pred.epi: Posterior predictive check.
In EpiILM: Spatial and Network Based Individual Level Models for Epidemics

Description Usage Arguments Value References See Also Examples

Computing the posterior predictive check based on different summary statistics.

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pred.epi (object, xx, criterion , n.samples, burnin = NULL, tmin = NULL,

		  Sformula = NULL, Tformula = NULL, showProgressBar = interactive())

`object`	An object of class `epidata` that can be the output of `epidata` or `as.epidata`
`xx`	An object of class `epimcmc` that is the output of `epimcmc`.
`criterion`	The (multivariate) statistical criteria used in the posterior predictive check. It has three options: “newly infectious” which is a multivariate statistics represented by the number of newly infectious individuals over time, “epidemic length” represents the length of epidemic, and “peak time” represents the time of the peak of epidemic.
`n.samples`	The number of epidemics that needs to be simulated in the posterior predictive check procedure.
`burnin`	A scalar value which represents the number of samples needs to be discarded from the MCMC output.
`tmin`	The first time point at which the infection occurs, default value is one.
`Sformula`	An object of class formula. See formula. Individual-level covariate information associated with susceptibility can be passed through this argument. An expression of the form `~ model` is interpreted as a specification that the susceptibility function, Ω_S(i) is modelled by a linear predictor specified symbolically by the model term. Such a model consists of a series of terms separated by `+` and `-` operators. If there is no susceptibility covariate information, `Sformula` is null.
`Tformula`	An object of class formula. See formula. Individual-level covariate information associated with transmissibility can be passed through this argument. An expression of the form `~ -1+model` is interpreted as a specification that the transmissibility function, Ω_T(j) is modelled by a linear predictor specified symbolically by the model terms without the incorporation of the intercept term. Such a model consists of a series of terms separated by `+` and `-` operators. If there is no transmissibility covariate information, `Tformula` is null.
`showProgressBar`	logical. If TRUE a progress bar is shown.

An object of class pred.epi that contains the following:

type:: The compartmental framework model used in the analysis.
criterion:: The (multivariate) statistical criteria used in the posterior predictive check.
crit.sim:: The output of the evaluated criterion on the simulated epidemics.
crit.obs:: The output of the evaluated criterion on the observed epidemics.
tmax:: The last time point at which data is observed.
n.samples:: The number of simulated epidemics used in the posterior predictive check procedure.

Deardon R, Brooks, S. P., Grenfell, B. T., Keeling, M. J., Tildesley, M. J., Savill, N. J., Shaw, D. J., Woolhouse, M. E. (2010). Inference for individual level models of infectious diseases in large populations. Statistica Sinica, 20, 239-261.

epimcmc, epidata, epilike, plot.pred.epi.

## Example 1:  spatial SI model
# generate 100 individuals

set.seed(59991)

x <- runif(100, 0, 10)

y <- runif(100, 0, 10)

covariate <- cbind(runif(100, 0, 2), rbinom(100, 1, 0.5))

out <- epidata(type = "SI",n = 100, Sformula = ~covariate, tmax = 15,
               sus.par = c(0.1, 0.3, 0.01), beta = 5.0, x = x, y = y)

alphapar2 <- matrix(c(1, 1, 1, 1, 1, 1), ncol = 2, nrow = 3)

betapar2 <- c(1, 1)

epi<-epimcmc(object = out, tmin = 1, tmax = 15,
	       niter = 500, sus.par.ini = c(1, 1, 1), beta.ini = 1,
	       Sformula = ~covariate,
				 pro.sus.var = c(0.5, 0.3, 0.2), pro.beta.var = 0.1,
				 prior.sus.dist = c("gamma", "gamma", "gamma"),
				 prior.beta.dist = "gamma",
				 prior.sus.par = alphapar2, prior.beta.par = betapar2,
	       adapt = TRUE, acc.rate = 0.5)

epipred1 <- pred.epi (object = out, xx = epi,
				criterion = "newly infectious",
			  n.samples = 100, burnin = 200, tmin = 1,
			  Sformula = ~covariate)

plot(epipred1, col = "red", type = "b", lwd = 2)

epipred2 <- pred.epi (object = out, xx = epi,
				criterion = "peak time",
			  n.samples = 100, burnin = 200, tmin = 1,
			  Sformula = ~covariate)

plot(epipred2, col = "dark gray")