lslm function

Low rank spatial lag model (LSLM) estimation

This function estimates the low rank spatial lag model.

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

Returns

• 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

References

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

Author(s)

Daisuke Murakami

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