spMvGLM {spBayes} | R Documentation |
The function spMvGLM
fits multivariate stationary Bayesian
generalized linear spatial regression models. Given a set of knots, spMvGLM
fits a
predictive process model (see references below).
spMvGLM(formula, family="binomial", data = parent.frame(), coords, knots, starting, tuning, priors, cov.model, n.samples, verbose=TRUE, n.report=100, ...)
formula |
for a multivariate model with q response variables, this is a list of univariate formulas. See example below. |
family |
currently only supports binomial and
poisson data using the logit and log link functions, respectively. |
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 spMvGLM 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 , A , phi , and nu . The value portion of each tag
is a vector of parameter's starting value. For A the vector
is of length q(q-q)/2+q
and phi and nu are of length q. Here,
A holds the the lower-triangle elements in column major ordering of the Cholesky square root
of the spatial cross-covariance matrix. If the predictive
process is used then w must be of length qm; otherwise,
it must be of length qn. Alternatively, w can be set
as a scalar, in which case the value is repeated. |
tuning |
a list with each tag corresponding to a
parameter name. Valid list tags are beta , A ,
phi , nu , and w . The value portion of each tag defines the variance of the Metropolis normal proposal
distribution. The tuning value for beta can be a
vector of length p or the lower-triangle of the
pxp Cholesky square-root of the desired proposal variance matrix. For A , the vector is of length q(q-q)/2+q
and phi and nu are of length q. If the
predictive process is used then w
must be of length m; otherwise,
it must be of length n. Alternatively, w can be set
as a scalar, in which the value is repeated. |
priors |
a list with each tag corresponding to a
parameter name. Valid list tags are beta.flat ,
beta.normal , K.IW , Psi.IW , phi.unif , and
nu.unif . If beta.normal then covariate specific mean and variance hyperparameters are
passed as the first and second list elements, respectively. K is assumed to follow an
inverse-Wishart distribution, whereas the spatial range phi
and smoothness nu parameters are assumed to follow Uniform distributions. The
hyperparameters of the inverse-Wishart are
passed as a list of length two, with the first and second elements corresponding
to the df and qxq scale matrix, respectively. The hyperparameters
of the Uniform are also passed as a vector of length 2xq with consecutive elements representing the first
and second elements corresponding to the lower and upper support in
the order of the univariate models given in formula . |
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. |
An object of class spMvGLM
, 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.
Andrew O. Finley finleya@msu.edu,
Sudipto Banerjee baner009@umn.edu
Finley, A.O., S. Banerjee, and R.E. McRoberts. (2008) A Bayesian approach to quantifying uncertainty in multi-source forest area estimates. Environmental and Ecological Statistics, 15:241–258.
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.
## Not run: ################################ ##Spatial multivariate poisson ################################ ##Generate some data n <- 100 q <- 3 nltr <- q*(q-1)/2+q coords <- cbind(runif(n,1,100),runif(n,1,100)) theta <- rep(3/50,q) A <- matrix(0,q,q) A[lower.tri(A,TRUE)] <- rnorm(nltr,1,1) K <- A%*%t(A) Psi <- diag(0,q) c1 <- mvCovInvLogDet(coords=coords, knots=coords, cov.model="exponential", V=K, Psi=Psi, theta=theta, modified.pp=TRUE, SWM=FALSE) w <- mvrnorm(1,rep(0,nrow(c1$C)),c1$C) X <- mkMvX(list(matrix(1,n,1), matrix(1,n,1), matrix(1,n,1))) beta <- c(-1,0,1) y <- rpois(n*q, exp(X%*%beta+w)) y.1 <- y[seq(1,length(y),q)] y.2 <- y[seq(2,length(y),q)] y.3 <- y[seq(3,length(y),q)] ##Specify starting values and collect samples. For ##a true analysis, several longer chains should be ##run. A.starting <- diag(1,q)[lower.tri(diag(1,q), TRUE)] beta.starting <- coefficients(glm(y~X-1, family="poisson")) beta.tuning <- t(chol(vcov(glm(y~X-1, family="poisson")))) n.samples <- 15000 m.1 <- spMvGLM(list(y.1~1,y.2~1,y.3~1), family="poisson", coords=coords, knots=c(8,8,0), starting= list("beta"=beta.starting, "phi"=rep(0.06,q), "A"=A.starting, "w"=0), tuning= list("beta"=beta.tuning, "phi"=rep(0.01,q), "A"=rep(0.005,nltr), "w"=0.001), priors= list("beta.Flat", "phi.Unif"=rep(c(0.03, 0.3),q), "K.IW"=list(q+1, diag(0.1,q))), cov.model="exponential", n.samples=n.samples, verbose=TRUE, n.report=500) m.1$p.samples[,paste("phi_",1:q,sep="")] <- 3/m.1$p.samples[,paste("phi_",1:q,sep="")] burn.in <- 0.75*n.samples print(summary(mcmc(m.1$p.samples[burn.in:n.samples,]))) beta.hat <- colMeans(m.1$p.samples[burn.in:n.samples,1:q]) w.hat <- rowMeans(m.1$sp.effects[,burn.in:n.samples]) y.hat <- exp(X%*%beta.hat+w.hat) y.hat.1 <- y.hat[seq(1,length(y.hat),q)] y.hat.2 <- y.hat[seq(2,length(y.hat),q)] y.hat.3 <- y.hat[seq(3,length(y.hat),q)] ##Take a look par(mfrow=c(3,2)) surf <- mba.surf(cbind(coords,y.1),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf, main="Observed counts") contour(surf, drawlabels=FALSE, add=TRUE) text(coords, labels=y.1, cex=1, col="blue") surf <- mba.surf(cbind(coords,y.hat.1),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf, main="Fitted counts") contour(surf, add=TRUE) contour(surf, drawlabels=FALSE, add=TRUE) text(coords, labels=round(y.hat.1,0), cex=1, col="blue") surf <- mba.surf(cbind(coords,y.2),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf) contour(surf, drawlabels=FALSE, add=TRUE) text(coords, labels=y.2, cex=1, col="blue") surf <- mba.surf(cbind(coords,y.hat.2),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf) contour(surf, drawlabels=FALSE, add=TRUE) text(coords, labels=round(y.hat.2,0), cex=1, col="blue") surf <- mba.surf(cbind(coords,y.3),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf) contour(surf, drawlabels=FALSE, add=TRUE) text(coords, labels=y.3, cex=1, col="blue") surf <- mba.surf(cbind(coords,y.hat.3),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf) contour(surf, drawlabels=FALSE, add=TRUE) text(coords, labels=round(y.hat.3,0), cex=1, col="blue") ## End(Not run)