spatstat (version 1.23-2)

markcorrint: Mark Correlation Integral

Description

Estimates the mark correlation integral of a marked point pattern.

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.

Value

• An object of class "fv" (see fv.object). Essentially a data frame containing numeric columns
• r
  the values of the argument $r$ at which the mark correlation integral $K_f(r)$ has been estimated
• theo
  the 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).

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.

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.

See Also

markcorr to estimate the mark correlation function.

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)