Leave-one-out cross validation for spatio-temporal radial basis function

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Description

It generates the RMSPE value, which is given by the radial basis function with smoothing eta and robustness rho parameters.

Usage

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rbfST.cv(formula, data, eta, rho, n.neigh, func)

Arguments

formula

formula that defines the dependent variable as a linear model of independent variables (covariates or the principal coordinates); suppose the dependent variable has name z_{st}, for a rbfST detrended use z_{st}~1, for a rbfST with trend, suppose z_{st} is linearly dependent on x and y, use the formula z_{st}~x+y (linear trend).

data

SpatialPointsDataFrame: should contain the spatio-temporal dependent variable, independent variables (statics and/or dynamics), spatial coordinates and the time as an integer or numerical variable.

eta

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

rho

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

n.neigh

number of nearest observations that should be used for a rbfST prediction, where nearest is defined in terms of the spatio-temporal locations.

func

spatio-temporal radial basis function; model type: "GAU", "EXPON", "TRI", "TPS", "CRS", "ST", "IM" and "M", are currently available

Value

returns the RMSPE value

References

Melo, C. E. (2012). Analisis geoestadistico espacio tiempo basado en distancias y splines con aplicaciones. PhD. Thesis. Universitat de Barcelona. 276 p. [link]

See Also

rbfST, graph.rbfST

Examples

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data(croatiadb)
coordinates(croatiadb) <- ~x+y
rbfST.cv(MTEMP~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10, croatiadb, eta=0.0108, rho=0.00004, 
          n.neigh=25, func="TPS")