# fitBmme: Fit a Brownian Motion with Measurement Error In smam: Statistical Modeling of Animal Movements

## Description

Given discretely observed animal movement locations, fit a Brownian motion model with measurement errors.

## Usage

 ```1 2``` ```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. `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. `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 esimated 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.

`fitMovRes`

## Examples

 ```1 2 3 4 5``` ```set.seed(123) tgrid <- seq(0, 500, by = 1) dat <- rbmme(tgrid, sigma = 1, delta = 0.5) fit <- fitBmme(dat) fit ```

### Example output

```\$estimate
[1] 0.9230639 0.6144865

\$var.est
[,1]         [,2]
[1,]  0.001791077 -0.001081307
[2,] -0.001081307  0.001553433

\$loglik
[1] -1626.087

\$convergence
[1] 0
```

smam documentation built on May 30, 2017, 7:23 a.m.