graph.rbf: Graph that describes the behavior of the optimized _eta_ and...

In geospt: Geostatistical Analysis and Design of Optimal Spatial Sampling Networks

Graph that describes the behavior of the optimized eta and rho parameters, associated with a radial basis function

Description

Function for plotting the RMSPE for several values of the smoothing parameter eta with the same dataset. A curve is fitted to the points, and then the optimal eta that provides the smallest RMSPE is determined from the curve, by the optimize function from the stats package.

Usage

graph.rbf(formula, data, eta.opt, rho.opt, n.neigh, func, np, x0, eta.dmax,
rho.dmax, P.T, iter, ...)

Arguments

formula	formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name z, for a rbf detrended use z~1; for a rbf with trend, suppose z is linearly dependent on x and y, use the formula z~x+y (linear trend).
data	SpatialPointsDataFrame: should contain the dependent variable, independent variables, and coordinates.
eta.opt	logical, indicating whether the parameter eta should be regarded as fixed (eta.opt = FALSE) or should be estimated (eta.opt = TRUE)
rho.opt	logical, indicating whether the parameter rho should be regarded as fixed (rho.opt = FALSE) or should be estimated (rho.opt = TRUE)
n.neigh	number of nearest observations that should be used for a rbf prediction, where nearest is defined in terms of the spatial locations
func	function to be optimized. The following radial basis function model types are currently available: gaussian "GAU", exponential "EXPON", trigonometric "TRI", thin plate spline "TPS", completely regularized spline "CRS", spline with tension "ST", inverse multiquadratic "IM", and multiquadratic "M", are currently available
np	number of points, where the radial basis function is calculated
x0	starting point for searching the optimum. Defaults to c(0.5, 0.5), eta and rho respectively. Use this statement only if eta and rho are equal to TRUE.
eta.dmax	maximum value of the range of the eta parameter that will be evaluated by the optimize function
rho.dmax	maximum value of the range of the rho parameter that will be evaluated by the optimize function
P.T	logical. Print Table (TRUE) or not (FALSE). Default P.T=NULL.
iter	The maximum allowed number of function evaluations.
...	further parameters to be passed to the minimization functions optimize or bobyqa, typically arguments of the type control() which control the behavior of the minimization algorithm. See documentation about the selected minimization function for further details.

Value

Returns a graph that describes the behavior of the optimized eta or rho parameter, and a table of values associated with the graph including optimal smoothing eta or rho parameters. If both eta and rho are FALSE simultaneously, then the function returns a list with; the best value obtained from the combinations smoothing eta and rho parameters and a lattice plot of class "trellis" with RMSPE pixel values associated with combinations of eta and rho parameters. Finally if both eta and rho are TRUE, the function will return a list with the best combination of values of the smoothing eta or rho parameters and the RMSPE associated with these.

References

Johnston, K., Ver, J., Krivoruchko, K., Lucas, N. 2001. Using ArcGIS Geostatistical Analysis. ESRI.

Examples

data(preci)
coordinates(preci)<-~x+y
# optimizing eta
graph.rbf(prec~1, preci, eta.opt=TRUE, rho.opt=FALSE, n.neigh=9, func="TPS", 
    np=40, eta.dmax=0.2, P.T=TRUE)
## Not run: 
# optimizing rho
graph.rbf(prec~x+y, preci, eta.opt=FALSE, rho.opt=TRUE, n.neigh=9, func="M", 
    np=20, rho.dmax=2, P.T=TRUE)
# optimizing eta and rho
tps.lo <- graph.rbf(prec~1, preci, eta.opt=TRUE, rho.opt=TRUE, n.neigh=9, func="TPS", 
    eta.dmax=2, rho.dmax=2, x0=c(0.1,0.1), iter=40)
tps.lo$Opt  # best combination of eta and rho obtained
# other optimization options
opt.u <- uobyqa(c(0.1,0.1), rbf.cv1, control = list(maxfun=40), formula=prec~1, data=preci, 
                n.neigh=9, func="TPS")
opt.n <- newuoa(c(0.1,0.1), rbf.cv1, control = list(maxfun=40), formula=prec~1, data=preci, 
                n.neigh=9, func="TPS")
# lattice of RMSPE values associated with a range of eta and rho, without optimization
tps.l <- graph.rbf(prec~1, preci, eta.opt=FALSE, rho.opt=FALSE, n.neigh=9, func="TPS", 
    np=10, eta.dmax=2, rho.dmax=2)
tps.l$opt.table  # best combination of eta and rho obtained from lattice
tps.ls$pplot     # lattice of RMSPE

## End(Not run)

geospt documentation built on Oct. 11, 2023, 1:07 a.m.