spDIC: Calculates model DIC and associated statistics given a bayesLMRef, bayesLMConjugate, spGGT, spLM, spMvLM, bayesGeostatExact object

Description

The function spDIC calculates model DIC and associated statistics given a bayesLMRef, bayesLMConjugate, spGGT, spLM, spMvLM, or bayesGeostatExact object.

Usage

spDIC(sp.obj, DIC.marg=TRUE, DIC.unmarg=TRUE,
         start=1, end, thin=1, verbose=TRUE, ...)

Arguments

sp.obj

an object returned by bayesLMRef, bayesLMConjugate, spGGT, sp

DIC.marg

a logical value indicating if marginalized DIC and associated statistics should be calculated. Note, this argument is ignored when sp.obj specifies a non-spatial model.

DIC.unmarg

a logical value indicating if unmarginalized DIC and associated statistics should be calculated. Note, this argument is ignored when sp.obj specifies a non-spatial model.

start

specifies the first sample included in the DIC calculation. This is useful for those who choose to acknowledge chain burn-in.

end

specifies the last sample included in the prediction calculation. The default is to use all posterior samples in sp.obj.

thin

a sample thinning factor. The default of 1 considers all samples between start and end. For example, if thin = 10 then 1 in 10 samples are considered between start and end.

verbose

if TRUE calculation progress is printed to the screen; otherwise, nothing is printed to the screen.

...

currently no additional arguments.

Value

A list with some of the following tags:
DICa matrix holding DIC and associated statistics when sp.obj specifies a non-spatial model.
DIC.marga matrix holding marginalized DIC and associated statistics.
DIC.unmarga matrix holding unmarginalized DIC and associated statistics.
sp.effectsif DIC.ummarg is true and if sp.obj specifies a spatial model without pre-calculated spatial effects then spDIC calculates the spatial effects.

Details

Please refer to Section 3.3 in the vignette.

References

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.

Examples

Run this code

###########################################
##          DIC for spLM
###########################################

##Use some more observations
data(rf.n200.dat)

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

##############################
##With and without predictive
##process
##############################
m.1a <- spLM(Y~1, coords=coords, knots=c(5, 5, 0),
             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(spDIC(m.1a, start=100, thin=2, DIC.marg=TRUE, DIC.unmarg=TRUE))

m.1b <- spLM(Y~1, coords=coords, knots=c(7, 7, 0),
             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(spDIC(m.1b, start=100, thin=2, DIC.marg=TRUE, DIC.unmarg=TRUE))

m.2 <- 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(spDIC(m.2, start=100, thin=2, DIC.marg=TRUE, DIC.unmarg=TRUE))

###########################################
##    DIC for bayesGeostatExact
###########################################
data(FORMGMT.dat)

n = nrow(FORMGMT.dat)
p = 5 ##an intercept an four covariates

n.samples <- 10

coords <- cbind(FORMGMT.dat$Longi, FORMGMT.dat$Lat)

phi <- 3/0.07

beta.prior.mean <- rep(0, times=p)
beta.prior.precision <- matrix(0, nrow=p, ncol=p)

alpha <- 1/1.5

sigma.sq.prior.shape <- 2.0
sigma.sq.prior.rate <- 10.0

##With covariates
m.3 <-
  bayesGeostatExact(Y~X1+X2+X3+X4, data=FORMGMT.dat,
                      n.samples=n.samples,
                      beta.prior.mean=beta.prior.mean,
                      beta.prior.precision=beta.prior.precision,
                      coords=coords, phi=phi, alpha=alpha,
                      sigma.sq.prior.shape=sigma.sq.prior.shape,
                      sigma.sq.prior.rate=sigma.sq.prior.rate,
                      sp.effects=FALSE)

print(spDIC(m.3, DIC.marg=TRUE, DIC.unmarg=FALSE))

##Without covariates
p <- 1 ##intercept only
beta.prior.mean <- 0
beta.prior.precision <- 0

m.4 <-
  bayesGeostatExact(Y~1, data=FORMGMT.dat,
                      n.samples=n.samples,
                      beta.prior.mean=beta.prior.mean,
                      beta.prior.precision=beta.prior.precision,
                      coords=coords, phi=phi, alpha=alpha,
                      sigma.sq.prior.shape=sigma.sq.prior.shape,
                      sigma.sq.prior.rate=sigma.sq.prior.rate,
                      sp.effects=FALSE)

print(spDIC(m.4, DIC.marg=TRUE, DIC.unmarg=FALSE))

##Lower DIC is better, so go with the covariates.

###########################################
##         DIC for spGGT
###########################################
data(FBC07.dat)

Y.2 <- FBC07.dat[1:100,"Y.2"]
coords <- as.matrix(FBC07.dat[1:100,c("coord.X", "coord.Y")])

##m.5 some model with spGGT.
K.prior <- prior(dist="IG", shape=2, scale=5)
Psi.prior <- prior(dist="IG", shape=2, scale=5)
phi.prior <- prior(dist="UNIF", a=0.06, b=3)

var.update.control <-
  list("K"=list(starting=5, tuning=0.1, prior=K.prior),
       "Psi"=list(starting=5, tuning=0.1, prior=Psi.prior),
       "phi"=list(starting=0.1, tuning=0.5, prior=phi.prior)
       )

beta.control <- list(update="GIBBS", prior=prior(dist="FLAT"))

run.control <- list("n.samples"=1000, "sp.effects"=TRUE)

m.5 <-
  spGGT(formula=Y.2~1, run.control=run.control,
         coords=coords, var.update.control=var.update.control,
         beta.update.control=beta.control,
         cov.model="exponential")

##Now with the spGGT object, m.5, calculate the DIC
##for both the unmarginalized and marginalized models.
##The likelihoods for these models are given by equation 6 and 7
##within the vignette.

DIC <- spDIC(m.5)
print(DIC)

###########################################
##     Compare DIC between non-spatial
##           and spatial models
###########################################

data(FBC07.dat)
Y.2 <- FBC07.dat[1:150,"Y.2"]
coords <- as.matrix(FBC07.dat[1:150,c("coord.X", "coord.Y")])

##############################
##Non-spatial model
##############################
m.1 <- bayesLMConjugate(Y.2~1, n.samples = 2000,
                          beta.prior.mean=0, beta.prior.precision=0,
                          prior.shape=-0.5, prior.rate=0)

summary(m.1$p.samples)

dic.m1 <- spDIC(m.1)

##> dic.m1
##                  [,1]
##bar.D       503.023678
##D.bar.Omega 501.059965
##pD            1.963713
##DIC         504.987392

##############################
##Spatial model
##############################
m.2 <- spLM(Y.2~1, coords=coords, knots=c(6,6,0),
             starting=list("phi"=0.1,"sigma.sq"=5, "tau.sq"=5),
             sp.tuning=list("phi"=0.03, "sigma.sq"=0.03, "tau.sq"=0.03),
             priors=list("phi.Unif"=c(0.06, 3), "sigma.sq.IG"=c(2, 5),
               "tau.sq.IG"=c(2, 5)),
             cov.model="exponential",
             n.samples=2000, verbose=TRUE, n.report=100)

summary(m.2$p.samples)

dic.m2 <- spDIC(m.2)

##> dic.m2
##$DIC.marg
##                 value
##bar.D       479.904433
##D.bar.Omega 476.856815
##pD            3.047617
##DIC         482.952050

##$DIC.unmarg
##                value
##bar.D       330.50408
##D.bar.Omega 258.64266
##pD           71.86142
##DIC         402.36550

## End(Not run)

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