Defines an object representing a signed measure or vector-valued measure on a spatial domain.
msr(qscheme, discrete, density, check=TRUE)A quadrature scheme (object of class "quad" usually
extracted from a fitted point process model).
Vector or matrix containing the values (masses) of the discrete component
of the measure, for each of the data points in qscheme.
Vector or matrix containing values of the density of the
diffuse component of the measure, for each of the
quadrature points in qscheme.
Logical. Whether to check validity of the arguments.
An object of class "msr" that can be plotted
by plot.msr.
This function creates an object that represents a signed or vector valued measure on the two-dimensional plane. It is not normally called directly by the user.
A signed measure is a classical mathematical object (Diestel and Uhl, 1977) which can be visualised as a collection of electric charges, positive and/or negative, spread over the plane. Electric charges may be concentrated at specific points (atoms), or spread diffusely over a region.
An object of class "msr" represents a signed (i.e. real-valued)
or vector-valued measure in the spatstat package.
Spatial residuals for point process models
(Baddeley et al, 2005, 2008) take the form of a real-valued
or vector-valued measure. The function
residuals.ppm returns an object of
class "msr" representing the residual measure.
The function msr would not normally be called directly by the
user. It is the low-level creator function that
makes an object of class "msr" from raw data.
The first argument qscheme is a quadrature scheme (object of
class "quad"). It is typically created by quadscheme or
extracted from a fitted point process model using
quad.ppm. A quadrature scheme contains both data points
and dummy points. The data points of qscheme are used as the locations
of the atoms of the measure. All quadrature points
(i.e. both data points and dummy points)
of qscheme are used as sampling points for the density
of the continuous component of the measure.
The argument discrete gives the values of the
atomic component of the measure for each data point in qscheme.
It should be either a numeric vector with one entry for each
data point, or a numeric matrix with one row
for each data point.
The argument density gives the values of the density
of the diffuse component of the measure, at each
quadrature point in qscheme.
It should be either a numeric vector with one entry for each
quadrature point, or a numeric matrix with one row
for each quadrature point.
If both discrete and density are vectors
(or one-column matrices) then the result is a signed (real-valued) measure.
Otherwise, the result is a vector-valued measure, with the dimension
of the vector space being determined by the number of columns
in the matrices discrete and/or density.
(If one of these is a \(k\)-column matrix and the other
is a 1-column matrix, then the latter is replicated to \(k\) columns).
The class "msr" has methods for print,
plot and [.
There is also a function Smooth.msr for smoothing a measure.
Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005) Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B 67, 617--666.
Baddeley, A., Moller, J. and Pakes, A.G. (2008) Properties of residuals for spatial point processes. Annals of the Institute of Statistical Mathematics 60, 627--649.
Diestel, J. and Uhl, J.J. Jr (1977) Vector measures. Providence, RI, USA: American Mathematical Society.
Halmos, P.R. (1950) Measure Theory. Van Nostrand.
plot.msr,
Smooth.msr,
[.msr,
with.msr,
split.msr,
Ops.msr,
measureVariation.
# NOT RUN {
X <- rpoispp(function(x,y) { exp(3+3*x) })
fit <- ppm(X, ~x+y)
rp <- residuals(fit, type="pearson")
rp
rs <- residuals(fit, type="score")
rs
colnames(rs)
# An equivalent way to construct the Pearson residual measure by hand
Q <- quad.ppm(fit)
lambda <- fitted(fit)
slam <- sqrt(lambda)
Z <- is.data(Q)
m <- msr(Q, discrete=1/slam[Z], density = -slam)
m
# }
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