rhohat {spatstat} | R Documentation |
Computes a smoothing estimate of the intensity of a point process, as a function of a spatial covariate.
rhohat(object, covariate, ..., transform=FALSE, dimyx=NULL, eps=NULL, n = 512, bw = "nrd0", adjust=1, from = NULL, to = NULL, bwref=bw, covname)
object |
A point pattern (object of class |
covariate |
Either a |
transform |
Logical value determining the smoothing method. See Details. |
dimyx,eps |
Arguments passed to |
bw |
Smoothing bandwidth or bandwidth rule
(passed to |
adjust |
Smoothing bandwidth adjustment factor
(passed to |
n, from, to |
Arguments passed to |
bwref |
Optional. An alternative value of |
... |
Additional arguments passed to |
covname |
Optional. Character string to use as the name of the covariate. |
If object
is a point pattern, this command assumes that
object
is a realisation of a Poisson point process with
intensity function lambda(u) of the form
lambda(u) = rho(Z(u))
where
Z is the spatial covariate function given by covariate
,
and rho(z) is a function to be estimated.
This command computes an estimator of rho(z)
proposed by Baddeley and Turner (2005).
If object
is a fitted point process model, suppose X
is
the original data point pattern to which the model was fitted. Then
this command assumes X
is a realisation of a Poisson point
process with intensity function of the form
lambda(u) = rho(Z(u)) * kappa(u)
where kappa(u) is the intensity of the fitted model
object
. A modified version of the Baddeley-Turner (2005)
smoothing estimator is computed.
If transform=FALSE
, the smoothing method is
fixed bandwidth kernel smoothing, using density.default
.
If transform=TRUE
, the smoothing method is variable-bandwidth kernel
smoothing, implemented by applying the Probability Integral Transform
to the covariate values, yielding values in the range 0 to 1,
then applying edge-corrected fixed-bandwidth smoothing on the interval
[0,1], and back-transforming.
A function value table (object of class "fv"
)
containing the estimated values of rho for a sequence
of values of Z.
Also belongs to the class "rhohat"
which has special methods for print
, plot
and predict
.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Baddeley, A. and Chang, Y.-M. and Song, Y. and Turner, R. Diagnostics for transformation of covariates in spatial Poisson point process models. Submitted for publication.
Baddeley, A. and Turner, R. (2005) Modelling spatial point patterns in R. In: A. Baddeley, P. Gregori, J. Mateu, R. Stoica, and D. Stoyan, editors, Case Studies in Spatial Point Pattern Modelling, Lecture Notes in Statistics number 185. Pages 23–74. Springer-Verlag, New York, 2006. ISBN: 0-387-28311-0.
X <- rpoispp(function(x,y){exp(3+3*x)}) rho <- rhohat(X, "x") rho <- rhohat(X, function(x,y){x}) plot(rho) curve(exp(3+3*x), lty=3, col=2, add=TRUE) fit <- ppm(X, ~x) rr <- rhohat(fit, "y")