fitBMME {smam}

Fit a Brownian Motion with Measurement Error

Description

Given discretely observed animal movement locations, fit a Brownian motion model with measurement errors. Using segment to fit part of observations to the model. A practical application of this feature is seasonal analysis.

Usage

fitBMME(
  data,
  start = NULL,
  segment = NULL,
  method = "Nelder-Mead",
  optim.control = list()
)

fitBmme(data, start = NULL, method = "Nelder-Mead", optim.control = list())

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 two component, one for sigma (sd of BM) and the other for delta (sd for measurement error). If unspecified (NULL), a moment estimator will be used assuming equal sigma and delta.

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.

method

the method argument to feed optim.

optim.control

a list of control that is passed down to optim.

Details

The joint density of the increment data is multivariate normal with a sparse (tri-diagonal) covariance matrix. Sparse matrix operation from package Matrix is used for computing efficiency in handling large data.

Value

A list of the following components:

estimate

the estimated parameter vector

var.est

variance matrix of the estimator

loglik

loglikelihood evaluated at the estimate

convergence

convergence code from optim

References

Pozdnyakov V., Meyer, TH., Wang, Y., and Yan, J. (2013) On modeling animal movements using Brownian motion with measurement error. Ecology 95(2): p247–253. doi:doi:10.1890/13-0532.1.

See Also

fitMR

Examples

set.seed(123)
tgrid <- seq(0, 500, by = 1)
dat <- rBMME(tgrid, sigma = 1, delta = 0.5)

## using whole dataset to fit BMME
fit <- fitBMME(dat)
fit

## using part of dataset to fit BMME
batch <- c(rep(0, 100), rep(1, 200), rep(0, 50), rep(2, 100), rep(0, 51))
dat.segment <- cbind(dat, batch)
fit.segment <- fitBMME(dat.segment, segment = "batch")
head(dat.segment)
fit.segment