Error calibration
The first step to handling errors is to quantify them. Make sure that your data’s “dilution of precision” (DOP) and error columns import correctly into ctmm. In the following wood turtle dataset, we have some calibration data and a turtle track. Note that the calibration data must be collected from the same model device as the tracking data, and their data formatting bust be similar enough that the same location classes are detected by as.telemetry.
library(ctmm)
data(turtle)
names(turtle[[1]]) # data are not yet calibrated, but HDOP and location class is present## [1] "t" "HDOP" "class" "x" "y"## [1] "60s" "90s" "F231" "F403"
The uere command is used to estimate the RMS UERE parameter(s) from calibration data. Do not use this command on animal tracking data.
## , , horizontal
##
## low est high
## 2D 22.786528 29.598802 36.397467
## 3D 6.477391 6.946024 7.414237For GPS data, the RMS UERE will typically be 10-15 meters. Here we have two location classes, “2D” and “3D”, which for this device have substantially different RMS UERE values. The UERE parameters can then be assigned to a dataset with the uere()<- command.
## , , horizontal
##
## low est high
## 2D 22.786528 29.598802 36.397467
## 3D 6.477391 6.946024 7.414237
If you have Argos data, they will import with calibration already applied to the horizontal dimensions, but not the vertical dimension.
## [1] "gps" "argos"## [1] "timestamp" "longitude" "latitude" "t" "COV.angle" "HDOP"
## [7] "COV.major" "COV.minor" "VAR.xy" "class" "z" "VDOP"
## [13] "x" "y" "COV.x.x" "COV.x.y" "COV.y.y"
Error model selection
Not all GPS devices provide reliable DOP values and sometimes it is not obvious what error information will prove to be the most predictive. Generally speaking, as.telemetry will attempt to import the “best” column from among those that estimate error, DOP value, number of satellites and fix type, including timed-out fixes (see the timeout argument in help(as.telemetry)). Researchers may want to import their data with different error information, run uere.fit for each error model, and then select among the candidate models. Here we do this by comparing the turtle calibration data with and without HDOP values.
First, we consider whether or not the HDOP and location class information are informative.
t.noHDOP <- lapply(turtle,function(t){ t$HDOP <- NULL; t })
t.noclass <- lapply(turtle,function(t){ t$class <- NULL; t })
t.nothing <- lapply(turtle,function(t){ t$HDOP <- NULL; t$class <- NULL; t })In other cases, manipulation will need to be performed before importing, so that as.telemetry can format the telemetry object properly. Running uere.fit now results in errors calibrated under the assumption of homoskedastic errors.
UERE.noHDOP <- uere.fit(t.noHDOP[1:2])
UERE.noclass <- uere.fit(t.noclass[1:2])
UERE.nothing <- uere.fit(t.nothing[1:2])We can now apply model selection to the UERE model fits by summarizing them in a list.
## ΔAICc Z[red]²
## HDOP.class 0.0000 2.366617
## HDOP 286.5747 3.908826
## class 418.5174 3.696585
## homoskedastic 637.2580 4.681067We can see that the combination of location class and HDOP values yield the best error model, both in terms of AICc and in terms of reduced Z squared. Reduced Z squared is a goodness-of-fit statistic akin to reduced chi squared, but designed for comparing error models.
We had two calibration datasets, so we can also see if there is any substantial difference between the two GPS tags. We do this by making a list of individual UERE objects to compare to the previous joint UERE model.
## ΔAICc Z[red]²
## joint 0.000000 2.366617
## individual 3.314758 2.367412In this case, performance of the individualized and joint error models are comparable, and AICc selects the joint model.
