spmoran (version 0.1.7)

besf: Memory-free implementation of the RE-ESF model for very large datasets

Description

This function estimates the RE-ESF model through a parallel computation whose memory consumption is independent of the sample size.

Usage

besf( y, x = NULL, coords,  method = "reml", covmodel="exp",
      enum = 200, bsize = 3000, cl=NULL)

Arguments

y

Vector of explained variables (N x 1)

x

Matrix of explanatory variables (N x K). Default is NULL

coords

Matrix of spatial point coordinates (N x 2)

method

Estimation method. Restricted maximum likelihood method ("reml") and maximum likelihood method ("ml") are available. Default is "reml"

covmodel

Type of kernel to model spatial dependence. The currently available options are "exp" for the exponential kernel, "gau" for the Gaussian kernel, and "sph" for the spherical kernel

enum

Number of eigenvectors and eigenvalues to be extracted (scalar). Default is 200

bsize

Block/badge size. bsize x bsize elements are iteratively processed during the parallelized computation. Default is 3000

cl

Number of cores used for the parallel computation. If cl=NULL, which is the default, the number of available cores is detected and used

Value

b

Matrix with columns for the estimated coefficients on x, their standard errors, t-values, and p-values (K x 4)

s

Vector of estimated variance parameters (2 x 1). The first and the second elements denote the standard error and the Moran's I value of the estimated spatially dependent component, respectively. The Moran's I value is scaled to take a value between 0 (no spatial dependence) and 1 (the maximum possible 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

e

Vector whose elements are residual standard error (resid_SE), adjusted conditional R2 (adjR2(cond)), restricted log-likelihood (rlogLik), Akaike information criterion (AIC), and Bayesian information criterion (BIC). When method = "ml", restricted log-likelihood (rlogLik) is replaced with log-likelihood (logLik)

r

Vector of estimated random coefficients on Moran's eigenvectors (L x 1)

sf

Vector of estimated spatial dependent component (N x 1)

pred

Vector of predicted values (N x 1)

resid

Vector of residuals (N x 1)

other

List of other outcomes, which are internally used

References

Griffith, D. A. (2003). Spatial autocorrelation and spatial filtering: gaining understanding through theory and scientific visualization. Springer Science & Business Media.

Murakami, D. and Griffith, D.A. (2015) Random effects specifications in eigenvector spatial filtering: a simulation study. Journal of Geographical Systems, 17 (4), 311-331.

Murakami, D. and Griffith, D.A. (2019) A memory-free spatial additive mixed modeling for big spatial data. ArXiv.

See Also

besf, meigen, meigen_f

Examples

# NOT RUN {
require(spdep)
data(boston)
y	<- boston.c[, "CMEDV" ]
x	<- boston.c[,c("CRIM","ZN","INDUS", "CHAS", "NOX","RM", "AGE",
                       "DIS" ,"RAD", "TAX", "PTRATIO", "B", "LSTAT")]
xgroup  <- boston.c[,"TOWN"]
coords  <- boston.c[,c("LAT","LON")]
# res	  <- besf(y = y, x = x, coords=coords)
# res$b
# res$s
# res$e

# }