spmoran (version 0.2.0)

resf: Spatial regression with random effects eigenvector spatial filtering (RE-ESF)

Description

RE-ESF-based spatial regression modeling. This model estimates residual spatial dependence, constant coefficients, non-spatially varying coefficients (NVC; coefficients varying with respect to explanatory variable value), and group effects.

Usage

resf( y, x = NULL, xgroup = NULL, nvc = FALSE, nvc_sel = TRUE,
      nvc_num = 5, meig, method = "reml", penalty = "bic" )

Arguments

y

Vector of explained variables (N x 1)

x

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

xgroup

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

nvc

If TRUE, non-spatiallly varying coefficients (NVCs; coefficients varying with respect to explanatory variable value) are asumed. If FALSE, constant coefficients are assumed. Default is FALSE

nvc_sel

If TRUE, type of each coefficient (NVC or constant) is selected through a BIC (default) or AIC minimization. If FALSE, NVCs are assumed across x. Alternatively, nvc_sel can be given by column number(s) of x. For example, if nvc_sel = 2, the coefficient on the second explanatory variable is NVC and the other coefficients are constants. Default is TRUE

nvc_num

Number of basis functions used to model NVC. An intercept and nvc_num natural spline basis functions are used to model each NVC. Default is 5

meig

Moran 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"

penalty

Penalty to select type of coefficients (NVC or constant) to stablize the estimates. The current options are "bic" for the Baysian information criterion-type penalty (N x log(K)) and "aic" for the Akaike information criterion (2K). Default is "bic"

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

c_vc

Matrix of estimated NVCs on x (N x K). Effective if nvc = TRUE

cse_vc

Matrix of standard errors for the NVCs on x (N x K). Effective if nvc = TRUE

ct_vc

Matrix of t-values for the NVCs on x (N x K). Effective if nvc = TRUE

cp_vc

Matrix of p-values for the NVCs on x (N x K). Effective if nvc = TRUE

s

Vector of estimated variance parameters (2 x 1). The first and the second elements are the standard error and the Moran's I value of the estimated spatially dependent process, 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_c

Vector of standard errors of the NVCs on xconst

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)

vc

List indicating whether NVC are removed or not during the BIC/AIC minimization. 1 indicates not removed whreas 0 indicates removed

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

meigen, meigen_f, besf

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)
# meig<- meigen_f(coords=coords)  ## for large samples

######## Regression considering residual spatially dependence
res	  <- resf(y = y, x = x, meig = meig)
res

######## Regression considering residual spatially dependence and NVC
######## (coefficients or NVC is selected)
#res2 <- resf(y = y, x = x, meig = meig, nvc = TRUE)

######## Regression considering residual spatially dependence and NVC
######## (all the coefficients are NVCs)
#res3 <- resf(y = y, x = x, meig = meig, nvc = TRUE, nvc_sel=FALSE)

######## Regression considering residual spatially dependence and group effects
#res4 <- resf(y = y, x = x, meig = meig, xgroup = xgroup)

######## Regression considering group-level spatially dependence and group effects
#meig_g<- meigen(coords=coords, s_id = xgroup)
#res5 <- resf(y = y, x = x, meig = meig_g, xgroup = xgroup)

# }