markcorrint

From spatstat v1.16-2 by Adrian Baddeley

Mark Correlation Integral

Estimates the mark correlation integral of a marked point pattern.

Keywords: spatial, nonparametric

Usage

markcorrint(X, f = NULL, r = NULL,
              correction = c("isotropic", "Ripley", "translate"), ...,
              f1 = NULL, normalise = TRUE, returnL = FALSE, fargs = NULL)

Arguments

X: The observed point pattern. An object of class "ppp" or something acceptable to as.ppp.
f: Optional. Test function $f$ used in the definition of the mark correlation function. An Rfunction with at least two arguments. There is a sensible default.
r: Optional. Numeric vector. The values of the argument $r$ at which the mark correlation function $k_f(r)$ 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.
...: Ignored.
f1: An alternative to f. If this argument is given, then $f$ is assumed to take the form $f(u,v)=f_1(u)f_1(v)$.
normalise: If normalise=FALSE, compute only the numerator of the expression for the mark correlation.
returnL: Compute the analogue of the K-function if returnL=FALSE or the analogue of the L-function if returnL=TRUE.
fargs: Optional. A list of extra arguments to be passed to the function f or f1.

Details

Given a marked point pattern X, this command estimates the weighted indefinite integral $$K_f(r) = 2 \pi \int_0^r s k_f(s) ds$$ of the mark correlation function $k_f(r)$. See markcorr for a definition of the mark correlation function.

The use of the weighted indefinite integral was advocated by Penttinen et al (1992). The relationship between $K_f$ and $k_f$ is analogous to the relationship between the classical K-function $K(r)$ and the pair correlation function $g(r)$.

If returnL=FALSE then the function $K_f(r)$ is returned; otherwise the function $$L_f(r) = \sqrt{K_f(r)/pi}$$ is returned.

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 correlation integral $K_f(r)$ has been estimated
theothe theoretical value of $K_f(r)$ when the marks attached to different points are independent, namely $\pi r^2$
together with a column or columns named "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the mark correlation integral $K_f(r)$ obtained by the edge corrections named (if returnL=FALSE).

References

Penttinen, A., Stoyan, D. and Henttonen, H. M. (1992) Marked point processes in forest statistics. Forest Science 38 (1992) 806-824.

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008) Statistical analysis and modelling of spatial point patterns. Chichester: John Wiley.

Examples

# CONTINUOUS-VALUED MARKS:
    # (1) Spruces
    # marks represent tree diameter
    data(spruces)
    # mark correlation function
    ms <- markcorrint(spruces)
    plot(ms)

    # (2) simulated data with independent marks
    X <- rpoispp(100)
    X <- X %mark% runif(X$n)
    Xc <- markcorrint(X)
    plot(Xc)
    
    # MULTITYPE DATA:
    # Hughes' amacrine data
    # Cells marked as 'on'/'off'
    data(amacrine)
    M <- markcorrint(amacrine, function(m1,m2) {m1==m2},
                  correction="translate")
    plot(M)

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

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