Generate bootstrap estimates of overlap

bootstrap takes two sets of times of observations and calculates bootstrap estimates of the chosen estimator of overlap. Alternatively, bootstrap estimates can be calculated in a 2-stage process: (1) create a matrix of bootstrap samples for each data set, using mm_resample(); (2) pass these matrices to mm_boot_estimates() to obtain the bootstrap estimates.

A vector of bootstrap estimates can then be used to produce confidence intervals with mm_boot_CI().

Usage

mm_bootstrap(
  A,
  B,
  nb,
  smooth = TRUE,
  kmax = 3,
  adjust = NA,
  n_grid = 128,
  type = c("Dhat1", "Dhat4", "Dhat5"),
  cores = 1
)

mm_resample(x, nb, smooth = TRUE, kmax = 3, adjust = 1, n_grid = 512)

mm_boot_estimates(
  Amat,
  Bmat,
  kmax = 3,
  adjust = c(0.8, 1, 4),
  n_grid = 128,
  type = c("all", "Dhat1", "Dhat4", "Dhat5"),
  cores = 1
)

Arguments

A: A numeric vector of time-of-day observations (in radians) for species A.
B: A numeric vector of time-of-day observations (in radians) for species B.
nb: the number of bootstrap samples required
smooth: if TRUE, smoothed bootstrap samples are produced.
kmax: An integer indicating the maximum number of modes allowed in the activity pattern. Default is 3.
adjust: A numeric value to adjust the bandwidth of the kernel density estimation. Default is 1.
n_grid: An integer specifying the number of grid points for density estimation. Default is 128.
type: the name of the estimator to use, or "all" to produce all three estimates. See mm_overlap_estimates() for recommendations on which to use.
cores: the number of cores to use for parallel processing. If NA, all but one of the available cores will used. Parallel processing may take longer than serial processing if the bootstrap runs quickly.
x: a numeric vector of time-of-capture data in radians, ie. on [0, \(2\pi\)] scale
Amat, Bmat: matrices of resampled data for each species produced by resample; see Value below.

Value

The function mm_bootstrap() returns a vector of bootstrap estimates. If estimation fails for a bootstrap sample, the corresponding value will be NA.

The function mm_resample() returns a numeric matrix with each column corresponding to a bootstrap sample. Times are in radians. It may return a matrix of NAs if smooth = TRUE and bandwidth estimation fails.

The Function mm_boot_estimates with type = "all" returns a numeric matrix with three columns, one for each estimator of overlap, otherwise a vector of bootstrap estimates.

References

Ridout & Linkie (2009) Estimating overlap of daily activity patterns from camera trap data. Journal of Agricultural, Biological, and Environmental Statistics 14:322-337

Author

Mike Meredith, Martin Ridout.

Examples


# Generate random data for two species
set.seed(42)
species_A <- runif(100, 1.2, 2 * pi)
species_B <- runif(100, 0.23, 2 * pi)

est <- mm_overlap_estimates(species_A, species_B, type="Dhat4")

boots <- mm_bootstrap(species_A, species_B, 1000, type="Dhat4", cores=1)
mean(boots)
#> [1] 0.8304592
hist(boots)

mm_boot_CI(est, boots)
#>            lower     upper
#> norm   0.7975707 0.9708611
#> norm0  0.7706923 0.9439828
#> basic  0.8051838 0.9740576
#> basic0 0.7674959 0.9363697
#> perc   0.7406175 0.9094913

# alternatively:
species_A_gen <- mm_resample(species_A, 1000)
species_B_gen <- mm_resample(species_B, 1000)
boots <- mm_boot_estimates(species_A_gen, species_B_gen, type="Dhat4", cores=1)
mean(boots)
#> [1] 0.8338819