fitted.ppm
Fitted Conditional Intensity for Point Process Model
Given a point process model fitted to a point pattern, compute the fitted conditional intensity or fitted trend of the model at the points of the pattern, or at the points of the quadrature scheme used to fit the model.
Usage
# S3 method for ppm
fitted(object, …, type="lambda",
dataonly=FALSE, new.coef=NULL, leaveoneout=FALSE,
drop=FALSE, check=TRUE, repair=TRUE,
ignore.hardcore=FALSE, dropcoef=FALSE)Arguments
- object
The fitted point process model (an object of class
"ppm")- …
Ignored.
- type
String (partially matched) indicating whether the fitted value is the conditional intensity (
"lambda"or"cif") or the first order trend ("trend") or the logarithm of conditional intensity ("link").- dataonly
Logical. If
TRUE, then values will only be computed at the points of the data point pattern. IfFALSE, then values will be computed at all the points of the quadrature scheme used to fit the model, including the points of the data point pattern.- new.coef
Numeric vector of parameter values to replace the fitted model parameters
coef(object).- leaveoneout
Logical. If
TRUEthe fitted value at each data point will be computed using a leave-one-out method. See Details.- drop
Logical value determining whether to delete quadrature points that were not used to fit the model.
- check
Logical value indicating whether to check the internal format of
object. If there is any possibility that this object has been restored from a dump file, or has otherwise lost track of the environment where it was originally computed, setcheck=TRUE.- repair
Logical value indicating whether to repair the internal format of
object, if it is found to be damaged.- ignore.hardcore
Advanced use only. Logical value specifying whether to compute only the finite part of the interaction potential (effectively removing any hard core interaction terms).
- dropcoef
Internal use only.
Details
The argument object must be a fitted point process model
(object of class "ppm"). Such objects are produced by the
model-fitting algorithm ppm).
This function evaluates the conditional intensity
\(\hat\lambda(u, x)\)
or spatial trend \(\hat b(u)\) of the fitted point process
model for certain locations \(u\),
where x is the original point pattern dataset to which
the model was fitted.
The locations \(u\) at which the fitted conditional intensity/trend
is evaluated, are the points of the
quadrature scheme used to fit the model in ppm.
They include the data points (the points of the original point pattern
dataset x) and other ``dummy'' points
in the window of observation.
If leaveoneout=TRUE, fitted values will be computed
for the data points only, using a ‘leave-one-out’ rule:
the fitted value at X[i] is effectively computed by
deleting this point from the data and re-fitting the model to the
reduced pattern X[-i], then predicting the value at
X[i]. (Instead of literally performing this calculation,
we apply a Taylor approximation using the influence function
computed in dfbetas.ppm.
The argument drop is explained in quad.ppm.
Use predict.ppm to compute the fitted conditional
intensity at other locations or with other values of the
explanatory variables.
Value
A vector containing the values of the fitted conditional intensity, fitted spatial trend, or logarithm of the fitted conditional intensity.
Entries in this vector correspond to the quadrature points (data or
dummy points) used to fit the model. The quadrature points can be
extracted from object by union.quad(quad.ppm(object)).
References
Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005). Residual analysis for spatial point processes (with discussion). Journal of the Royal Statistical Society, Series B 67, 617--666.
See Also
Examples
# NOT RUN {
str <- ppm(cells ~x, Strauss(r=0.1))
lambda <- fitted(str)
# extract quadrature points in corresponding order
quadpoints <- union.quad(quad.ppm(str))
# plot conditional intensity values
# as circles centred on the quadrature points
quadmarked <- setmarks(quadpoints, lambda)
plot(quadmarked)
if(!interactive()) str <- ppm(cells ~ x)
lambdaX <- fitted(str, leaveoneout=TRUE)
# }