spLM {spBayes}R Documentation

Function for fitting univariate Bayesian spatial regression models

Description

The function spLM fits Gaussian univariate stationary Bayesian spatial regression models. Given a set of knots, spLM fits a predictive process model (see references below).

Usage

spLM(formula, data = parent.frame(), coords, knots,
      starting, sp.tuning, priors, cov.model,
      modified.pp = TRUE, n.samples,
      verbose=TRUE, n.report=100, ...)

Arguments

formula a symbolic description of the regression model to be fit. See example below.
data an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which spLM is called.
coords an n x 2 matrix of the observation coordinates in R^2 (e.g., easting and northing).
knots either a m x 2 matrix of the predictive process knot coordinates in R^2 (e.g., easting and northing) or a vector of length two or three with the first and second elements recording the number of columns and rows in the desired knot grid. The third, optional, element sets the offset of the outermost knots from the extent of the coords extent.
starting a list with each tag corresponding to a parameter name. Valid list tags are beta, sigma.sq, tau.sq, phi, and nu. The value portion of each of each tag is the parameter's starting value.
sp.tuning a list with each tag corresponding to a parameter name. Valid list tags are sigma.sq, tau.sq, phi, and nu. The value portion of each of each tag defines the variance of the Metropolis normal proposal distribution.
modified.pp a logical value indicating if the modified predictive process should be used (see references below for details). Note, if a predictive process model is not used (i.e., knots is not specified) then this argument is ignored.
priors a list with each tag corresponding to a parameter name. Valid list tags are sigma.sq.ig, tau.sq.ig, phi.unif, and nu.unif (Beta priors are assumed flat). Variance parameters, simga.sq and tau.sq, are assumed to follow an inverse-Gamma distribution, whereas the spatial range phi and smoothness nu parameters are assumed to follow Uniform distributions. The hyperparameters of the inverse-Gamma are passed as a vector of length two, with the first and second elements corresponding to the shape and scale, respectively. The hyperparameters of the Uniform are also passed as a vector of length two with the first and second elements corresponding to the lower and upper support, respectively.
cov.model a quoted key word that specifies the covariance function used to model the spatial dependence structure among the observations. Supported covariance model key words are: "exponential", "matern", "spherical", and "gaussian". See below for details.
n.samples the number of MCMC iterations.
verbose if TRUE, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen.
n.report the interval to report Metropolis acceptance and MCMC progress.
... currently no additional arguments.

Value

An object of class spLM, which is a list with the following tags:

coords the n x 2 matrix specified by coords.
knot.coords the m x 2 matrix as specified by knots.
p.samples a coda object of posterior samples for the defined parameters.
acceptance the Metropolis sampling acceptance rate.
sp.effects a matrix that holds samples from the posterior distribution of the spatial random effects. The rows of this matrix correspond to the n point observations and the columns are the posterior samples.

The return object might include additional data used for subsequent prediction and/or model fit evaluation.

Author(s)

Andrew O. Finley finleya@msu.edu,
Sudipto Banerjee baner009@umn.edu

References

Banerjee, S., A.E. Gelfand, A.O. Finley, and H. Sang. (2008) Gaussian Predictive Process Models for Large Spatial Datasets. Journal of the Royal Statistical Society Series B, 70:825–848.

Finley, A.O., S. Banerjee, P. Waldmann, and T. Ericsson. (2008). Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial datasets. Biometrics. DOI: 10.1111/j.1541-0420.2008.01115.x

Finley, A.O,. H. Sang, S. Banerjee, and A.E. Gelfand. (2008). Improving the performance of predictive process modeling for large datasets. Computational Statistics and Data Analysis, DOI: 10.1016/j.csda.2008.09.008

Banerjee, S., Carlin, B.P., and Gelfand, A.E. (2004). Hierarchical modeling and analysis for spatial data. Chapman and Hall/CRC Press, Boca Raton, Fla.

See Also

spGGT, spMvLM

Examples

## Not run: 
data(rf.n200.dat)

Y <- rf.n200.dat$Y
coords <- as.matrix(rf.n200.dat[,c("x.coords","y.coords")])
w <- rf.n200.dat$w

##############################
##Simple spatial regression
##############################
m.1 <- spLM(Y~1, coords=coords,
             starting=list("phi"=0.6,"sigma.sq"=1, "tau.sq"=1),
             sp.tuning=list("phi"=0.01, "sigma.sq"=0.05, "tau.sq"=0.05),
             priors=list("phi.Unif"=c(0.3, 3), "sigma.sq.IG"=c(2, 1),
               "tau.sq.IG"=c(2, 1)),
             cov.model="exponential",
             n.samples=1000, verbose=TRUE, n.report=100)

print(summary(m.1$p.samples))
plot(m.1$p.samples)

##Requires MBA package to
##make surfaces
library(MBA)
par(mfrow=c(1,2))
obs.surf <-
  mba.surf(cbind(coords, Y), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(obs.surf, xaxs = "r", yaxs = "r", main="Observed response")
points(coords)
contour(obs.surf, add=T)

w.hat <- rowMeans(m.1$sp.effects)
w.surf <-
  mba.surf(cbind(coords, w.hat), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(w.surf, xaxs = "r", yaxs = "r", main="Estimated random effects")
points(coords)
points(m.1$knot.coords, pch=19, cex=1)
contour(w.surf, add=T)

##############################
##Predictive process
##############################
##Use some more observations
data(rf.n500.dat)

Y <- rf.n500.dat$Y
coords <- as.matrix(rf.n500.dat[,c("x.coords","y.coords")])
w <- rf.n500.dat$w

m.2 <- spLM(Y~1, coords=coords, knots=c(6,6,0),
             starting=list("phi"=0.6,"sigma.sq"=1, "tau.sq"=1),
             sp.tuning=list("phi"=0.01, "sigma.sq"=0.01, "tau.sq"=0.01),
             priors=list("phi.Unif"=c(0.3, 3), "sigma.sq.IG"=c(2, 1),
               "tau.sq.IG"=c(2, 1)),
             cov.model="exponential",
             modified.pp=FALSE, n.samples=2000, verbose=TRUE, n.report=100)

print(summary(m.2$p.samples))
plot(m.2$p.samples)

##Requires MBA package to
##make surfaces
library(MBA)
par(mfrow=c(1,2))
obs.surf <-
  mba.surf(cbind(coords, w), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(obs.surf, xaxs = "r", yaxs = "r", main="Observed response")
points(coords)
contour(obs.surf, add=T)

w.hat <- rowMeans(m.2$sp.effects)
w.surf <-
  mba.surf(cbind(coords, w.hat), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(w.surf, xaxs = "r", yaxs = "r", main="Estimated random effects")
contour(w.surf, add=T)
points(coords, pch=1, cex=1)
points(m.2$knot.coords, pch=19, cex=1)
legend(1.5,2.5, legend=c("Obs.", "Knots"), pch=c(1,19), bg="white")

##############################
##Modified predictive process
##############################
m.3 <- spLM(Y~1, coords=coords, knots=c(6,6,0),
             starting=list("phi"=0.6,"sigma.sq"=1, "tau.sq"=1),
             sp.tuning=list("phi"=0.01, "sigma.sq"=0.01, "tau.sq"=0.01),
             priors=list("phi.Unif"=c(0.3, 3), "sigma.sq.IG"=c(2, 1),
               "tau.sq.IG"=c(2, 1)),
             cov.model="exponential",
             n.samples=2000, verbose=TRUE, n.report=100)

print(summary(m.3$p.samples))
plot(m.3$p.samples)

##Requires MBA package to
##make surfaces
library(MBA)
par(mfrow=c(1,2))
obs.surf <-
  mba.surf(cbind(coords, w), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(obs.surf, xaxs = "r", yaxs = "r", main="Observed response")
points(coords)
contour(obs.surf, add=T)

w.hat <- rowMeans(m.3$sp.effects)
w.surf <-
  mba.surf(cbind(coords, w.hat), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(w.surf, xaxs = "r", yaxs = "r", main="Estimated random effects")
contour(w.surf, add=T)
points(coords, pch=1, cex=1)
points(m.3$knot.coords, pch=19, cex=1)
legend(1.5,2.5, legend=c("Obs.", "Knots"), pch=c(1,19), bg="white")

## End(Not run)

[Package spBayes version 0.1-2 Index]