# MCMC samples from the transformed Gaussian model Draw MCMC samples from the transformed Gaussian model with known link function ```r 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 ) ``` ## 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. ## Returns 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. ## Details Simulates from the posterior distribution of this model. ## Examples ```r ## 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 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) ## End(Not run) ```

mcstrga function