# msr

0th

Percentile

##### Signed or Vector-Valued Measure

Defines an object representing a signed measure or vector-valued measure on a spatial domain.

Keywords
models, spatial
##### Usage
msr(qscheme, discrete, density, check=TRUE)
##### Arguments
qscheme
A quadrature scheme (object of class "quad" usually extracted from a fitted point process model).
discrete
Vector or matrix containing the values (masses) of the discrete component of the measure, for each of the data points in qscheme.
density
Vector or matrix containing values of the density of the diffuse component of the measure, for each of the quadrature points in qscheme.
check
Logical. Whether to check validity of the arguments.
##### Details

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.

##### Value

• An object of class "msr" that can be plotted by plot.msr.

##### References

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.

plot.msr, smooth.msr, [.msr

• msr
##### Examples
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
m