fitMM {smam}

Fit a Moving-Moving Model with 2 Embedded Brownian Motion

Description

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'.

Usage

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.

Value

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

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.

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)