fitMR function

Fit a Moving-Resting Model with Embedded Brownian Motion

Fit a Moving-Resting Model with Embedded Brownian Motion with animal movement data at discretely observation times by maximizing a composite likelihood constructed from the marginal density of increment. Using segment to fit part of observations to the model. A practical application of this feature is seasonal analysis.

fitMR(
  data,
  start,
  segment = NULL,
  likelihood = c("full", "composite"),
  logtr = FALSE,
  method = "Nelder-Mead",
  optim.control = list(),
  integrControl = integr.control()
)

fitMovRes(
  data,
  start,
  likelihood = c("full", "composite"),
  logtr = FALSE,
  method = "Nelder-Mead",
  optim.control = list(),
  integrControl = integr.control()
)

Arguments

• data: a data.frame whose first column is the observation time, and other columns are location coordinates. If segment is not NULL, additional column with the same name given by segment should be included. This additional column is used to indicate which part of observations shoule be used to fit model. The value of this column can be any integer with 0 means discarding this observation and non-0 means using this obversvation. Using different non-zero numbers indicate different segments. (See vignette for more details.)

• start: starting value of the model, a vector of three components in the order of rate for moving, rate for resting, and volatility.

• segment: character variable, name of the column which indicates segments, in the given data.frame. The default value, NULL, means using whole dataset to fit the model.

• likelihood: a character string specifying the likelihood type to maximize in estimation. This can be "full" for full likelihood or "composite' for composite likelihood.

• logtr: logical, if TRUE parameters are estimated on the log scale.

• method: the method argument to feed optim.

• optim.control: a list of control to be passed to optim.

• integrControl: a list of control parameters for the integrate

  function: rel.tol, abs.tol, subdivision.

Returns

a list of the following components: - estimate: the esimated parameter vector

• loglik: maximized loglikelihood or composite loglikelihood evaluated at the estimate

• convergence: convergence code from optim

• likelihood: likelihood type (full or composite) from the input

Examples

## Not run:

## time consuming example
tgrid <- seq(0, 10, length=500)
set.seed(123)
## make it irregularly spaced
tgrid <- sort(sample(tgrid, 30)) # change to 400 for a larger sample
dat <- rMR(tgrid, 1, 2, 25, "m")

## fit whole dataset to the MR model
fit.fl <- fitMR(dat, start=c(2, 2, 20), likelihood = "full")
fit.fl

fit.cl <- fitMR(dat, start=c(2, 2, 20), likelihood = "composite")
fit.cl

## fit part of dataset to the MR model
batch <- c(rep(0, 5), rep(1, 7), rep(0, 4), rep(2, 10), rep(0, 4))
dat.segment <- cbind(dat, batch)
fit.segment <- fitMR(dat.segment, start = c(2, 2, 20), segment = "batch",
                     likelihood = "full")
head(dat.segment)
fit.segment
## End(Not run)

References

Yan, J., Chen, Y., Lawrence-Apfel, K., Ortega, I. M., Pozdnyakov, V., Williams, S., and Meyer, T. (2014) A moving-resting process with an embedded Brownian motion for animal movements. Population Ecology. 56(2): 401--415.

Pozdnyakov, V., Elbroch, L., Labarga, A., Meyer, T., and Yan, J. (2017) Discretely observed Brownian motion governed by telegraph process: estimation. Methodology and Computing in Applied Probability. doi:10.1007/s11009-017-9547-6.