rhohat(object, covariate, ...,
transform=FALSE,
dimyx=NULL, eps=NULL,
n = 512, bw = "nrd0", adjust=1, from = NULL, to = NULL,
bwref=bw,
covname)"ppp"),
a quadrature scheme (object of class "quad")
or a fitted point process model (object of class "ppm").function(x,y) or a pixel image (object of
class "im") providing the values of the covariate at any
location.
Alternatively one of the strings "x" or "y"
signifying the Cartesian as.mask to control the pixel
resolution at which the covariate will be evaluated.density.default).density.default).density.default to
control the number and range of values at which the function
will be estimated.bw to use when smoothing
the reference density (the density of the covariate values
observed at all locations in the window).density.default."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.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.
methods.rhohatX <- 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")Run the code above in your browser using DataLab