dbmss (version 1.2.4)

MEnvelope: Estimation of the confidence envelope of the M function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of M according to the confidence level.

Usage

MEnvelope(NumberOfSimulations, Alpha = .05, X, r, ReferenceType, NeighborType, 
      SimulationType = "RandomLocation", CaseControl = FALSE)

Arguments

NumberOfSimulations

The number of simulations to draw.

Alpha

The risk level.

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.

SimulationType

A string describing the null hypothesis to simulate. The null hypothesis may be "RandomLocation": points are redistributed accross actual locations; "RandomLabeling": randomizes point types, keeping locations unchanged; "PopulationIn

Value

• A list:
• Simulations
  A matrix containing the simulated values (each line is a simulation, each column a value of M(R)
• Min
  A vector: the lower bound of the envelope
• Max
  A vector: the upper bound of the envelope

Details

This envelope is local, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

References

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024. Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

See Also

M.r

Examples

data(paracou16)
# Keep only 50% of points to run this example
X <- rthin(paracou16, 0.5)
plot(X)

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

# Calculate confidence envelope (should be 1000 simulations, reduced to 4 to save time)
NumberOfSimulations <- 4
Alpha <- .10
LocalEnvelope.X <- MEnvelope(NumberOfSimulations, Alpha, X, r, 
    "V. Americana", "Q. Rosea", "RandomLabeling")

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