predict0 function

Spatial and spatio-temporal predictions

It is a function for spatial/spatio-temporal pprediction using the model estimated from esf, resf, or resf_vc function.

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

Returns

• 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 mod, there is another column of the predicted values in the transformed/normalized scale (pred_trans). In addition, if compute_quantile =TRUE, predictive standard error (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 (spatio-temporally) varying coefficients (S(T)VCs) on x0 (N_0 x K)

• bse_vc: Matrix of estimated standard errors for the S(T)VCs (N_0 x K)

• t_vc: Matrix of estimated t-values for the S(T)VCs (N_0 x K)

• p_vc: Matrix of estimated p-values for the S(T)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)