Simulates a multivariate time series of counts based on the Poisson/Negative Binomial model as described in Paul and Held (2011).

# S3 method for hhh4
simulate(object, nsim = 1, seed = NULL, y.start = NULL,
subset = 1:nrow(object$stsObj), coefs = coef(object), components = c("ar","ne","end"), simplify = nsim>1, ...) ## Arguments object an object of class "hhh4". nsim number of time series to simulate. Defaults to 1. seed an object specifying how the random number generator should be initialized for simulation (via set.seed). The initial state will also be stored as an attribute "seed" of the result. The original state of the .Random.seed will be restored at the end of the simulation. By default (NULL), neither initialization nor recovery will be done. This behaviour is copied from the simulate.lm method. y.start vector or matrix (with ncol(object$stsObj) columns) with starting counts for the epidemic components. If NULL, the observed means in the respective units of the data in object during subset are used.

subset

time period in which to simulate data. Defaults to (and cannot exceed) the whole period defined by the underlying "sts" object.

coefs

coefficients used for simulation from the model in object. Default is to use the fitted parameters. Note that the coefs-vector must be in the same order and scaling as coef(object), which especially means reparamPsi = TRUE (as per default when using the coef-method to extract the parameters). The overdispersion parameter in coefs is the inverse of the dispersion parameter size in rnbinom.

components

character vector indicating which components of the fitted model object should be active during simulation. For instance, a simulation with components="end" is solely based on the fitted endemic mean.

simplify

logical indicating if only the simulated counts (TRUE) or the full "sts" object (FALSE) should be returned for every replicate. By default a full "sts" object is returned iff nsim=1.

...

unused (argument of the generic).

## Details

Simulates data from a Poisson or a Negative Binomial model with mean $$\mu_{it} = \lambda_{it} y_{i,t-1} + \phi_{it} \sum_{j \neq i} w_{ji} y_{j,t-1} + \nu_{it}$$ where $$\lambda_{it}>0$$, $$\phi_{it}>0$$, and $$\nu_{it}>0$$ are parameters which are modelled parametrically. The function uses the model and parameter estimates of the fitted object to simulate the time series.

With the argument coefs it is possible to simulate from the model as specified in object, but with different parameter values.

## Value

If simplify=FALSE: an object of class "sts" (nsim = 1) or a list of those (nsim > 1).

If simplify=TRUE: an object of class "hhh4sims", which is an array of dimension c(length(subset), ncol(object$stsObj), nsim), where the third dimension is dropped if nsim=1 (yielding a matrix). The originally observed counts during the simulation period, object$stsObj[subset,], are attached for reference (used by the plot-methods) as an attribute "stsObserved", and the initial condition y.start as attribute "initial".

## References

Paul, M. and Held, L. (2011) Predictive assessment of a non-linear random effects model for multivariate time series of infectious disease counts. Statistics in Medicine, 30, 1118--1136

## Author

Michaela Paul and Sebastian Meyer

## Examples

data(influMen)
# convert to sts class and extract meningococcal disease time series
meningo <- disProg2sts(influMen)[,2]

# fit model
fit <- hhh4(meningo, control = list(ar = list(f = ~ 1),
end = list(f = addSeason2formula(S = 1, period = 52)),
family = "NegBin1"))
plot(fit)

# simulate from model
simData <- simulate(fit, seed=1234)

# plot simulated data
plot(simData, main = "simulated data", xaxis.labelFormat=NULL)

# consider a Poisson instead of a NegBin model
coefs <- coef(fit)
coefs["overdisp"] <- 0

simData2 <- simulate(fit, seed=123, coefs = coefs)
plot(simData2, main = "simulated data: Poisson model", xaxis.labelFormat = NULL)

# consider a model with higher autoregressive parameter
coefs <- coef(fit)
coefs[1] <- log(0.5)

simData3 <- simulate(fit, seed=321, coefs = coefs)
plot(simData3, main = "simulated data: lambda = 0.5", xaxis.labelFormat = NULL)