rbf {geospt}

gaussian, exponential, trigonometric, thin plate spline, inverse multiquadratic, and multiquadratic radial basis function prediction

Description

Function for gaussian (GAU), exponential (EXPON), trigonometric (TRI), thin plate spline (TPS), completely regularized spline (CRS), spline with tension (ST), inverse multiquadratic (IM), and multiquadratic (M) radial basis function (rbf), where rbf is in a local neighbourhood

Usage

rbf(formula, data, eta, rho, newdata, n.neigh, func)

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

the optimal smoothing parameter, we recommend using the parameter found by minimizing the root-mean-square prediction errors using cross-validation

rho

the optimal parameter robustness, we recommend using the parameter found by minimizing the root-mean-square prediction errors using cross-validation. eta and rho parameters can be optimized simultaneously, through the bobyqa function from nloptr or minqa packages

newdata

data frame or spatial object with prediction/simulation locations; should contain attribute columns with the independent variables (if present) and (if locations is a formula) the coordinates with names, as defined in locations where you want to generate new predictions

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

radial basis function model type, e.g. "GAU", "EXPON", "TRI", "TPS", "CRS", "ST", "IM" and "M", are currently available

Details

rbf function generates individual predictions from gaussian (GAU), exponential (EXPON), trigonometric (TRI) thin plate spline (TPS), completely regularized spline (CRS), spline with tension (ST), inverse multiquadratic (IM), and multiquadratic (M) functions

Value

Attributes columns contain coordinates, predictions, and the variance column contains NA's

Examples

data(preci)
coordinates(preci) <- ~x+y

# prediction case: one point
point <- data.frame(3,4)
names(point) <- c("x","y")
coordinates(point) <- ~x+y
rbf(prec~x+y, preci, eta=0.1460814, rho=0, newdata=point,n.neigh=10, func="TPS")

# prediction case: a grid of points
puntos<-expand.grid(x=seq(min(preci$x),max(preci$x),0.05), y=seq(min(preci$y),
max(preci$y),0.05))
coordinates(puntos) <- ~x+y
pred.rbf <- rbf(prec~x+y, preci, eta=0.1460814, rho=0, newdata=puntos, n.neigh=10, func="TPS")
coordinates(pred.rbf) = c("x", "y")
gridded(pred.rbf) <- TRUE

# show prediction map
spplot(pred.rbf["var1.pred"], cuts=40, col.regions=bpy.colors(100),
main = "rainfall map TPS", key.space=list(space="right", cex=0.8))