predict0_vc: Prediction of explained variables and spatially varying coefficients

Description

This function predicts explained variables and spatially varying coefficients using a Moran's eigenvector-based spatially varying coefficient model. The Nystrom extension is used to minimize the expected prediction error

Usage

predict0_vc( mod, meig0, x0 = NULL, xconst0 = NULL )

Arguments

mod

spatially varying coefficient model estimates. Output from resf_vc

meig0

Moran's eigenvectors at predicted sites. Output from meigen0

Matrix of explanatory variables at predicted sites whose coefficients are allowed to vary across geographical space (N_0 x K). Default is NULL

xconst0

Matrix of explanatory variables at predicted sites whose coefficients are assumed constant across space (N_0 x K_const). Default is NULL

Value

pred

Matrix with the first column for the predicted values. The second and the third columns are the trend component (i.e., component explained by x0 and xconst0) and the spatial component in the predicted values (N x 3)

b_vc

Matrix of estimated spatially varying coefficients (SVCs) on x0 (N_0 x K)

bse_vc

Matrix of estimated standard errors for the SVCs (N_0 x K)

t_vc

Matrix of estimated t-values for the SVCs (N_0 x K)

p_vc

Matrix of estimated p-values for the SVCs (N_0 x K)

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.

Murakami, D., Yoshida, T., Seya, H., Griffith, D.A., and Yamagata, Y. (2017) A Moran coefficient-based mixed effects approach to investigate spatially varying relationships. Spatial Statistics, 19, 68-89.

Examples

Run this code

# NOT RUN {
require(spdep)
data(boston)
samp    <- sample( dim( boston.c )[ 1 ], 300)

d       <- boston.c[ samp, ]    ## Data at observed sites
y	      <- d[, "CMEDV"]
x       <- d[,c("CRIM", "ZN", "INDUS", "RM" ,"LSTAT")]
xconst  <- d[,c("NOX", "CHAS", "AGE", "DIS", "RAD", "TAX", "PTRATIO", "B" )]
coords  <- d[,c("LAT","LON")]

d0      <- boston.c[-samp, ]    ## Data at unobserved sites
x0      <- d0[,c("CRIM", "ZN", "INDUS", "RM" ,"LSTAT")]
xconst0 <- d0[,c("NOX", "CHAS", "AGE", "DIS", "RAD", "TAX", "PTRATIO", "B" )]
coords0 <- d0[,c("LAT","LON")]

############ Model estimation
meig 	  <- meigen( coords = coords )
mod	    <- resf_vc(y=y, x=x, xconst=xconst, meig=meig)

############ Spatial prediction of y and spatially varying coefficients
meig0 	<- meigen0( meig = meig, coords0 = coords0 )
pred0   <- predict0_vc( mod = mod, x0 = x0, xconst0=xconst0, meig0 = meig0 )
pred0$pred[1:10,]
pred0$b_vc[1:10,]
pred0$bse_vc[1:10,]
pred0$t_vc[1:10,]
pred0$p_vc[1:10,]

############ or spatial prediction of spatially varying coefficients
pred00  <- predict0_vc( mod = mod, meig0 = meig0 )
pred00$b_vc[1:10,]
pred00$bse_vc[1:10,]
pred00$t_vc[1:10,]
pred00$p_vc[1:10,]
# }

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