fsglmm: Fitting Projection Based Laplace Approximation for Spatial...
In fastLaplace: A Fast Laplace Method for Spatial Generalized Linear Mixed Model

Description Usage Arguments Value References Examples

View source: R/fll_contin.R

fsglmm is used to fit reduced-dimensional spatial generalized linear mixed models for continuous spatial domain.

fsglmm(
  formula,
  kappa,
  inits,
  data,
  coords,
  family,
  ntrial = 1,
  offset = NA,
  method.optim,
  method.integrate,
  rank = NULL,
  control = list()
)

`formula`	an object of class "formula."
`kappa`	the smoothness parameter for the matern process (either 0.5, 1.5, 2.5 or 10).
`inits`	starting values for the parameters.
`data`	a data frame containing variables in the model.
`coords`	a matrix of dimension N x 2 representing the longitude and latitude of each observation.
`family`	a character string of the error distribution and link function to be used in the model.
`ntrial`	a numeric vector for a binomial model.
`offset`	this is used to specify an a priori a known component to be included in the linear predictor during fitting.
`method.optim`	the method to be used for outer optimization. "CG" for Conjugate Gradient Method.
`method.integrate`	the method to be used for inner optimization. "NR" for Newton Raphson Method.
`rank`	an integer of 'rank' to be used for projections. Default is 5 percent of observations.
`control`	a list of control parameters.

a list containing the following components:

summary a summary of the fitted model

vcov a symmetric matrix giving an estimate of the Hessian at the solution found.

mle2 an object of class "mle2"

family the family used.

kappa the matern smoothness parameter used.

Delta a matrix containing the estimated random effects of the reduced dimensional model.

U a matrix whose columns contain the estimated eigenvectors of the reduced dimensional model.

D a matrix whose diagonal components contain the estimated eigenvalues of the reduced dimensional model.

coords the matrix of coordinates used.

Jaewoo Park and Sangwan Lee - "A Projection-based Laplace Approximation for Spatial Latent Variable Models"

if(requireNamespace("mgcv")){
sigma2 = 1
phi = 0.2
beta.true = c(1,1)
n = 400
n.pred = 100
coords.all <- matrix(runif((n+n.pred)*2),ncol=2,nrow=n+n.pred)
X.all <- matrix(runif((n+n.pred)*2),ncol=2,nrow=(n+n.pred))
dist.all <- fields::rdist(coords.all,coords.all)
V.all <- sigma2*(1+sqrt(5)/phi*dist.all+5/(3*phi^2)*dist.all^2)*exp(-sqrt(5)/phi*dist.all)
set.seed(1)
r.e.all <- mgcv::rmvn(1,rep(0,nrow(coords.all)),V.all)
pi.all <- X.all%*%beta.true + r.e.all
p.all <- exp(pi.all)/(1+exp(pi.all))
Y.all <- sapply(p.all, function(x) sample(0:1, 1, prob = c(1-x, x)))
Y <- as.matrix(Y.all[1:n],nrow = n)
X <- X.all[1:n,]
coords <- coords.all[1:n,]
data <- data.frame(cbind(Y,X))
colnames(data) = c("Y","X1","X2")
mod.glm <- glm(Y~-1+X1+X2,family="binomial",data=data)
mod.glm.esp <- predict(mod.glm,data, type="response")
mod.glm.s2 <- var(Y - mod.glm.esp)
mod.glm.phi <- 0.1*max(dist(coords))
startinit <- c(mod.glm$coef,log(mod.glm.s2),log(mod.glm.phi))
names(startinit) <- c("X1","X2","logsigma2","logphi")
result.bin <- fsglmm(Y~-1+X1+X2, kappa=2.5, inits = startinit,
 data = data,coords = coords, family = "binomial", ntrial = 1,
 offset = NA,method.optim = "CG", method.integrate = "NR",rank = 50)
}