twinstimtwinstim model as described in Meyer et al. (2012) requires
the specification of the spatial and temporal interaction functions
($f$ and $g$, respectively),
i.e. how infectivity decays with increasing spatial and temporal
distance from the source of infection.
It is of course possible to define own functions (which are
implemented as list objects with required components described in the
# predefined spatial interaction functions
siaf.constant()
siaf.gaussian(nTypes = 1, logsd = TRUE, density = FALSE, F.adaptive = TRUE,
effRangeMult = 6, validpars = NULL)
siaf.lomax(nTypes = 1, logpars = TRUE, density = FALSE,
effRangeProb = NULL, validpars = NULL)
siaf.powerlaw(nTypes = 1, logpars = TRUE,
effRangeProb = NULL, validpars = NULL)
siaf.powerlawL(nTypes = 1, logpars = TRUE,
effRangeProb = NULL, validpars = NULL)# predefined temporal interaction functions
tiaf.constant()
tiaf.exponential(nTypes = 1)
nTypes=1. Otherwise nTypesTRUE, 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 (unF.adaptive = TRUE, then an adaptive bandwidth of
adapt*sd will be used in the midpoint-cubature
(see polyCub.midpoint) of the Gaussian interaction
kernel, weffRangeMult=6 numerical
integration only considers the $6 \sigma$ area around theNULL (default),
which disables the integral approxilogsd=FALSE or logpars=FALSE and one
prefers not to use method="L-BFGS-B" for fitting the
twinstim, then siaf). It must accept
two arguments, the first one being a (2-column) coordinate matrix, the
second one a parameter vector. For marked twinstim, it must
accept the type of the event (integer code) as its third argument
(either a single type for all locations or separate types for each
location)."owin" domain (first argument).
The third and fourth argument are
the parameter vector and the (single) type, respectively.
There may be additional arguments, which can then be specified in
the control.siaf$F argument list of twinstim. If this
function is missing, a general default (polyCub) will be
used, with extra arguments method (default: "SV") and
corresponding accuracy parameters.r (first argument). Further arguments are as for f. It
must not be vectorized (will always be called with single radius
and a single type). If this function is specified, integration of
the siaf over the spatial influence region of an event will
be faster if the region is actually circular. This is the case if
the event is located at least a distance eps.s from the border
of the observation region W, or if the distance to the border
is larger than the effective integration range (if specified, see
effRange below).effRange
contains the numerically essential proportion of the
integral mass. For the Gaussian kernel the default is
function (logsd) 6*exp(logsd). The return value must be a
vector of length nTypes (effective range for each type). This
function is only used if Fcircle is also specified.f but
returns a matrix with as many rows as there were coordinates in the
input and npars columns. This derivative is necessary for the
calculation of the score function in twinstim(), which is
advantageous for the numerical log-likelihood maximization.deriv (passed as
second argument) over a polygonal "owin" domain (first argument).
The third and fourth argument are
the parameter vector and the (single) type, respectively.
There may be additional arguments, which can then be specified in
the control.siaf$Deriv argument list of twinstim. If this
function is missing, a general default (polyCub) will be
used, with extra arguments method (default: "SV") and
corresponding accuracy parameters.twinstim
models). Its first argument is the size of the sample to
generate, further arguments are as for f (but the optional
third argument specifies a single event type only). The function must
return a two-column matrix of the sampled locations.
Note that the simulation method actually samples only one location
at a time, thus it is sufficient to have a working
function(n=1, pars, type).f (i.e. the length of its second argument).tiaf). It must accept
two arguments, the first one being a vector of time points, the
second one a parameter vector. For marked twinstim, it must
accept the type of the event (integer code) as its third argument
(either a single type for all locations or separate types for each
location).g, for instance a vector
of time points (not just a single one).g but
returns a matrix with as many rows as there were time points in the
input and npars columns. This derivative is necessary for the
calculation of the score function in twinstim(), which is
advantageous for the numerical log-likelihood maximization.deriv (with respect to
time). It must accept the same arguments as deriv, g and
G and returns a matrix with as many rows as there were time
points in the input and npars columns. The integrated
derivative is necessary for the score function in twinstim.g (i.e. the length of its second argument).validpars as a way to specify parameter constraints:twinstim (with arguments
lower and upper), and positivity constraints by using
log-parametrizations. This component is not necessary (and ignored) if
npars == 0. Meyer, S. (2010):
Spatio-Temporal Infectious Disease Epidemiology based on Point Processes.
Master's Thesis, Ludwig-Maximilians-Universit
twinstim.# constant temporal dispersal
tiaf.constant()
# Type-dependent Gaussian spatial interaction function using an adaptive
# two-dimensional midpoint-rule to integrate it over polygonal domains
siaf.gaussian(2, F.adaptive=TRUE)
# Type-independent power-law kernel
siaf.powerlaw() # siaf.lomax() is deprecated
# "lagged" power-law
siaf.powerlawL()Run the code above in your browser using DataLab