Hardcore: The Hard Core Point Process Model

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Creates an instance of the hard core point process model which can then be fitted to point pattern data.

Usage

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  Hardcore(hc=NA)

Arguments

hc

The hard core distance

Details

A hard core process with hard core distance h and abundance parameter beta is a pairwise interaction point process in which distinct points are not allowed to come closer than a distance h apart.

The probability density is zero if any pair of points is closer than h units apart, and otherwise equals

f(x_1,…,x_n) = alpha . beta^n(x)

where x[1],…,x[n] represent the points of the pattern, n(x) is the number of points in the pattern, and alpha is the normalising constant.

The function ppm(), which fits point process models to point pattern data, requires an argument of class "interact" describing the interpoint interaction structure of the model to be fitted. The appropriate description of the hard core process pairwise interaction is yielded by the function Hardcore(). See the examples below.

If the hard core distance argument hc is missing or NA, it will be estimated from the data when ppm is called. The estimated value of hc is the minimum nearest neighbour distance multiplied by n/(n+1), where n is the number of data points.

Value

An object of class "interact" describing the interpoint interaction structure of the hard core process with hard core distance hc.

Author(s)

\adrian

and \rolf

References

Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.

Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.

See Also

Strauss, StraussHard, MultiHard, ppm, pairwise.family, ppm.object

Examples

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   Hardcore(0.02)
   # prints a sensible description of itself

   ## Not run: 
   ppm(cells, ~1, Hardcore(0.05))
   # fit the stationary hard core process to `cells'
   
## End(Not run)

   # estimate hard core radius from data
   ppm(cells, ~1, Hardcore())
   ppm(cells, ~1, Hardcore)

   ppm(cells, ~ polynom(x,y,3), Hardcore(0.05))
   # fit a nonstationary hard core process
   # with log-cubic polynomial trend

Example output

Loading required package: nlme
Loading required package: rpart

spatstat 1.51-0       (nickname: 'Poetic Licence') 
For an introduction to spatstat, type 'beginner' 

Pairwise interaction family
Interaction:Hard core process
Hard core distance:	0.02
Stationary Hard core process

First order term:  beta = 74.40153

Hard core distance:	0.05

For standard errors, type coef(summary(x))
Stationary Hard core process

First order term:  beta = 282.7782

Hard core distance:	0.08168525

For standard errors, type coef(summary(x))
Stationary Hard core process

First order term:  beta = 282.7782

Hard core distance:	0.08168525

For standard errors, type coef(summary(x))
Nonstationary Hard core process

Log trend:  ~x + y + I(x^2) + I(x * y) + I(y^2) + I(x^3) + I(x^2 * y) + I(x * 
y^2) + I(y^3)

Fitted trend coefficients:
(Intercept)           x           y      I(x^2)    I(x * y)      I(y^2) 
  4.6413531  -3.6516352   0.2595011   6.5862445   4.1469949  -2.6755211 
     I(x^3)  I(x^2 * y)  I(x * y^2)      I(y^3) 
 -3.7101975  -0.2365586  -4.4952131   2.9835314 

Hard core distance:	0.05

For standard errors, type coef(summary(x))

spatstat documentation built on Nov. 21, 2017, 9:06 a.m.