# Plot the Spatial or Temporal Interaction Function of a `twimstim`

`twinstim_iafplot.Rd`

The function plots the fitted temporal or (isotropic) spatial
interaction function of a `twinstim`

object.
The implementation is illustrated in Meyer et al. (2017, Section 3),
see `vignette("twinstim")`

.

## Usage

```
iafplot(object, which = c("siaf", "tiaf"), types = NULL,
scaled = c("intercept", "standardized", "no"), truncated = FALSE,
log = "", conf.type = if (length(pars) > 1) "MC" else "parbounds",
conf.level = 0.95, conf.B = 999, xgrid = 101,
col.estimate = rainbow(length(types)), col.conf = col.estimate,
alpha.B = 0.15, lwd = c(3,1), lty = c(1,2),
verticals = FALSE, do.points = FALSE,
add = FALSE, xlim = NULL, ylim = NULL, xlab = NULL, ylab = NULL,
legend = !add && (length(types) > 1), ...)
```

## Arguments

- object
object of class

`"twinstim"`

containing the fitted model.- which
argument indicating which of the two interaction functions to plot. Possible values are

`"siaf"`

(default) for the spatial interaction \(f(x)\) as a function of the distance \(x\), and`"tiaf"`

for the temporal interaction function \(g(t)\).- types
integer vector indicating for which event

`types`

the interaction function should be plotted in case of a marked`"twinstim"`

. The default`types=NULL`

checks if the interaction function is type-specific: if so,`types=1:nrow(object$qmatrix)`

is used, otherwise`types=1`

.- scaled
character string determining if/how the the interaction function should be scaled. Possible choices are:

- "intercept":
multiplication by the epidemic intercept.

- "standardized":
division by the value at 0 distance such that the function starts at 1.

- "no":
no scaling.

The first one is the default and required for the comparison of estimated interaction functions from different models. For backward compatibility,

`scaled`

can also be a boolean, where`TRUE`

refers to`"intercept"`

scaling and`FALSE`

to`"no"`

scaling.- truncated
logical indicating if the plotted interaction function should take the maximum range of interaction (

`eps.t`

/`eps.s`

) into account, i.e., drop to zero at that point (if it is finite after all). If there is no common range of interaction, a`rug`

indicating the various ranges will be added to the plot if`truncated=TRUE`

. If`truncated`

is a scalar, this value is used as the point`eps`

where the function drops to 0.- log
a character string passed to

`plot.default`

indicating which axes should be logarithmic. If`add=TRUE`

,`log`

is set according to`par("xlog")`

and`par("ylog")`

.- conf.type
type of confidence interval to produce.

If`conf.type="MC"`

(or`"bootstrap"`

),`conf.B`

parameter vectors are sampled from the asymptotic (multivariate) normal distribution of the ML estimate of the interaction function parameters; the interaction function is then evaluated on the`xgrid`

(i.e. temporal or spatial distances from the host) for each parameter realization to obtain a`conf.level`

confidence interval at each point of the`xgrid`

(or to plot the interaction functions of all Monte-Carlo samples if`conf.level=NA`

). Note that the resulting plot is`.Random.seed`

-dependent for the Monte-Carlo type of confidence interval.

If`conf.type="parbounds"`

, the`conf.level`

Wald confidence intervals for the interaction function parameters are calculated and the interaction function is evaluated on the`xgrid`

(distances from the host) for all combinations of the bounds of the parameters and the point-wise extremes of those functions are plotted. This type of confidence interval is only valid in case of a single parameter, i.e.`scaled + nsiafpars == 1`

, but could also be used as a rough indication if the Monte-Carlo approach takes too long. A warning is thrown if the`"parbounds"`

type is used for multiple parameters.

If`conf.type="none"`

or`NA`

or`NULL`

, no confidence interval will be calculated.- conf.level
the confidence level required. For

`conf.type = "MC"`

it may also be specified as`NA`

, in which case all`conf.B`

sampled functions will be plotted with transparency value given by`alpha.B`

.- conf.B
number of samples for the

`"MC"`

(Monte Carlo) confidence interval.- xgrid
either a numeric vector of x-values (distances from the host) where to evaluate

`which`

, or a scalar representing the desired number of evaluation points in the interval`c(0,xlim[2])`

.

If the interaction function is a step function (`siaf.step`

or`tiaf.step`

),`xgrid`

is ignored and internally set to`c(0, knots)`

.- col.estimate
vector of colours to use for the function point estimates of the different

`types`

.- col.conf
vector of colours to use for the confidence intervals of the different

`types`

.- alpha.B
alpha transparency value (as relative opacity) used for the

`conf.B`

sampled interaction functions in case`conf.level = NA`

- lwd, lty
numeric vectors of length two specifying the line width and type of point estimates (first element) and confidence limits (second element), respectively.

- verticals,do.points
graphical settings for step function kernels. These can be logical (as in

`plot.stepfun`

) or lists of graphical parameters.- add
add to an existing plot?

- xlim, ylim
vectors of length two containing the x- and y-axis limit of the plot. The default y-axis range (

`ylim=NULL`

) is from 0 to the value of the (scaled) interaction function at \(x = 0\). The default x-axis (`xlim=NULL`

) starts at 0, and the upper limit is determined as follows (in decreasing order of precedence):If

`xgrid`

is a vector of evaluation points,`xlim[2]`

is set to`max(xgrid)`

.`eps.t`

/`eps.s`

if it is unique and finite.If the interaction function is a step function with

`maxRange<Inf`

, i.e. it drops to 0 at`maxRange`

,`xlim[2]`

is set to`maxRange`

.Otherwise, it is set to the length of the observation period (

`which="tiaf"`

) or the diagonal length of the bounding box of the observation region (`which="siaf"`

), respectively.

- xlab, ylab
labels for the axes with

`NULL`

providing sensible defaults.- legend
logical indicating if a legend for the

`types`

should be added. It can also be a list of arguments passed to`legend`

to tweak the default settings.- ...
additional arguments passed to the default

`plot`

method.

## Value

A plot is created -- see e.g. Figure 3(b) in Meyer et al. (2012).

The function invisibly returns a matrix of the plotted values of the
interaction function (evaluated on `xgrid`

, by type). The first
column of the matrix contains the distance \(x\), and the remaining

`length(types)`

columns contain the (scaled) function values for
each type.

The pointwise confidence intervals of the interaction functions are returned in similar matrices as attributes: if

`length(types)==1`

, there is a single attribute `"CI"`

,
whereas for multiple types, the attributes are named

`paste0("CI.",typeNames)`

(where the `typeNames`

are
retrieved from `object$qmatrix`

).

## References

Meyer, S., Elias, J. and Höhle, M. (2012):
A space-time conditional intensity model for invasive meningococcal
disease occurrence. *Biometrics*, **68**, 607-616.
doi:10.1111/j.1541-0420.2011.01684.x

Meyer, S., Held, L. and Höhle, M. (2017):
Spatio-temporal analysis of epidemic phenomena using the R package
surveillance.
*Journal of Statistical Software*, **77** (11), 1-55.
doi:10.18637/jss.v077.i11

## See also

`plot.twinstim`

, which calls this function.

## Examples

```
data("imdepifit")
iafplot(imdepifit, "tiaf", scaled=FALSE) # tiaf.constant(), not very exciting
iafplot(imdepifit, "siaf", scaled=FALSE)
# scaled version uses a Monte-Carlo-CI
set.seed(1) # result depends on .Random.seed
iafplot(imdepifit, "siaf", scaled=TRUE, conf.type="MC", conf.B=199,
col.conf=gray(0.4), conf.level=NA) # show MC samples
```