surveillance (version 1.4-1)

twinstim_iaf: Temporal and spatial interaction functions for twinstim

Description

Predefined functional forms for the spatial and temporal dispersal ($f$ and $g$, respectively) for use in twinstim models as described in Meyer et al. (2012).

Usage

siaf.constant()
siaf.gaussian(nTypes, logsd = TRUE, density = FALSE, effRangeMult = 6,
              validpars = NULL)
siaf.lomax(nTypes = 1, logpars = TRUE, density = FALSE, effRangeProb = 0.99,
           validpars = NULL)
tiaf.constant()
tiaf.exponential(nTypes)

Arguments

nTypes

Number of different types, i.e. $|\mathcal{K}|$

logsd

Parametrize standard deviation parameter $\sigma>0$ on log scale to enforce parameter constraint. Default: TRUE

density

logical. If TRUE, a density is used as the interaction function: for siaf.gaussian, the density of the bivariate, isotropic normal distribution, for siaf.lomax, $f(||\bold{s}||)$ is the density of the (un

effRangeMult

Determines the effective range for numerical integration in terms of multiples of $\sigma$, i.e. with effRangeMult=6 numerical integration only considers the 6-sigma area around the event instead of the whole observation region W.

validpars

See twinstim. If logsd = FALSE, you should either use constrained optimisation (L-BFGS-B) or set validpars to function (pars) pars > 0.

logpars

logical. Parametrize the Lomax distribution with log(scale) and log(shape) to enforce positive parameters. The alternative (FALSE) is not implemented.

effRangeProb

Determines the effective range for numerical integration in terms of the corresponding quantile of the univariate Lomax distribution.

Value

• A list containing the interaction function, its derivative, ...

encoding

latin1

References

Meyer, S., Elias, J. and H�{oe}hle, M. (2012): A space-time conditional intensity model for invasive meningococcal disease occurrence. Biometrics, 68, 607-616. DOI-Link: http://dx.doi.org/10.1111/j.1541-0420.2011.01684.x

Meyer, S. (2010): Spatio-Temporal Infectious Disease Epidemiology based on Point Processes. Master's Thesis, Ludwig-Maximilians-Universit�{ae}t M�{ue}nchen. Available as http://epub.ub.uni-muenchen.de/11703/

See Also

twinstim.

Examples

#Finetype indenepdent spatial interaction function used in the twinstim paper
siaf_log1 <- siaf.gaussian(1, logsd = TRUE, density = FALSE, effRangeMult = 6)