SDALGCPPred: Spatial prediction using plug-in of MCML estimates
In SDALGCP: Spatially Discrete Approximation to Log-Gaussian Cox Processes for Aggregated Disease Count Data

Description Usage Arguments Details Value Author(s) References See Also Examples

This function performs spatial continuous and discrete prediction, fixing the model parameters at the Monte Carlo maximum likelihood estimates of a SDALGCP model.

SDALGCPPred(
  para_est,
  cellsize,
  continuous = TRUE,
  control.mcmc = NULL,
  pred.loc = NULL,
  divisor = 1,
  plot.correlogram = F,
  messages = TRUE,
  parallel = FALSE
)

`para_est`	an object of class "SDALGCP" obtained as a result of a call to `SDALGCPMCML`.
`cellsize`	the size of the computational grid
`continuous`	logical; to choose which prediction to do perform, discrete or continuous. the default is continuous.
`control.mcmc`	output from `controlmcmcSDA`, if not provided, it uses the values used for the parameter estimation
`pred.loc`	optional, the dataframe of the predictive grid.
`divisor`	optional, the value to use to convert the dimension of the polygon, default is 1 which implies no conversion
`plot.correlogram`	logical; if plot.correlogram=TRUE the autocorrelation plot of the conditional simulations is displayed.
`messages`	logical; if messages=TRUE then status messages are printed on the screen (or output device) while the function is running. Default is messages=TRUE.
`parallel`	to parallelize some part of the function.

The function perform prediction of the spatially discrete incidence and covariate adjusted relative risk, and spatially continuous relative risk. The discrete inference uses the Metropolis-Adjusted Langevin Hasting sampling from Laplace.sampling. And the continuous inference is typically change of support inference.

pred.draw: the samples of the prediction

pred: the prediction of the relative risk

predSD: the standard error of the prediction

Pred.loc: The coordinates of the predictive locations

Olatunji O. Johnson o.johnson@lancaster.ac.uk

Emanuele Giorgi e.giorgi@lancaster.ac.uk

Peter J. Diggle p.diggle@lancaster.ac.uk

Banerjee, S., Carlin, B. P., & Gelfand, A. E. (2014). Hierarchical modeling and analysis for spatial data. CRC press.

plot.Pred.SDALGCP, SDAContinuousPred, SDADiscretePred, plot_continuous, plot_discrete

### Prepare the input of the model
data(PBCshp)
data <- as.data.frame(PBCshp@data)  #get the data
### Write the formula of the model
FORM <- X ~ propmale + Income + Employment + Education + Barriers + Crime +
Environment +  offset(log(pop))
### set the discretised phi
phi <- seq(500, 1700, length.out = 20)
#### get the initial parameter
model <- glm(formula=FORM, family="poisson", data=data)
beta.start <-coef(model)
sigma2.start <- mean(model$residuals^2)
phi.start <- median(phi)
par0 <- c(beta.start, sigma2.start, phi.start)
# setup the control arguments for the MCMC
n <- 545
h <- 1.65/(n^(1/6))
control.mcmc <- controlmcmcSDA(n.sim = 10000, burnin = 2000,
                 thin= 8, h=h, c1.h = 0.01, c2.h = 1e-04)
###Run the model

my_est <- SDALGCPMCML(formula=FORM, data=data, my_shp=PBCshp, delta=100, phi=phi, method=1,
                     weighted=FALSE,  plot=TRUE, par0=par0, control.mcmc=control.mcmc)
Con_pred <- SDALGCPPred(para_est=my_est,  cellsize=300, continuous=TRUE)