Creates an instance of the hard core point process model which can then be fitted to point pattern data.
The hard core distance
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,…,x[n] represent the points of the pattern, n(x) is the number of points in the pattern, and alpha is the normalising constant.
ppm(), which fits point process models to
point pattern data, requires an argument
"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
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.
An object of class
describing the interpoint interaction
structure of the hard core
process with hard core distance
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.
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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
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))
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