Spatial regression with differential regularization (fully implemented in R code)
R_smooth.FEM.basis(locations, observations, FEMbasis, lambda, covariates, GCV)A #observations-by-2 matrix where each row specifies the spatial coordinates of the corresponding observations in the vector observations.
A #observations vector with the observed data values over the domain. The locations of the observations can be specified with the locations argument.
Otherwise if only the vector of observations is given, these are consider to be located in the corresponding node in the table nodes of the mesh. In this last
case, an NA value in the observations vector indicates that there is no observation associated to the corresponding node.
A FEMbasis object describing the Finite Element basis, as created by create.FEM.basis.
A scalar or vector of smoothing parameters.
A #observations-by-#covariates matrix where each row represents the covariates associated with the corresponding observed data value in observations.
Boolean. If TRUE the following quantities are computed: the trace of the smoothing matrix, the estimated error standard deviation, and
the Generalized Cross Validation criterion, for each value of the smoothing parameter specified in lambda.
A list with the following quantities:
fit.FEMA FEM object that represents the fitted spatial field.
PDEmisfit.FEMA FEM object that represents the Laplacian of the estimated spatial field.
betaIf covariates is not NULL, a vector of length #covariates with the regression coefficients associated with each covariate.
edfIf GCV is TRUE, a scalar or vector with the trace of the smoothing matrix for each value of the smoothing parameter specified in lambda.
stderrIf GCV is TRUE, a scalar or vector with the estimate of the standard deviation of the error for each value of the smoothing parameter specified in lambda.
GCVIf GCV is TRUE, a scalar or vector with the value of the GCV criterion for each value of the smoothing parameter specified in lambda.
Sangalli, L.M., Ramsay, J.O. & Ramsay, T.O., 2013. Spatial spline regression models. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 75(4), pp.681.703.
smooth.FEM.basis, smooth.FEM.PDE.basis, smooth.FEM.PDE.sv.basis