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Estimation of the D function

Dhat.Rd

Estimates the D function

Usage

Dhat(X, r = NULL, Cases, Controls = NULL, Intertype = FALSE, CheckArguments = TRUE)

Arguments

X

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

r

A vector of distances. If NULL, a sensible default value is chosen (512 intervals, from 0 to half the diameter of the window) following spatstat.

Cases

One of the point types.

Controls

One of the point types. If NULL, controls are all types except for cases.

Intertype

Logical; if TRUE, D is computed as Di in Marcon and Puech (2012).

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.

Details

The Di function allows comparing the structure of the cases to that of the controls around cases, that is to say the comparison is made around the same points. This has been advocated by Arbia et al. (2008) and formalized by Marcon and Puech (2012).

Value

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

References

Arbia, G., Espa, G. and Quah, D. (2008). A class of spatial econometric methods in the empirical analysis of clusters of firms in the space. Empirical Economics 34(1): 81-103.

Diggle, P. J. and Chetwynd, A. G. (1991). Second-Order Analysis of Spatial Clustering for Inhomogeneous Populations. Biometrics 47(3): 1155-1163.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

Note

The computation of Dhat relies on spatstat functions Kest and Kcross.

See also

Khat, DEnvelope, Kest, Kcross

Examples

data(paracou16)
autoplot(paracou16)


# Calculate D
r <- 0:30
(Paracou <- Dhat(paracou16, r, "V. Americana", "Q. Rosea", Intertype = TRUE))
#> Function value object (class ‘fv’)
#> for the function r -> D(r)
#> ................................................................
#>      Math.label     Description                                 
#> r    r              distance argument r                         
#> theo D[theo](r)     theoretical Poisson D(r)                    
#> iso  hat(D)[iso](r) Ripley isotropic correction estimate of D(r)
#> ................................................................
#> Default plot formula:  .~r
#> where “.” stands for ‘theo’, ‘iso’
#> Recommended range of argument r: [0, 30]
#> Available range of argument r: [0, 30]

# Plot (after normalization by pi.r^2)
autoplot(Paracou, ./(pi*r^2) ~ r)