INLABMA (version 0.1-6)

sem.inla: Fit spatial econometrics models with INLA

Description

These functions fit some spatial econometrics models for a given value of rho (the spatial autocorrelation parameter). sem.inla fits a spatial error model, slm fits a spatial lag model and sdm.inla fits a spatial Durbin model.

Usage

sem.inla(formula, d, W, rho, improve = TRUE, impacts = FALSE, fhyper = NULL,  probit = FALSE, ...)
slm.inla(formula, d, W, rho, mmatrix = NULL, improve = TRUE, impacts = FALSE,  fhyper = NULL, probit = FALSE, ...)
sdm.inla(formula, d, W, rho, mmatrix = NULL, intercept = TRUE, impacts = FALSE, improve = TRUE, fhyper = NULL, probit = FALSE, ...)

Arguments

formula

Formula with the response variable, the fixed effects and, possibly, other non-linear effects.

d

Data.frame with the data.

W

Adjacency matrix.

rho

Value of the spatial autocorrelation paramter.

mmatrix

Design matrix of fixed effects.

intercept

Logical. Whether an intercept has been included in the model.

improve

Logical. Whether improve model fitting (this may require more computing time).

impacts

Logical. Whether impacts are computed.

fhyper

Options to be passed to the definition of the hyper-parameters in the spatial effects.

probit

Logical. Whether a probit model is used. Note this is only used when computing the impacts and that argument family must be set accordingly.

...

Other arguments passed to function inla.

Value

An inla object.

Details

These functions fit a spatial econometrics model with a fixed value of the spatial autocorrelation parameter rho.

In addition, the marginal -log-likelihood is corrected to account for the variance-covariance matrix of the error term or random effects.

References

Roger S. Bivand, Virgilio Gmez-Rubio, Hvard Rue (2014). Approximate Bayesian inference for spatial econometrics models. Spatial Statistics, Volume 9, 146-165.

Roger S. Bivand, Virgilio Gmez-Rubio, Hvard Rue (2015). Spatial Data Analysis with R-INLA with Some Extensions. Journal of Statistical Software, 63(20), 1-31. URL http://www.jstatsoft.org/v63/i20/.

See Also

leroux.inla

Examples

## Not run: 
# 
# if(requireNamespace("INLA", quietly = TRUE)) {
# require(INLA)
# require(spdep)
# 
# data(columbus)
# 
# lw <- nb2listw(col.gal.nb, style="W")
# 
# #Maximum Likelihood (ML) estimation
# colsemml <- errorsarlm(CRIME ~ INC + HOVAL, data=columbus, lw, method="eigen", 
# 	quiet=FALSE)
# colslmml <- lagsarlm(CRIME ~ INC + HOVAL, data=columbus, lw, method="eigen", 
# 	type="lag", quiet=FALSE)
# colsdmml <- lagsarlm(CRIME ~ INC + HOVAL, data=columbus, lw, method="eigen", 
# 	type="mixed", quiet=FALSE)
# 
# #Define grid on rho
# rrho<-seq(-1, .95, length.out=40)
# 
# #Adjacency matrix
# W <- as(as_dgRMatrix_listw(nb2listw(col.gal.nb)), "CsparseMatrix")
# #Index for spatial random effects
# columbus$idx<-1:nrow(columbus)
# 
# #Formula
# form<- CRIME ~ INC + HOVAL
# 
# zero.variance = list(prec=list(initial = 25, fixed=TRUE))
# 
# 
# 
# seminla<-mclapply(rrho, function(rho){
# 
#                 sem.inla(form, d=columbus, W=W, rho=rho,
#                         family = "gaussian", impacts=FALSE,
#                         control.family = list(hyper = zero.variance),
#                         control.predictor=list(compute=TRUE),
#                         control.compute=list(dic=TRUE, cpo=TRUE),
#                         control.inla=list(print.joint.hyper=TRUE), 
# 				#tolerance=1e-20, h=1e-6),
# 			verbose=FALSE
#                 )
# 
# })
# 
# 
# 
# slminla<-mclapply(rrho, function(rho){
# 
#                 slm.inla(form, d=columbus, W=W, rho=rho,
#                         family = "gaussian", impacts=FALSE,
#                         control.family = list(hyper = zero.variance),
#                         control.predictor=list(compute=TRUE),
#                         control.compute=list(dic=TRUE, cpo=TRUE),
#                         control.inla=list(print.joint.hyper=TRUE), 
# 				#tolerance=1e-20, h=1e-6),
# 			verbose=FALSE
#                 )
# })
# 
# 
# sdminla<-mclapply(rrho, function(rho){
# 
#                 sdm.inla(form, d=columbus, W=W, rho=rho,
#                         family = "gaussian", impacts=FALSE,
#                         control.family = list(hyper = zero.variance),
#                         control.predictor=list(compute=TRUE),
#                         control.compute=list(dic=TRUE, cpo=TRUE),
#                         control.inla=list(print.joint.hyper=TRUE), 
# 				#tolerance=1e-20, h=1e-6),
# 			verbose=FALSE
#                 )
# })
# 
# #BMA using a uniform prior (in the log-scale) and using a Gaussian 
# #approximation to the marginal
# sembma<-INLABMA(seminla, rrho, 0, usenormal=TRUE)
# slmbma<-INLABMA(slminla, rrho, 0, usenormal=TRUE)
# sdmbma<-INLABMA(sdminla, rrho, 0, usenormal=TRUE)
# 
# #Display results
# plot(sembma$rho$marginal, type="l", ylim=c(0,5))
# lines(slmbma$rho$marginal, lty=2)
# lines(sdmbma$rho$marginal, lty=3)
# #Add ML estimates
# abline(v=colsemml$lambda, col="red")
# abline(v=colslmml$rho, col="red", lty=2)
# abline(v=colsdmml$rho, col="red", lty=3)
# #Legend
# legend(-1,5, c("SEM", "SLM", "SDM"), lty=1:3)
# }
# 
# ## End(Not run)