predict0 {spmoran}

Spatial predictions

Description

It is a function for spatial prediction using the model estimated from esf, resf, or resf_vc function.

Usage

predict0( mod, meig0, x0 = NULL, xconst0 = NULL, xgroup0 = NULL, offset0 = NULL,
weight0 = NULL, compute_se=FALSE, compute_quantile = FALSE )

Arguments

mod

Output from esf resf

, or resf_vc

meig0

Moran eigenvectors at prediction sites. Output from meigen0

x0

Matrix of explanatory variables at prediction sites (N_0 x K). Each column of x0 must correspond to those in x in the input model (mod). Default is NULL

xconst0

Effective for resf_vc. Matrix of explanatory variables at prediction sites whose coefficients are assumed constant across space (N_0 x K_const). Each column of xconst0 must correspond to those in xconst in the input model. Default is NULL

xgroup0

Matrix/vector of group IDs at prediction sites that may be integer or name by group (N_0 x K_g). Default is NULL

offset0

Vector of offset variables at prediction sites (N_0 x 1). Effective if y is count (see nongauss_y). Default is NULL

weight0

Vector of weights for prediction sites (N_0 x 1). Required if compute_se = TRUE or compute_quantile = TRUE, and weight in the input model is not NULL

compute_se

If TRUE, predictive standard error is evaulated. It is currently supported only for continuous variables. If nongauss is specified in the input model (mod), standard error for the transformed y is evaluated. Default is FALSE

compute_quantile

If TRUE, Matrix of the quantiles for the predicted values (N x 15) is evaulated. It is currently supported only for continuous variables. Default is FALSE

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). If tr_num > 0 or tr_nonneg ==TRUE (i.e., y is transformed) in the input model resf, another column including the predicted values in the transformed/normalized scale (pred_trans) is added. In addition, if compute_quantile =TRUE, predictive standard errors (pred_se) is evaluated and added as another column

pred_quantile

Effective if compute_quantile = TRUE. Matrix of the quantiles for the predicted values (N x 15). It is useful for evaluating uncertainty in the predictive values

b_vc

Matrix of estimated spatially (and non-spatially) varying coefficients (S(N)VCs) on x0 (N_0 x K)

bse_vc

Matrix of estimated standard errors for the S(N)VCs (N_0 x K)

t_vc

Matrix of estimated t-values for the S(N)VCs (N_0 x K)

p_vc

Matrix of estimated p-values for the S(N)VCs (N_0 x K)

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

See Also

meigen0

Examples

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("ZN", "LSTAT")]
xconst  <- d[,c("CRIM", "NOX", "AGE", "DIS", "RAD", "TAX", "PTRATIO", "B", "RM")]
coords  <- d[,c("LON", "LAT")]

d0      <- boston.c[-samp, ]    ## Data at unobserved sites
y0      <- d0[, "CMEDV"]
x0      <- d0[,c("ZN", "LSTAT")]
xconst0 <- d0[,c("CRIM", "NOX", "AGE", "DIS", "RAD", "TAX", "PTRATIO", "B", "RM")]
coords0 <- d0[,c("LON", "LAT")]

meig 	  <- meigen( coords = coords )
meig0 	<- meigen0( meig = meig, coords0 = coords0 )

############ Spatial prediction ############
#### model with residual spatial dependence
mod	    <- resf(y=y, x=x, meig=meig)
pred0   <- predict0( mod = mod, x0 = x0, meig0 = meig0 )
pred0$pred[1:5,]  # Predicted values

#### model with spatially varying coefficients (SVCs)
mod	    <- resf_vc(y=y, x=x, xconst=xconst, meig=meig )
pred0   <- predict0( mod = mod, x0 = x0, xconst0=xconst0, meig0 = meig0 )
pred0$pred[1:5,]  # Predicted values
pred0$b_vc[1:5,]  # SVCs
pred0$bse_vc[1:5,]# standard errors of the SVCs
pred0$t_vc[1:5,]  # t-values of the SNVCs
pred0$p_vc[1:5,]  # p-values of the SNVCs

plot(y0,pred0$pred[,1]);abline(0,1)