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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, ...)



an object of class "hhh4".


number of time series to simulate. Defaults to 1.


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.


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.


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


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.


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.


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).


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.


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). 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". The [-method for "hhh4sims" takes care of subsetting these attributes appropriately.


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


Michaela Paul and Sebastian Meyer

See also

plot.hhh4sims and scores.hhh4sims and the examples therein for nsim > 1.


# 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(~1, period = 52)),
              family = "NegBin1"))

# simulate from model (generates an "sts" object)
simData <- simulate(fit, seed=1234)

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

# use simplify=TRUE to return an array of simulated counts
simCounts <- simulate(fit, seed=1234, simplify=TRUE)
dim(simCounts)  # nTime x nUnit x nsim
stopifnot(observed(simData) == c(simCounts))
# plot the first year of simulated counts (+ initial + observed)
plot(simCounts[1:52,,], type = "time", xaxis.labelFormat = NULL)
# see help(plot.hhh4sims) for other plots, mainly useful for nsim > 1

# simulate from a Poisson instead of a NegBin model
# keeping all other parameters fixed at their original estimates
coefs <- replace(coef(fit), "overdisp", 0)
simData2 <- simulate(fit, seed=123, coefs = coefs)
plot(simData2, main = "simulated data: Poisson model", xaxis.labelFormat = NULL)

# simulate from a model with higher autoregressive parameter
coefs <- replace(coef(fit), "ar.1", log(0.9))
simData3 <- simulate(fit, seed=321, coefs = coefs)
plot(simData3, main = "simulated data: lambda = 0.5", xaxis.labelFormat = NULL)

## more sophisticated: simulate beyond initially observed time range

# extend data range by one year (non-observed domain), filling with NA values
nextend <- 52
timeslots <- c("observed", "state", "alarm", "upperbound", "populationFrac")
addrows <- function (mat, n) mat[c(seq_len(nrow(mat)), rep(NA, n)),,drop=FALSE]
extended <- Map(function (x) addrows(slot(meningo, x), n = nextend), x = timeslots)
# create new sts object with extended matrices
meningo2 <-"sts", c(list(start = meningo@start, frequency = meningo@freq,
                                  map = meningo@map), extended))

# fit to the observed time range only, via the 'subset' argument
fit2 <- hhh4(meningo2, control = list(
              ar = list(f = ~ 1),
              end = list(f = addSeason2formula(~1, period = 52)),
              family = "NegBin1",
              subset = 2:(nrow(meningo2) - nextend)))
# the result is the same as before
stopifnot(all.equal(fit, fit2, ignore = c("stsObj", "control")))
# \dontshow{
# one-week-ahead prediction only "works" for the first non-observed time point
# because the autoregressive component relies on non-missing past counts
oneStepAhead(fit2, tp = rep(nrow(meningo2)-nextend, 2), type = "final", verbose = FALSE)
# however, methods won't work as observed is NA
# }
# long-term probabilistic forecast via simulation for non-observed time points
meningoSim <- simulate(fit2, nsim = 100, seed = 1,
                       subset = seq(nrow(meningo)+1, nrow(meningo2)),
                       y.start = tail(observed(meningo), 1))
apply(meningoSim, 1:2, function (ysim) quantile(ysim, c(0.1, 0.5, 0.9)))
# three plot types are available for "hhh4sims", see also ?plot.hhh4sims
plot(meningoSim, type = "time", average = median)
plot(meningoSim, type = "size", observed = FALSE)
if (requireNamespace("fanplot"))
    plot(meningoSim, type = "fan", means.args = list(),
         fan.args = list(ln = c(.1,.9), ln.col = 8))