lslm {spmoran}

Low rank spatial lag model (LSLM) estimation

Description

This function estimates the low rank spatial lag model.

Usage

lslm( y, x, weig, method = "reml", boot = FALSE, iter = 200 )

Arguments

y

Vector of explained variables (N x 1)

x

Matrix of explanatory variables (N x K)

weig

eigenvectors and eigenvalues of a spatial weight matrix. Output from weigen

method

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

boot

If it is TRUE, confidence intervals for the spatial dependence parameters (s), the mean direct effects (de), and the mean indirect effects (ie), are estimated through a parametric bootstrapping. Default is FALSE

iter

The number of bootstrap replicates. Default is 200

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 shrinkage parameters (2 x 1). The first and the second elements denote the estimated rho parameter (sp_rho) quantfying the scale of spatial dependence, and the standard error of the spatial dependent component (sp_SE), respectively. If boot = TRUE, their 95 percent confidence intervals and the resulting p-values are also provided

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)

de

Matrix with columns for the estimated mean direct effects on x. If boot = TRUE, their 95 percent confidence intervals and the resulting p-values are also provided

ie

Matrix with columns for the estimated mean indirect effects on x. If boot = TRUE, their 95 percent confidence intervals and the resulting p-values are also provided

r

Vector of estimated random coefficients on the spatial eigenvectors (L x 1)

pred

Vector of predicted values (N x 1)

resid

Vector of residuals (N x 1)

other

List of other outputs, which are internally used

Author(s)

Daisuke Murakami

References

Murakami, D., Seya, H. and Griffith, D.A. (2018) Low rank spatial econometric models. Arxiv.

See Also

weigen, lsem

Examples

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")]
coords  <- boston.c[,c("LON", "LAT")]
weig 	  <- weigen(coords)
res	    <- lslm(y=y,x=x,weig=weig)
## res  <- lslm(y=y,x=x,weig=weig, boot=TRUE)
res