fitMM function

Fit a Moving-Moving Model with 2 Embedded Brownian Motion

Fit a Moving-Moving Model with 2 Embedded Brownian Motion with animal movement data at discretely observation times by maximizing a full likelihood constructed from the marginal density of increment. 'estVarMM' uses parametric bootstrap to obtain variance matrix of estimators from 'fitMM'.

fitMM(
  data,
  start,
  logtr = FALSE,
  method = "Nelder-Mead",
  optim.control = list(),
  integrControl = integr.control()
)

estVarMM(
  est_theta,
  data,
  nBS,
  detailBS = FALSE,
  numThreads = 1,
  integrControl = integr.control()
)

Arguments

• data: data used to process estimation

• start: starting value of the model, a vector of four components in the order of rate for moving1, rate for moving2, and volatility1(larger), volatility2(smaller).

• 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.

• est_theta: estimators of MRME model

• nBS: number of bootstrap.

• detailBS: whether or not output estimation results during bootstrap, which can be used to generate bootstrap CI.

• numThreads: the number of threads for parallel computation. If its value is greater than 1, then parallel computation will be processed. Otherwise, serial computation will be processed.

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

Examples

## Not run:

## time consuming example
tgrid <- seq(0, 100, length=100)
set.seed(123)
dat <- rMM(tgrid, 1, 0.1, 1, 0.1, "m1")

## fit whole dataset to the MR model
fit <- fitMM(dat, start=c(1, 0.1, 1, 0.1))
fit

var <- estVarMM(fit$estimate, dat, nBS = 10, numThreads = 6)
var
## 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.