c("noon", "midnight"), add = F, rug = T, extend = "lightgray", main = "Data X", xlab = "Time", ylab = "Density", bty = "L")

#Density plot for B
densityPlot(act_b, xscale = 24, xcenter = c("noon", "midnight"), add = F, rug = T, extend = "lightgray", main = "Data Y", xlab = "Time", ylab = "Density", bty = "L")

And of course, we can plot the two datasets in same plot with overlap

overlapPlot(act_a, act_b, main = " ", linecol = c("black", "darkgreen"), lty = c(1,3), bty = "L", xlab = "Time", ylab = "Density")
legend("topright", inset = c(0,0), title = "Data", c("X", "Y"), lty= c(1,3), col = c("gray25", "seagreen"), bty = "n")

Session

sessionInfo()

## R version 3.6.0 (2019-04-26)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Mojave 10.14.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] activity_1.2  overlap_0.3.2
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.1      mvtnorm_1.0-11  digest_0.6.20   magrittr_1.5   
##  [5] evaluate_0.14   pbapply_1.4-1   stringi_1.4.3   boot_1.3-23    
##  [9] rmarkdown_1.14  tools_3.6.0     stringr_1.4.0   xfun_0.8       
## [13] yaml_2.2.0      parallel_3.6.0  compiler_3.6.0  circular_0.4-93
## [17] htmltools_0.3.6 knitr_1.23

Animal activity analysis

Francisco E. Fonturbel and Javier Cuadra

26/jun/2019

03 - Kernel Density Plots

Density plots

Overlap coefficient dhat5

Overlap assessment

Session