mcstrga: MCMC samples from the transformed Gaussian model

Description

Draw MCMC samples from the transformed Gaussian model with known link function

Usage

mcstrga(
  formula,
  data,
  weights,
  subset,
  offset,
  atsample,
  corrfcn = "matern",
  linkp,
  phi,
  omg,
  kappa,
  Nout,
  Nthin = 1,
  Nbi = 0,
  betm0,
  betQ0,
  ssqdf,
  ssqsc,
  tsqdf,
  tsqsc,
  corrpriors,
  corrtuning,
  longlat = FALSE,
  test = FALSE
)

Value

A list containing the objects MODEL, DATA,

FIXED, MCMC and call. The MCMC samples are stored in the object MCMC as follows:

z A matrix containing the MCMC samples for the spatial random field. Each column is one sample.
mu A matrix containing the MCMC samples for the mean response (a transformation of z). Each column is one sample.
beta A matrix containing the MCMC samples for the regressor coefficients. Each column is one sample.
ssq A vector with the MCMC samples for the partial
tsq A vector with the MCMC samples for the measurement error variance.
phi A vector with the MCMC samples for the spatial range parameter, if sampled.
omg A vector with the MCMC samples for the relative nugget parameter, if sampled.
logLik A vector containing the value of the log-likelihood evaluated at each sample.
acc_ratio The acceptance ratio for the joint update of the parameters phi and omg, if sampled.
sys_time The total computing time for the MCMC sampling.
Nout, Nbi, Nthin As in input. Used internally in other functions.

The other objects contain input variables. The object call

contains the function call.

Arguments

formula: A representation of the model in the form response ~ terms. The response must be set to NA's at the prediction locations (see the example in mcsglmm for how to do this using stackdata). At the observed locations the response is assumed to be a total of replicated measurements. The number of replications is inputted using the argument weights.
data: An optional data frame containing the variables in the model.
weights: An optional vector of weights. Number of replicated samples.
subset: An optional vector specifying a subset of observations to be used in the fitting process.
offset: See lm.
atsample: A formula in the form ~ x1 + x2 + ... + xd with the coordinates of the sampled locations.
corrfcn: Spatial correlation function. See geoBayes_correlation for details.
linkp: Parameter of the link function. A scalar value.
phi: Optional starting value for the MCMC for the spatial range parameter phi. Defaults to the mean of its prior. If corrtuning[["phi"]] is 0, then this argument is required and it corresponds to the fixed value of phi. This can be a vector of the same length as Nout.
omg: Optional starting value for the MCMC for the relative nugget parameter omg. Defaults to the mean of its prior. If corrtuning[["omg"]] is 0, then this argument is required and it corresponds to the fixed value of omg. This can be a vector of the same length as Nout.
kappa: Optional starting value for the MCMC for the spatial correlation parameter kappa (Matern smoothness or exponential power). Defaults to the mean of its prior. If corrtuning[["kappa"]] is 0 and it is needed for the chosen correlation function, then this argument is required and it corresponds to the fixed value of kappa. This can be a vector of the same length as Nout.
Nout: Number of MCMC samples to return. This can be a vector for running independent chains.
Nthin: The thinning of the MCMC algorithm.
Nbi: The burn-in of the MCMC algorithm.
betm0: Prior mean for beta (a vector or scalar).
betQ0: Prior standardised precision (inverse variance) matrix. Can be a scalar, vector or matrix. The first two imply a diagonal with those elements. Set this to 0 to indicate a flat improper prior.
ssqdf: Degrees of freedom for the scaled inverse chi-square prior for the partial sill parameter.
ssqsc: Scale for the scaled inverse chi-square prior for the partial sill parameter.
tsqdf: Degrees of freedom for the scaled inverse chi-square prior for the measurement error parameter.
tsqsc: Scale for the scaled inverse chi-square prior for the measurement error parameter.
corrpriors: A list with the components phi, omg and kappa as needed. These correspond to the prior distribution parameters. For phi and omg it must be a vector of length 4. The generalized inverse gamma prior is assumed and the input corresponds to the parameters scale, shape, exponent, location in that order (see Details). For kappa it must be a vector of length 2. A uniform prior is assumed and the input corresponds to the lower and upper bounds in that order.
corrtuning: A vector or list with the components phi, omg and kappa as needed. These correspond to the random walk parameter for the Metropolis-Hastings step. Smaller values increase the acceptance ratio. Set this to 0 for fixed parameter value.
longlat: How to compute the distance between locations. If FALSE, Euclidean distance, if TRUE Great Circle distance. See spDists.
test: Whether this is a trial run to monitor the acceptance ratio of the random walk for phi and omg. If set to TRUE, the acceptance ratio will be printed on the screen every 100 iterations of the MCMC. Tune the phisc and omgsc parameters in order to achive 20 to 30% acceptance. Set this to a positive number to change the default 100. No thinning or burn-in are done when testing.

Details

Simulates from the posterior distribution of this model.

Examples

Run this code

if (FALSE) {
### Load the data
data(rhizoctonia)
rhiz <- na.omit(rhizoctonia)
rhiz$IR <- rhiz$Infected/rhiz$Total # Incidence rate of the
                              # rhizoctonia disease

### Define the model
corrf <- "spherical"
ssqdf <- 1
ssqsc <- 1
tsqdf <- 1
tsqsc <- 1
betm0 <- 0
betQ0 <- diag(.01, 2, 2)
phiprior <- c(200, 1, 1000, 100) # U(100, 300)
phisc <- 1
omgprior <- c(3, 1, 1000, 0) # U(0, 3)
omgsc <- 1
linkp <- 1

## MCMC parameters
Nout <- 100
Nbi <- 0
Nthin <- 1

samplt <- mcstrga(Yield ~ IR, data = rhiz,
                  atsample = ~ Xcoord + Ycoord, corrf = corrf,
                  Nout = Nout, Nthin = Nthin,
                  Nbi = Nbi, betm0 = betm0, betQ0 = betQ0,
                  ssqdf = ssqdf, ssqsc = ssqsc,
                  tsqdf = tsqdf, tsqsc = tsqsc,
                  corrprior = list(phi = phiprior, omg = omgprior),
                  linkp = linkp,
                  corrtuning = list(phi = phisc, omg = omgsc, kappa = 0),
                  test=10)

sample <- update(samplt, test = FALSE)
}

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