addlearn_local: Additional learning of local processes and prediction for...

In spmoran: Fast Spatial and Spatio-Temporal Regression using Moran Eigenvectors

Additional learning of local processes and prediction for large samples

Description

This function performs an additional learning of local variations in spatially varying coefficients (SVC). While the SVC model implemented in resf_vc or besf_vc can be less accurate for large samples (e.g., n > 5,000) due to a degeneracy/over-smoothing problem, this additional learning mitigates this problem by synthesizing/averaging the model with local SVC models. The resulting spatial prediction implemented in this function is expected to be more accurate than the resf_vc function.

Note that this function is not yet supported for spatio-temporal models with !is.null(meig$coords_z).

Usage

addlearn_local( mod, meig0 = NULL, x0 = NULL, xconst0=NULL, xgroup0=NULL,
           cl_num=NULL, cl=NULL, parallel=FALSE, ncores=NULL )

Arguments

mod	Outpot from resf_vc or besf_vc function
meig0	Moran eigenvectors at prediction sites. Output from meigen0
x0	Matrix of explanatory variables at prediction sites whose coefficients are allowed to vary across geographical space (N_0 x K). Default is NULL
xconst0	Matrix of explanatory variables at prediction sites whose coefficients are assumed constant (or NVC) across space (N_0 x K_const). Default is NULL
xgroup0	Matrix of group indeces at prediction sites that may be group IDs (integers) or group names (N_0 x K_g). Default is NULL
cl_num	Number of local sub-models being aggregated/averaged. If NULL, the number is determined so that the number of samples per sub-model equals approximately 600. Default is NULL
cl	Vector of cluster ID for each sample (N x 1). If specified, the local sub-models are given by this ID. If NULL, k-means clustering based on spatial coordinates is performed to obtain spatial clusters each of which contain approximately 600 samples. Default is NULL
parallel	If TRUE, the model is estimated through parallel computation. The default is FALSE if mod is an resf_vc object while TRUE if mod is an besf_vc object
ncores	Number of cores used for the parallel computation. If ncores = NULL and parallel = TRUE, the number of available cores - 2 is used. Default is NULL

Value

b_vc	Matrix of estimated spatially varying coefficients (SVCs) on x (N x K)
bse_vc	Matrix of standard errors for the SVCs on x (N x k)
z_vc	Matrix of z-values for the SVCs on x (N x K)
p_vc	Matrix of p-values for the SVCs on x (N x K)
c	Matrix with columns for the estimated coefficients on xconst, their standard errors, z-values, and p-values (K_c x 4)
b_g	List of K_g matrices with columns for the estimated group effects, their standard deviations, and t-values
s	List of 2 elements summarizing variance parameters characterizing SVCs of each local sub-model. The first element contains standard deviations of each SVCs while the second elementcontains their Moran's I values that are scaled to take a value between 0 (no spatial dependence) and 1 (strongest positive spatial dependence). Based on Griffith (2003), the scaled Moran'I value is interpretable as follows: 0.25-0.50:weak; 0.50-0.70:moderate; 0.70-0.90:strong; 0.90-1.00:marked
s_global	The same variance parameters for the globa sub-model
s_g	Vector of standard deviations of the group effects
e	Error statistics. It includes residual standard error (resid_SE), adjusted conditional R2 (adjR2(cond)), restricted log-likelihood (rlogLik), Akaike information criterion (AIC), and Bayesian information criterion (BIC)
pred	Matrix of predicted values for y (pred) and their standard errors (pred_se) (N x 2)
resid	Vector of residuals (N x 1)
cl	Vector of cluster ID being used (N x 1)
pred0	Matrix of predicted values for y (pred) and their standard errors (pred_se) at prediction sites (N_0 x 2)
b_vc0	Matrix of estimated spatially varying coefficients (SVCs) at prediction sites (N_0 x K)
bse_vc0	Matrix of standard errors for the SVCs at prediction sites (N_0 x k)
z_vc0	Matrix of z-values for the SVCs at prediction sites (N x K)
p_vc0	Matrix of p-values for the SVCs at prediction sites (N x K)
other	List of other outputs, which are internally used

Author(s)

Daisuke Murakami

References

Murakami, D., Sugasawa, S., T., Seya, H., and Griffith, D.A. (2024) Sub-model aggregation-based scalable eigenvector spatial filtering: application to spatially varying coefficient modeling. Geographical Analysis, DOI: 10.1111/gean.12393.

See Also

resf_vc, besf_vc

Examples

require(spdep)
data(house)
dat0    <- data.frame(house@coords,house@data)
dat     <- dat0[dat0$yrbuilt>=1980,]

###### purpose 1: improve SVC modeling accuracy ######
###### (i.e., addressing the over-smoothing problem) #
y	      <- log(dat[,"price"])
x       <- dat[,c("age","rooms")]
xconst  <- dat[,c("lotsize","s1994","s1995","s1996","s1997","s1998")]
coords  <- dat[ ,c("long","lat")]
meig    <- meigen_f( coords )

## Not run
# res0  <- resf_vc(y = y,x = x, xconst = xconst, meig = meig)
# res   <- addlearn_local(res0) # It adjusts SVCs to model local patterns
# res

####### parallel version for very large samples (e.g., n >100,000)
# bes0  <- besf_vc(y = y,x = x, xconst = xconst, coords=coords)
# bes	  <- addlearn_local( bes0 )


####### purpose 2: improve predictive accuracy ########

#samp    <- sample( dim( dat )[ 1 ], 2500)
#d       <- dat[ samp, ]    ## Data at observed sites
#y	     <- log(d[,"price"])
#x       <- d[,c("age","rooms")]
#xconst  <- d[,c("lotsize","s1994","s1995","s1996","s1997","s1998")]
#coords  <- d[ ,c("long","lat")]

#d0      <- dat[-samp, ]    ## Data at observed sites
#y0	     <- log(d0[,"price"])
#x0      <- d0[,c("age","rooms")]
#xconst0 <- d0[,c("lotsize","s1994","s1995","s1996","s1997","s1998")]
#coords0 <- d0[ ,c("long","lat")]

#meig    <- meigen_f( coords )
#res0    <- resf_vc(y = y,x = x, xconst = xconst, meig = meig)
#meig0   <- meigen0( meig=meig, coords0=coords0 )
#res     <- addlearn_local(res0, meig0=meig0, x0=x0, xconst0=xconst0) #
#pred    <- res$pred0       ## Predictive values

spmoran documentation built on Oct. 13, 2024, 1:07 a.m.