MCMC samples from the Spatial GLMM
Description
Draw MCMC samples from the Spatial GLMM with known link function
Usage
1 2 3 4 5 6  mcsglmm(formula, family = c("gaussian", "binomial", "poisson", "Gamma",
"GEV.binomial", "GEVD.binomial", "Wallace.binomial"), data, weights, subset,
atsample, Nout, Nthin = 1, Nbi = 0, betm0, betQ0, ssqdf, ssqsc, phipars,
omgpars, corrfcn = c("matern", "spherical", "powerexponential"), kappa,
linkp, phisc, omgsc, zstart, phistart, omgstart, dispersion = 1,
longlat = FALSE, test = FALSE)

Arguments
formula 
A representation of the model in the form

family 
The distribution of the data. The

data 
An optional data frame containing the variables in the model. 
weights 
An optional vector of weights. Number of replicated samples for Gaussian and gamma, number of trials for binomial, time length for Poisson. 
subset 
An optional vector specifying a subset of observations to be used in the fitting process. 
atsample 
A formula in the form 
Nout 
Number of MCMC samples to return. 
Nthin 
The thinning of the MCMC algorithm. 
Nbi 
The burnin 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 chisquare prior for the partial sill parameter. 
ssqsc 
Scale for the scaled inverse chisquare prior for the partial sill parameter. 
phipars 
Parameters for the generalized inverse gamma prior
for the spatial range parameter 
omgpars 
Parameters for the generalized inverse gamma prior
for the relative nugget parameter 
corrfcn 
Spatial correlation function. See

kappa 
Spatial correlation parameter. Smoothness parameter for Matern, exponent for the power family. 
linkp 
Parameter of the link function. For binomial, a positive number for the degrees of freedom of the robit family or "logit" or "probit". For the other families any number for the exponent of the BoxCox transformation. 
phisc 
Random walk parameter for 
omgsc 
Random walk parameter for 
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 
omgstart 
Optional starting value for the MCMC for the relative
nugget parameter 
dispersion 
The fixed dispersion parameter. 
longlat 
How to compute the distance between locations. If

test 
Whether this is a trial run to monitor the acceptance
ratio of the random walk for 
Details
The fourparameter prior for phi
is defined by
propto (phi  phiprior[4])^(phiprior[2]1) * exp(((phiphiprior[4])/phiprior[1])^phiprior[3])
for phi > phiprior[4]. The prior for omg
is similar.
The prior parameters correspond to scale, shape, exponent, and
location. See arXiv:1005.3274
for details of this
distribution.
The GEV (Generalised Extreme Value) link is defined by
mu = 1  \exp[max(0, 1 + nu x)^(1/nu)]
for any real nu. At nu = 0 it reduces to the complementary loglog link.
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 sill parameter. 
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 loglikelihood evaluated at each sample. 
acc_ratio
The acceptance ratio for the joint update of the parametersphi
andomg
. 
sys_time
The total computing time for the MCMC sampling. 
Nout
,Nbi
,Nthin
As in input. Used internally in other functions. 
response
The value of the response variable at the observed locations. 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
,dispersion
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54  ## Not run:
data(rhizoctonia)
### Create prediction grid
predgrid < mkpredgrid2d(rhizoctonia[c("Xcoord", "Ycoord")],
par.x = 100, chull = TRUE, exf = 1.2)
### Combine observed and prediction locations
rhizdata < stackdata(rhizoctonia, predgrid$grid)
### Define the model
corrf < "spherical"
kappa < 0
ssqdf < 1
ssqsc < 1
betm0 < 0
betQ0 < .01
phiprior < c(100, 1, 1000, 100) # U(100, 200)
phisc < 3
omgprior < c(2, 1, 1, 0) # Exp(mean = 2)
omgsc < .1
linkp < "probit"
### MCMC sizes
Nout < 100
Nthin < 1
Nbi < 0
### Trial run
emt < mcsglmm(Infected ~ 1, 'binomial', rhizdata, weights = Total,
atsample = ~ Xcoord + Ycoord,
Nout = Nout, Nthin = Nthin, Nbi = Nbi,
betm0 = betm0, betQ0 = betQ0, ssqdf = ssqdf, ssqsc = ssqsc,
phipars = phiprior, omgpars = omgprior, linkp = linkp,
corrfcn = corrf, kappa = kappa, phisc = phisc, omgsc = omgsc,
dispersion = 1, test = 10)
### Full run
emc < mcsglmm(Infected ~ 1, 'binomial', rhizdata, weights = Total,
atsample = ~ Xcoord + Ycoord,
Nout = Nout, Nthin = Nthin, Nbi = Nbi,
betm0 = betm0, betQ0 = betQ0, ssqdf = ssqdf, ssqsc = ssqsc,
phipars = phiprior, omgpars = omgprior, linkp = linkp,
corrfcn = corrf, kappa = kappa, phisc = phisc, omgsc = omgsc,
dispersion = 1, test = FALSE)
plot.ts(cbind(phi = emc$phi, omg = emc$omg, beta = c(emc$beta),
ssq = emc$ssq), nc = 2)
emcmc < mcmcmake(emc)
summary(emcmc[, c("phi", "omg", "beta", "ssq")])
## End(Not run)

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