dbmss (version 2.2-5)

mhat: Estimation of the M function

Description

Estimates the M function

Usage

Mhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType, CaseControl = FALSE, CheckArguments = TRUE)

Arguments

X

A weighted, marked planar point pattern (wmppp.object) or a Dtable object.

r

A vector of distances. If NULL, a default value is set: 64 unequally spaced values are used up to half the maximum distance between points $d_m$. The first value is 0, first steps are small ($d_m/800$) then increase progressively up to $d_m/40$.

ReferenceType

One of the point types.

NeighborType

One of the point types. By default, the same as reference type.

CaseControl

Logical; if TRUE, the case-control version of M is computed. ReferenceType points are cases, NeighborType points are controls.

CheckArguments

Logical; if TRUE, the function arguments are verified. Should be set to FALSE to save time in simulations for example, when the arguments have been checked elsewhere.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Details

M is a weighted, cumulative, relative measure of a point pattern structure. Its value at any distance is the ratio of neighbors of the NeighborType to all points around ReferenceType points, normalized by its value over the windows.

References

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762. Marcon, E., F. Puech, et al. (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

See Also

MEnvelope, Kdhat

Examples

data(paracou16)
plot(paracou16)

# Calculate M
plot(Mhat(paracou16, , "V. Americana", "Q. Rosea"))