I am trying to fit a Hidden Markov Model to some animal movement data.
However, when multiple rows of my data have the exact same x and y coordinate values (no movement of the animal), the modeling function introduces a 0 for step and NA for angle. The resulting coefficients of the HMM are coherent in terms of biological interpretation, but when it comes to further plotting, I cannot because of these Na's.
To fit the HMM, I am using the moveHMM library in R.
> packageVersion("moveHMM")
[1] ‘1.9’
> sessionInfo()
R version 4.3.1 (2023-06-16 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 11 x64 (build 22000)
I have a dataset structured as follows:
> str(data)
'data.frame': 16515 obs. of 3 variables:
$ ID: num 1 1 1 1 1 1 1 1 1 1 ...
$ x : num 582629 582629 582628 582628 582628 ...
$ y : num -2195359 -2195359 -2195358 -2195358 -2195358 ...
Then, following the package guidelines (https://cran.r-project.org/web/packages/moveHMM/vignettes/moveHMM-guide.pdf), I transform the data to calculate steps and angles:
# Convert data to moveData object using prepData
move_data <- prepData(data, type = "UTM", coordNames = c("x", "y"))
And here comes the introduction of Na's:
> print(na_count_per_column)
ID step angle x y
0 1 1010 0 0
The modelling comes next:
# Fit the HMM with the adjusted parameters
hmm_model <- fitHMM(data = move_data, nbStates = 3, stepPar0 = stepPar0, anglePar0 = anglePar0, formula = ~1)
And gives a fair result:
> print(hmm_model)
Value of the maximum log-likelihood: 27526.22
Step length parameters:
----------------------
state 1 state 2 state 3
mean 3.426185e-15 8.306167e-02 4.9993906
sd 8.356259e+09 1.131159e-01 1.0002724
zero-mass 1.000000e+00 2.256299e-09 0.4078989
Turning angle parameters:
------------------------
state 1 state 2 state 3
mean 0.001312714 0.001319986 -3.313687e-10
concentration 2.827507199 22.348484965 1.000000e+01
Regression coeffs for the transition probabilities:
--------------------------------------------------
1 -> 2 1 -> 3 2 -> 1 2 -> 3 3 -> 1 3 -> 2
intercept -6.914171 -37.97005 -9.650105 -25.74398 -0.4295815 -1.285255
Transition probability matrix:
-----------------------------
[,1] [,2] [,3]
[1,] 9.990074e-01 0.000992619 3.231352e-17
[2,] 6.441467e-05 0.999935585 6.599375e-12
[3,] 3.376541e-01 0.143501890 5.188441e-01
Initial distribution:
--------------------
[1] 2.674974e-10 1.000000e+00 1.316610e-14
And then the issue arises:
> plot(hmm_model, type = "states")
Decoding states sequence... DONE
Error in if (maxdens > ymax & maxdens < 1.5 * ymax) { :
missing value where TRUE/FALSE needed
When trying the method on the elk data provided in the package, the plotting is successful. Even though, there are also some NA's being introduced.
> print(na_count_per_column)
ID step angle x y dist_water
0 4 10 0 0 0
Finally, as stated in the package guidelines,
within the package moveHMM,zero-inflation will automatically be included if there are zero steps.
If your data is not too sensitive (and the operation I'm about to suggest isn't too intractible), a little preprocessing might solve this.
A convolutional kernel run over your entire data set could apply a miniscule amount of PRNG Brownian noise/motion. This would prevent those discontinuities of absolutely zero motion.
R does support convolutional kernels.