predict0: Spatial prediction using eigenvector spatial filtering (ESF) or random effects ESF

Description

This function predicts explained variables using eigenvector spatial filtering (ESF) or random effects ESF. The Nystrom extension is used to perform a prediction minimizing the expected prediction error

Usage

predict0( mod, meig0, x0 = NULL, xgroup0 = NULL )

Arguments

mod

ESF or RE-ESF model estimates. Output from esf or resf

meig0

Moran eigenvectors at predicted sites. Output from meigen0

Matrix of explanatory variables at predicted sites (N_0 x K). Default is NULL

xgroup0

Matrix of group IDs that may be group IDs (integers) or group names (N_0 x K_group). Default is NULL

Value

pred

Matrix with the first column for the predicted values (pred). The second and the third columns are the predicted trend component (xb) and the residual spatial process (sf_residual). If xgroup0 is specified, the fourth column is the predicted group effects (group)

c_vc

Matrix of estimated non-spatially varying coefficients (NVCs) on x0 (N x K). Effective if nvc =TRUE in resf

cse_vc

Matrix of standard errors for the NVCs on x0 (N x K).Effective if nvc =TRUE in resf

ct_vc

Matrix of t-values for the NVCs on x0 (N x K). Effective if nvc =TRUE in resf

cp_vc

Matrix of p-values for the NVCs on x0 (N x K). Effective if nvc =TRUE in resf

References

Drineas, P. and Mahoney, M.W. (2005) On the Nystrom method for approximating a gram matrix for improved kernel-based learning. Journal of Machine Learning Research, 6 (2005), 2153-2175.

Examples

Run this code

# NOT RUN {
require(spdep)
data(boston)
samp    <- sample( dim( boston.c )[ 1 ], 400)

d       <- boston.c[ samp, ]  ## Data at observed sites
y	      <- d[, "CMEDV"]
x       <- d[,c("ZN","INDUS", "NOX","RM", "AGE", "DIS")]
coords  <- d[,c("LAT","LON")]

d0      <- boston.c[-samp, ][1,]  ## Data at unobserved sites
y0	    <- d0[, "CMEDV"]
x0      <- d0[,c("ZN","INDUS", "NOX","RM", "AGE", "DIS")]
coords0 <- d0[,c("LAT","LON")]

############ Model estimation
meig 	  <- meigen( coords = coords )
mod	    <- resf(y=y, x=x, meig=meig)
## or
# mod   <- esf(y=y,x=x,meig=meig)

############ Spatial prediction
meig0 	<- meigen0( meig = meig, coords0 = coords0 )
pred0   <- predict0( mod = mod, x0 = x0, meig0 = meig0 )
pred0$pred[1:10,]

######################## If NVCs are assumed
#mod2	  <- resf(y=y, x=x, meig=meig, nvc=TRUE)
#pred02  <- predict0( mod = mod2, x0 = x0, meig0 = meig0 )
#pred02$pred[1:10,]  # Predicted explained variables
#pred02$c_vc[1:10,]  # Predicted NVCs

# }