markconnect

From spatstat v1.16-2 by Adrian Baddeley

Mark Connection Function

Estimate the marked connection function of a multitype point pattern.

Keywords: spatial, nonparametric

Usage

markconnect(X, i, j, r=NULL,
         correction=c("isotropic", "Ripley", "translate"),
         method="density", ..., normalise=FALSE)

Arguments

X: The observed point pattern. An object of class "ppp" or something acceptable to as.ppp.
i: Number or character string identifying the type (mark value) of the points in X from which distances are measured.
j: Number or character string identifying the type (mark value) of the points in X to which distances are measured.
r: numeric vector. The values of the argument $r$ at which the mark connection function $p_{ij}(r)$ should be evaluated. There is a sensible default.
correction: A character vector containing any selection of the options "isotropic", "Ripley" or "translate". It specifies the edge correction(s) to be applied.
method: A character vector indicating the user's choice of density estimation technique to be used. Options are "density", "loess", "sm" and "smrep".
...: Arguments passed to the density estimation routine (density, loess or sm.density) selected by method.
normalise: If TRUE, normalise the pair connection function by dividing it by $p_i p_j$, the estimated probability that randomly-selected points will have marks $i$ and $j$.

Details

The mark connection function $p_{ij}(r)$ of a multitype point process $X$ is a measure of the dependence between the types of two points of the process a distance $r$ apart.

Informally $p_{ij}(r)$ is defined as the conditional probability, given that there is a point of the process at a location $u$ and another point of the process at a location $v$ separated by a distance $||u-v|| = r$, that the first point is of type $i$ and the second point is of type $j$. See Stoyan and Stoyan (1994).

If the marks attached to the points of X are independent and identically distributed, then $p_{ij}(r) \equiv p_i p_j$ where $p_i$ denotes the probability that a point is of type $i$. Values larger than this, $p_{ij}(r) > p_i p_j$, indicate positive association between the two types, while smaller values indicate negative association.

The argument X must be a point pattern (object of class "ppp") or any data that are acceptable to as.ppp. It must be a multitype point pattern (a marked point pattern with factor-valued marks).

The argument r is the vector of values for the distance $r$ at which $p_{ij}(r)$ is estimated. There is a sensible default.

This algorithm assumes that X can be treated as a realisation of a stationary (spatially homogeneous) random spatial point process in the plane, observed through a bounded window. The window (which is specified in X as X$window) may have arbitrary shape.

Biases due to edge effects are treated in the same manner as in Kest. The edge corrections implemented here are [object Object],[object Object] Note that the estimator assumes the process is stationary (spatially homogeneous).

The mark connection function is estimated using density estimation techniques. The user can choose between [object Object],[object Object],[object Object],[object Object]

Value

An object of class "fv" (see fv.object). Essentially a data frame containing numeric columns
rthe values of the argument $r$ at which the mark connection function $p_{ij}(r)$ has been estimated
theothe theoretical value of $p_{ij}(r)$ when the marks attached to different points are independent
together with a column or columns named "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function $p_{ij}(r)$ obtained by the edge corrections named.

References

Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.

Examples

# Hughes' amacrine data
    # Cells marked as 'on'/'off'
    data(amacrine)
    M <- markconnect(amacrine, "on", "off")
    plot(M)

    # Compute for all pairs of types at once
    plot(alltypes(amacrine, markconnect))

Documentation reproduced from package spatstat, version 1.16-2, License: GPL (>= 2)

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