gv.model {phylin}

Fit a model to the semi-variogram.

Description

Fits a model to a semi-variogram contructed with gen.variogram. Parameters for each model are estimated by nonlinear least squares.

Usage

gv.model(gv, model='spherical', sill = NA, range=NA, nugget = 0,
         ctrl=nls.control())

Arguments

gv

'gv' object from the gen.variogram function.

model

Model to fit the data. Available models are spherical (default), gaussian, exponential or linear. See details.

sill

The heigth (semi-variance) of the model when it stabilizes. Defaults to NA.

range

The length (real distance) where stabilization occurs. Defaults to NA.

nugget

Intercept in the y-axis. Defaults to 0.

ctrl

Nls control object for the fitting procedure. (check ?nls.control for more details).

Details

This function fits a model to the data, either by estimating the model parameters using nonlinear least squares or by user provided values. Notice that parameters with NA will be estimated by the nls function and parameters with values given are not estimated (by default, the nugget is not estimated and set to zero). The variogram model can be plotted using 'plot' function or used to predict to a new set of values using 'predict'. It is used to define weights for the krigging interpolation.

The parameters of the semi-variogram model (\gamma) are the distance (h), range (a), sill (c = c_0 + c_1; where c_1 is the partial sill), and nugget (c_0). The models available are:

1. gaussian:

   \gamma(h) = c_0 + c_1 \left(1-exp\left(-3\frac{h^2} {a^2}\right)\right)

2. exponential:

   \gamma(h) = c_0 + c_1 \left(1-exp\left(-\frac{3h}{a} \right)\right)

3. spherical:

   \gamma(h) = \left\{ \begin{array}{ll} c_0 + c_1\left(\frac{3}{2}\frac{h}{a} - \frac{1}{2}(\frac{h}{a})^3\right) & 0 < h \le a \\ c & h > a \end{array}\right.

4. pentaspherical:

   \gamma(h) = \left\{ \begin{array}{ll} c_0 + c_1\left(\frac{15}{8}\frac{h}{a} - \frac{5}{4}(\frac{h}{a})^3 + \frac{3}{8}(\frac{h}{a})^5\right) & 0 < h \le a \\ c & h > a \end{array}\right.

5. cubic:

   \gamma(h) = \left\{ \begin{array}{ll} c_0 + c_1\left(7(\frac{h}{a})^2 - \frac{35}{4}(\frac{h}{a})^3 + \frac{7}{2}(\frac{h}{a})^5 - \frac{3}{4}(\frac{h}{a})^7\right) & 0 < h \le a \\ c & h > a \end{array}\right.

6. linear:

   \gamma(h) = \left\{ \begin{array}{ll} c_0 + \left(\frac{c_1}{a}h\right) & 0 < h \le a \\ c & h > a \end{array}\right.

Value

Returns a 'gv' object with the model, input data, and parameter values.

Author(s)

Pedro Tarroso <[e-mail]>

References

Fortin, M. -J. and Dale, M. (2006) Spatial Analysis: A guide for Ecologists. Cambridge: Cambridge University Press.

Isaaks, E. H. and Srivastava, R. M. (1989) An Introduction to applied geostatistics. New York: Oxford University Press.

Legendre, P. and Legendre, L. (1998) Numerical ecology. 2nd english edition. Amesterdam: Elsevier

See Also

plot.gv predict.gv

Examples

data(vipers)
data(d.gen)

# create a distance matrix between samples
r.dist <- dist(vipers[,1:2])

# fit a variogram with defaults (shperical model) and estimation of range
gv <- gen.variogram(r.dist, d.gen)
gv <- gv.model(gv)

# plot variogram
plot(gv)

# fit a new variogram with linear with sill model and range 8
gv2 <- gv.model(gv, model='linear', range=8)
plot(gv2)