spmoran (version 0.1.7)

resf: Spatial regression with random effects eigenvector spatial filtering

Description

This function estimates the random effects eigenvector spatial filtering (RE-ESF) model.

Usage

resf( y, x = NULL, xgroup = NULL, meig, method = "reml" )

Arguments

y

Vector of explained variables (N x 1)

x

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

xgroup

Matrix of group indexes. The indeces may be group IDs (numbers) or group names (N x K_group). Default is NULL

meig

Moran's eigenvectors and eigenvalues. Output from meigen or meigen_f

method

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

Value

b

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

b_g

List of K_group matrices with columns for the estimated group effects, their standard errors, and t-values

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

s_g

Vector of estimated standard errors of the group effects

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

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.

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

See Also

besf, meigen, meigen_f

Examples

# NOT RUN {
require(spdep);require(Matrix)
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")]
meig 	<- meigen(coords=coords)
res	  <- resf(y = y, x = x, xgroup = xgroup, meig = meig)
res$b
res$b_g
res$s
res$s_g
res$e

#########Fast approximation
meig_f <- meigen_f(coords=coords)
res2   <- resf(y=y,x=x, xgroup = xgroup,meig=meig_f)
# }