dbmss (version 1.2.4)

M.r: Estimation of the M function

Description

Estimates the M function

Usage

M.r(X, r, ReferenceType, NeighborType, CaseControl = FALSE)

Arguments

X

A point pattern (ppp.object), marks must be a dataframe with two columns: PointType: labels, as factors. PointWeight: weights.

r

A vector of distances.

ReferenceType

One of the point types.

NeighborType

One of the point types.

CaseControl

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

Value

• A vector containing M(r) values.

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, Kd.r

Examples

data(paracou16)
plot(paracou16)

# Calculate M
r <- seq(0, 30, 2)
ActualValues.X <- M.r(paracou16, r, "V. Americana", "Q. Rosea")

# Plot
PlotResults(r, ActualValues.X, ylab="M", ReferenceValue=1)