# 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. ```r 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 ```r 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) ```

predict0 function