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))