predict0: Spatial predictions

In spmoran: Fast Spatial Regression using Moran Eigenvectors

Spatial predictions

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, offset0 = NULL,
weight0 = NULL, compute_se=FALSE, compute_quantile = FALSE )

Arguments

mod	Output from esf or resf
meig0	Moran eigenvectors at predicted sites. Output from meigen0
x0	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
offset0	Vector of offset variables at predicted sites (N_0 x 1). Effective if y is count (see nongauss_y). Default is NULL
weight0	Vector of weights for predicted sites (N_0 x 1). Required if compute_se = TRUE or compute_quantile = TRUE
compute_se	If TRUE, predictive standard error is evaulated. It is currently supported only for continuous variables. If nongauss is specified in 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 resf, another column including the predicted values in the transformed/normalized scale (pred_trans) is inserted as the second column. In addition, if compute_quantile =TRUE, predictive standard errors (pred_se) is evaluated and inserted as another column
pred_quantile	Effective if compute_quantile = TRUE. Matrix of the quantiles for the predicted values (N x 15). It is useful to evaluate uncertainty in the predictive value
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.

See Also

meigen0, predict0_vc

Examples

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("LON", "LAT")]

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

############ 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

spmoran documentation built on April 29, 2023, 1:13 a.m.