UHC Plots

In amt: Animal Movement Tools

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Background

Used-habitat calibration plots (UHC plots) are a graphical method for evaluating the calibration of a fitted HSF or (i)SSF model. The method uses a combination of parametric (to account for parameter uncertainty) and empirical bootstrapping to identify the distribution of used habitat, conditional on the fitted model and a test dataset. It can be used to identify problems in model specification, such as missing predictors and misspecified functional forms (e.g., linear rather than quadratic terms). For more details, see Fieberg et al. (2018).

Implementation in amt

We currently have an implementation of UHC plots in amt for objects of class fit_logit and glm (HSFs) and fit_clogit (iSSFs). The approach for both models is similar, making use of generic functions with appropriate methods depending on the class.

General workflow

For either an HSF or (i)SSF, the workflow is as follows:

1. Prepare data for analysis
2. Split data into training and testing datasets.
3. Use training dataset to fit candidate model(s) [HSF or (i)SSF].
4. Prepare UHC plots by passing the fitted model and the testing data to the function prep_uhc().
5. Create the UHC plots by calling plot() on the object returned in (4).

Examples

amt contains simulated habitat data. This was once stored as a RasterStack, but with conversion from raster to terra, it is no longer possible to store a SpatRaster as *.rda (the default binary format for included data). Instead, uhc_dat is a data.frame that can be converted to a SpatRaster with terra::rast(). For example:

hab <- rast(uhc_dat, type = "xyz", crs = "epsg:32612")

amt also contains location data simulated under (1) an HSF and (2) an iSSF to demonstrate the UHC plot workflow.

The SpatRaster (hab, once converted) contains 7 layers:

• forage: forage biomass in g/m^2^ (a resource)
• temp: mean annual temperature in °C (a condition)
• pred: predator density in predators/100 km^2^ (a risk)
• cover: land cover categories (1 = grassland, 2 = forest, 3 = wetland)
• dist_to_water: distance to the wetland category in m (does not affect selection)
• dist_to_cent: distance to the center of the raster in m (does not affect selection in HSF; avoidance of large distance to center in iSSF)
• rand: random integer from -4 to 4 (does not affect selection)

Note that temp, a condition, is modeled with a quadratic term in the simulations.

True parameter values under the simulation are in the description for each dataset, i.e., ?uhc_hsf_locs and ?uhc_issf_locs.

# Load all the packages we need
library(amt)
library(dplyr)
library(terra)
library(sf)

data(uhc_hab)
hab <- rast(uhc_hab, type = "xyz", crs = "epsg:32612")
# Convert "cover" layer to factor
levels(hab[[4]]) <- data.frame(id = 1:3,
                                    cover = c("grass", "forest", "wetland"))

# Affect habitat selection in simulation
plot(hab[[1:4]])

# Do not affect habitat selection in simulation
plot(hab[[5:7]])

HSF Example

The following is a demonstration of the workflow for an HSF.

Prepare data

First, we combine steps (1) and (2) by splitting into train/test data and then generating available locations and attributing with covariates and model weights.

# Load data
data(uhc_hsf_locs)

# Split into train (80%) and test (20%)
set.seed(1)
uhc_hsf_locs$train <- rbinom(n = nrow(uhc_hsf_locs),
                             size = 1, prob = 0.8)
train <- uhc_hsf_locs[uhc_hsf_locs$train == 1, ]
test <- uhc_hsf_locs[uhc_hsf_locs$train == 0, ]

# Available locations (entire raster extent)
avail_train <- random_points(st_as_sf(st_as_sfc(st_bbox(hab))),
                             n = nrow(train) * 10)

avail_test <- random_points(st_as_sf(st_as_sfc(st_bbox(hab))),
                            n = nrow(test) * 10)

# Combine with used
train_dat <- train |>
  make_track(x, y, crs = 32612) |>
  mutate(case_ = TRUE) |>
  bind_rows(avail_train) |>
  # Attach covariates
  extract_covariates(hab) |>
  # Assign large weights to available
  mutate(weight = case_when(
    case_ ~ 1,
    !case_ ~ 5000
  ))

test_dat <- test |>
  make_track(x, y, crs = 32612) |>
  mutate(case_ = TRUE) |>
  bind_rows(avail_test) |>
  # Attach covariates
  extract_covariates(hab)

# Note 'weight' column not created for test data
# (we assume all variables in test are candidate habitat variables)

Fit model(s)

Now we move onto step (3), where we fit candidate models. We'll start with a model that has an incorrect formulation. We will leave the quadratic term out for temp and leave cover out of the model.

hsf_wrong <- glm(case_ ~ forage + temp + pred,
                 data = train_dat, family = binomial(), weights = weight)

We will also fit the correct model, using the structure used to generate the data.

hsf_right <- glm(case_ ~ forage + temp + I(temp^2) + pred + cover,
                 data = train_dat, family = binomial(), weights = weight)

Prepare UHC plot data

Next, onto step (4), where we use prep_uhc() to prepare the UHC data. This is the function that does most of the heavy lifting (i.e., the boostrapping).

# Prep under wrong model
uhc_hsf_wrong <- prep_uhc(object = hsf_wrong, test_dat = test_dat,
                          n_samp = 100, verbose = FALSE) # In reality n_samp should be around 1000.

# Prep under right model
uhc_hsf_right <- prep_uhc(object = hsf_right, test_dat = test_dat,
                          n_samp = 100, verbose = FALSE)

Plot UHC plots

Finally, we are ready to plot (step 5). First, the wrong model.

plot(uhc_hsf_wrong)

Note that the used proportions for cover == "forest" and cover == "wetland" also fall above and below the modeled envelope, respectively. These are our clues that the model is incorrectly specified.

Note that dist_to_water also shows a mismatch between observed and predicted values. If we didn't already know that this was an unimportant variable, we might consider including it in our model. However, as we will see in the next set of plots, the correct model specification does correctly capture dist_to_water without needing to include it in the model.

Now, the right model.

plot(uhc_hsf_right)

We can see these issues have been resolved for our cover variables, indicating that our "right" model is, in fact, better calibrated than hsf_wrong. Additionally, there is no longer an issue with dist_to_water, confirming that we do not need to include it in the model.

Note that with a large number of bootstrap samples, the plots are quite complex and can take multiple seconds to render. If you are working with many candidate variables, this makes examining all the plot quite slow. We have included a few potential solutions to this problem:

• First, you can plot just a single variable, by subsetting the uhc_data object by either integers or the names of the variables.
• Second, you can convert the many lines to a single polygon representing a confidence enevelope (with a confidence level of your choice).

Subsetting:

# By index
plot(uhc_hsf_right[c(1, 3)])

# By names (vector of >1 names also allowed)
plot(uhc_hsf_right["cover"])

Envelope:

# Coerce to data.frame
df <- as.data.frame(uhc_hsf_right)

# Create confidence envelopes (95% and 100%)
env <- conf_envelope(df, levels = c(0.95, 1))

# Plot
plot(env)

iSSF Example

The following is a demonstration of the workflow for an iSSF.

Prepare data

First, we combine steps (1) and (2) by splitting into train/test data and then generating available locations and attributing with covariates and model weights.

# Load data
data(uhc_issf_locs)

# Format as steps
steps <- uhc_issf_locs |>
  make_track(x, y, t, crs = 32612) |>
  steps()

# Split into train (80%) and test (20%)
set.seed(1)
steps$train <- rbinom(n = nrow(steps),
                      size = 1, prob = 0.8)
train <- steps[steps$train == 1, ]
test <- steps[steps$train == 0, ]

# Generate available steps, attribute
train_dat <- train |>
  random_steps(n_control = 15) |>
  # Attach covariates
  extract_covariates(hab) |>
  # Additional movement parameters
  mutate(log_sl_ = log(sl_),
         cos_ta_ = cos(ta_)) |>
  # Drop 'train' column
  dplyr::select(-train) |> 
  # Get rid of any NAs (sometimes available steps fall outside of raster)
  na.omit()

test_dat <- test |>
  random_steps(n_control = 15) |>
  # Attach covariates
  extract_covariates(hab) |>
  # Additional movement parameters
  mutate(log_sl_ = log(sl_),
         cos_ta_ = cos(ta_)) |>
  # Drop 'train' column
  dplyr::select(-train) |> 
  # Get rid of any NAs (sometimes available steps fall outside of raster)
  na.omit()

Fit model(s)

Now we move onto step (3), where we fit candidate models. We'll start with a model that has an incorrect formulation.

issf_wrong <- fit_issf(train_dat, 
                       case_ ~ 
                         # Habitat
                         forage + 
                         # Movement
                         sl_ + log_sl_ + cos_ta_ +
                         # Strata
                         strata(step_id_), model = TRUE)

We will also fit the correct model, using the structure used to generate the data.

issf_right <- fit_issf(train_dat, 
                       case_ ~ 
                         # Habitat
                         forage + temp + I(temp^2) + pred + cover + dist_to_cent +
                         # Movement
                         sl_ + log_sl_ + cos_ta_ +
                         # Strata
                         strata(step_id_), model = TRUE)

Prepare UHC plot data

Next, onto step (4), where we use prep_uhc() to prepare the UHC data. This is the function that does most of the heavy lifting (i.e., the bootstrapping).

# Prep under wrong model
uhc_issf_wrong <- prep_uhc(object = issf_wrong, test_dat = test_dat,
                           n_samp = 20, verbose = FALSE)

# Prep under right model
uhc_issf_right <- prep_uhc(object = issf_right, test_dat = test_dat,
                           n_samp = 20, verbose = FALSE)

Plot UHC plots

Finally, we are ready to plot (step 5). First, the wrong model.

plot(uhc_issf_wrong)

We can see that every variable besides rand shows a mismatch between observed and expected.

Now, the right model.

plot(uhc_issf_right)

Every variable now shows matches between observed and expected.

Additional Methods

There is also a function to coerce a uhc_data object to data.frame. This would be useful, for example, if you wish to create a custom plot with ggplot2 or another package.

# Structure of `uhc_data` object
str(uhc_issf_right, 1)

# Coerce to data.frame
head(as.data.frame(uhc_issf_right), 10)

References

Fieberg, J.R., Forester, J.D., Street, G.M., Johnson, D.H., ArchMiller, A.A., and Matthiopoulos, J. 2018. Used-habitat calibration plots: A new procedure for validating species distribution, resource selection, and step-selection models. Ecography 41:737–752.

amt documentation built on June 25, 2024, 1:14 a.m.