spMvGLM | R Documentation |
The function spMvGLM
fits multivariate Bayesian
generalized linear spatial regression models. Given a set of knots,
spMvGLM
will also fit a predictive process model (see references below).
spMvGLM(formula, family="binomial", weights, data = parent.frame(), coords, knots, starting, tuning, priors, cov.model, amcmc, n.samples, verbose=TRUE, n.report=100, ...)
formula |
a list of q symbolic regression model descriptions to be fit. See example below. |
family |
currently only supports |
weights |
an optional n x q matrix of weights
to be used in the fitting process. The order of the
columns correspond to the univariate models in the formula list. Weights correspond to number of trials and offset for
each location for the |
data |
an optional data frame containing the variables in the
model. If not found in |
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 |
starting |
a list with each tag corresponding to a parameter name. Valid tags are |
tuning |
a list with tags |
priors |
a list with each tag corresponding to a
parameter name. Valid tags are |
cov.model |
a quoted keyword that specifies the covariance
function used to model the spatial dependence structure among the
observations. Supported covariance model key words are:
|
amcmc |
a list with tags |
n.samples |
the number of MCMC iterations. This argument is
ignored if |
verbose |
if |
n.report |
the interval to report Metropolis sampler acceptance and MCMC progress. |
... |
currently no additional arguments. |
If a binomial
model is specified the response vector is the
number of successful trials at each location and weights
is the
total number of trials at each location.
For a poisson
specification, the weights
vector is the
count offset, e.g., population, at each location. This differs from
the glm
offset
argument which is passed as the
log of this value.
A non-spatial model is fit when coords
is not specified. See
example below.
An object of class spMvGLM
, which is a list with the following
tags:
coords |
the n x 2 matrix specified by
|
knot.coords |
the m x 2 matrix as specified by |
p.beta.theta.samples |
a |
acceptance |
the Metropolis sampler
acceptance rate. If |
acceptance.w |
if this is a non-predictive process model and
|
acceptance.w.knots |
if this is a predictive process model and |
p.w.knots.samples |
a matrix that holds samples from the posterior distribution of the knots' spatial random effects. The rows of this matrix correspond to the q x m knot locations and the columns are the posterior samples. This is only returned if a predictive process model is used. |
p.w.samples |
a matrix that holds samples from the posterior distribution of the locations' spatial random effects. The rows of this matrix correspond to the q x 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., H. Sang, S. Banerjee, and A.E. Gelfand. (2009) Improving the performance of predictive process modeling for large datasets. Computational Statistics and Data Analysis, 53:2873-2884.
Finley, A.O., S. Banerjee, and A.E. Gelfand. (2015) spBayes for large univariate and multivariate point-referenced spatio-temporal data models. Journal of Statistical Software, 63:1–28. https://www.jstatsoft.org/article/view/v063i13.
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.
Roberts G.O. and Rosenthal J.S. (2006) Examples of Adaptive MCMC. http://probability.ca/jeff/ftpdir/adaptex.pdf Preprint.
spGLM
## Not run: library(MBA) ##Some useful functions rmvn <- function(n, mu=0, V = matrix(1)){ p <- length(mu) if(any(is.na(match(dim(V),p)))){stop("Dimension problem!")} D <- chol(V) t(matrix(rnorm(n*p), ncol=p)%*%D + rep(mu,rep(n,p))) } set.seed(1) ##Generate some data n <- 25 ##number of locations q <- 2 ##number of outcomes at each location nltr <- q*(q+1)/2 ##number of triangular elements in the cross-covariance matrix coords <- cbind(runif(n,0,1), runif(n,0,1)) ##Parameters for the bivariate spatial random effects theta <- rep(3/0.5,q) A <- matrix(0,q,q) A[lower.tri(A,TRUE)] <- c(1,-1,0.25) K <- A%*%t(A) Psi <- diag(0,q) C <- mkSpCov(coords, K, Psi, theta, cov.model="exponential") w <- rmvn(1, rep(0,nrow(C)), C) w.1 <- w[seq(1,length(w),q)] w.2 <- w[seq(2,length(w),q)] ##Covariate portion of the mean x.1 <- cbind(1, rnorm(n)) x.2 <- cbind(1, rnorm(n)) x <- mkMvX(list(x.1, x.2)) B.1 <- c(1,-1) B.2 <- c(-1,1) B <- c(B.1, B.2) weight <- 10 ##i.e., trials p <- 1/(1+exp(-(x%*%B+w))) y <- rbinom(n*q, size=rep(weight,n*q), prob=p) y.1 <- y[seq(1,length(y),q)] y.2 <- y[seq(2,length(y),q)] ##Call spMvLM fit <- glm((y/weight)~x-1, weights=rep(weight, n*q), family="binomial") beta.starting <- coefficients(fit) beta.tuning <- t(chol(vcov(fit))) A.starting <- diag(1,q)[lower.tri(diag(1,q), TRUE)] n.batch <- 100 batch.length <- 50 n.samples <- n.batch*batch.length starting <- list("beta"=beta.starting, "phi"=rep(3/0.5,q), "A"=A.starting, "w"=0) tuning <- list("beta"=beta.tuning, "phi"=rep(1,q), "A"=rep(0.1,length(A.starting)), "w"=0.5) priors <- list("beta.Flat", "phi.Unif"=list(rep(3/0.75,q), rep(3/0.25,q)), "K.IW"=list(q+1, diag(0.1,q))) m.1 <- spMvGLM(list(y.1~x.1-1, y.2~x.2-1), coords=coords, weights=matrix(weight,n,q), starting=starting, tuning=tuning, priors=priors, amcmc=list("n.batch"=n.batch,"batch.length"=batch.length,"accept.rate"=0.43), cov.model="exponential", n.report=25) burn.in <- 0.75*n.samples sub.samps <- burn.in:n.samples print(summary(window(m.1$p.beta.theta.samples, start=burn.in))$quantiles[,c(3,1,5)]) beta.hat <- t(m.1$p.beta.theta.samples[sub.samps,1:length(B)]) w.hat <- m.1$p.w.samples[,sub.samps] p.hat <- 1/(1+exp(-(x%*%beta.hat+w.hat))) y.hat <- apply(p.hat, 2, function(x){rbinom(n*q, size=rep(weight, n*q), prob=p)}) y.hat.mu <- apply(y.hat, 1, mean) ##Unstack to get each response variable fitted values y.hat.mu.1 <- y.hat.mu[seq(1,length(y.hat.mu),q)] y.hat.mu.2 <- y.hat.mu[seq(2,length(y.hat.mu),q)] ##Take a look par(mfrow=c(2,2)) surf <- mba.surf(cbind(coords,y.1),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf, main="Observed y.1 positive trials") contour(surf, add=TRUE) points(coords) zlim <- range(surf[["z"]], na.rm=TRUE) surf <- mba.surf(cbind(coords,y.hat.mu.1),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf, zlim=zlim, main="Fitted y.1 positive trials") contour(surf, add=TRUE) points(coords) surf <- mba.surf(cbind(coords,y.2),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf, main="Observed y.2 positive trials") contour(surf, add=TRUE) points(coords) zlim <- range(surf[["z"]], na.rm=TRUE) surf <- mba.surf(cbind(coords,y.hat.mu.2),no.X=100, no.Y=100, extend=TRUE)$xyz.est image(surf, zlim=zlim, main="Fitted y.2 positive trials") contour(surf, add=TRUE) points(coords) ## End(Not run)
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