table of rbf spatio-temporal cross validation, leave-one-out

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Description

It generates a table with the results of the evaluation of radial basis functions spatio-temporal (rbfST): gaussian (GAU), exponential (EXPON), trigonometric (TRI), thin plate spline (TPS), completely regularized spline (CRS), spline with tension (ST), inverse multiquadratic (IM), and multiquadratic (M) from the leave-one-out cross validation method.

Usage

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

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 rbf.st detrended use z_{st}~1, for a rbf.st 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

progress

whether a progress bar shall be printed for spatio-temporal radial basis functions; default=TRUE

Details

Leave-one-out cross validation (LOOCV) visits a data point, predicts the value at that location by leaving out the observed value, and proceeds with the next data point. The observed value is left out because rbf.st would otherwise predict the value itself.

Value

data frame contain prediction columns, observed values, residuals, the prediction variance, zscore (residual divided by standard error) which left with NA's, the fold column which is associated to cross-validation count, coordinates data and time. Prediction columns and residuals are obtained from cross-validation data points.

See Also

rbfST

Examples

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data(croatiadb)
coordinates(croatiadb) <- ~x+y
rbfST.tcv(MTEMP~X1+X2+X3+X4+X5+X6+X7+X8+X9+X10, croatiadb, eta=0.0108, rho=0.00004, 
          n.neigh=30, func="TPS")