MCMC samples from the transformed Gaussian model

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Description

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

Usage

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mcstrga(formula, data, weights, subset, atsample, Nout, Nthin = 1, Nbi = 0,
  betm0, betQ0, ssqdf, ssqsc, tsqdf, tsqsc, phipars, omgpars,
  corrfcn = c("matern", "spherical", "powerexponential"), kappa, linkp, phisc,
  omgsc, zstart, phistart, omgstart, longlat = FALSE, test = FALSE)

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.

atsample

A formula in the form ~ x1 + x2 + ... + xd with the coordinates of the sampled locations.

Nout

Number of MCMC samples to return.

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.

phipars

Parameters for the generalized inverse gamma prior for the range parameter phi. A four dimensional vector with parameters scale, shape, exponent, location in that order. See mcsglmm.

omgpars

Parameters for the generalized inverse gamma prior for the relative nugget parameter omg. A four dimensional vector with parameters scale, shape, exponent, location in that order. See mcsglmm.

corrfcn

Spatial correlation function. See ebsglmm for details.

kappa

Spatial correlation parameter. Smoothness parameter for Matern, exponent for the power family.

linkp

The exponent of the Box-Cox transformation.

phisc

Random walk parameter for phi. Smaller values increase the acceptance ratio. Set this to 0 for fixed phi. In this case the fixed value is given in the argument phistart.

omgsc

Random walk parameter for omg. Smaller values increase the acceptance ratio. Set this to 0 for fixed omg. In this case the fixed value is given in the argument omgstart.

zstart

Optional starting value for the MCMC for the GRF. This can be either a scalar, a vector of size n where n is the number of sampled locations.

phistart

Optional starting value for the MCMC for the spatial range parameter phi. Defaults to the mean of its prior. If phisc is 0, then this argument is required and it corresponds to the fixed value of phi.

omgstart

Optional starting value for the MCMC for the relative nugget parameter omg. Defaults to the mean of its prior. If omgsc is 0, then this argument is required and itcorresponds to the fixed value of omg.

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.

Value

A list containing the MCMC samples and other variables 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.

  • omg A vector with the MCMC samples for the relative nugget parameter.

  • nu The link function parameter translated to numeric code used internally.

  • 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.

  • sys_time The total computing time for the MCMC sampling.

  • Nout, Nbi, Nthin As in input. Used internally in other functions.

  • response The average of the response variable at the observed locations, i.e. its value divided by the corresponding weight. Used internally in other functions.

  • weights The response weights at the observed locations. Used internally in other functions.

  • modelmatrix The model matrix at the observed locations. Used internally in other functions.

  • family As in input. Used internally in other functions.

  • betm0, betQ0, ssqdf, ssqsc, corrfcn, kappa, tsqdf, tsqsc As in input. Used internally in other functions.

  • locations Coordinates of the observed locations. Used internally in other functions.

  • whichobs A logical vector indicated which rows in the data and in the MCMC samples for the spatial random field correspond to the observed locations.

Examples

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## Not run: 
### 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 <- 1.3
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,
                  phipars = phiprior, omgpars = omgprior,
                  linkp = linkp,
                  phisc = phisc, omgsc = omgsc, test=10)

sample <- 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,
                  phipars = phiprior, omgpars = omgprior,
                  linkp = linkp,
                  phisc = phisc, omgsc = omgsc, test=FALSE)

## End(Not run)