R: Inhomogeneous Marked G-Function

GmultiInhom {spatstat} | R Documentation

## Inhomogeneous Marked G-Function

### Description

For a marked point pattern, estimate the inhomogeneous version of the multitype G function, effectively the cumulative distribution function of the distance from a point in subset I to the nearest point in subset J, adjusted for spatially varying intensity.

### Usage

      GmultiInhom(X, I, J,
                 lambda = NULL, lambdaI = NULL, lambdaJ = NULL,
                 lambdamin = NULL, ...,
                 r = NULL,
                 ReferenceMeasureMarkSetI = NULL,
                 ratio = FALSE)

### Arguments

`X` | A spatial point pattern (object of class `"ppp"`.
`I` | A subset index specifying the subset of points from which distances are measured. Any kind of subset index acceptable to `[.ppp`.
`J` | A subset index specifying the subset of points to which distances are measured. Any kind of subset index acceptable to `[.ppp`.
`lambda` | Intensity estimates for each point of `X`. A numeric vector of length equal to `npoints(X)`. Incompatible with `lambdaI,lambdaJ`.
`lambdaI` | Intensity estimates for each point of `X[I]`. A numeric vector of length equal to `npoints(X[I])`. Incompatible with `lambda`.
`lambdaJ` | Intensity estimates for each point of `X[J]`. A numeric vector of length equal to `npoints(X[J])`. Incompatible with `lambda`.
`lambdamin` | A lower bound for the intensity, or at least a lower bound for the values in `lambdaJ` or `lambda[J]`.
`...` | Ignored.
`r` | Vector of distance values at which the inhomogeneous G function should be estimated. There is a sensible default.
`ReferenceMeasureMarkSetI` | Optional. The total measure of the mark set. A positive number.
`ratio` | Logical value indicating whether to save ratio information.

### Details

See Cronie and Van Lieshout (2015).

### Value

Object of class `"fv"` containing the estimate of the inhomogeneous multitype G function.

### Author(s)

Ottmar Cronie and Marie-Colette van Lieshout. Rewritten for spatstat by Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### References

Cronie, O. and Van Lieshout, M.N.M. (2015) Summary statistics for inhomogeneous marked point processes. Annals of the Institute of Statistical Mathematics DOI: 10.1007/s10463-015-0515-z

### See Also

`Ginhom`, `Gmulti`

### Examples

      X <- rescale(amacrine)
      I <- (marks(X) == "on")
      J <- (marks(X) == "off")
      mod <- ppm(X ~ marks * x)
      lam <- fitted(mod, dataonly=TRUE)
      lmin <- min(predict(mod)[["off"]]) * 0.9
      plot(GmultiInhom(X, I, J, lambda=lam, lambdamin=lmin))
      # equivalent
      plot(GmultiInhom(X, I, J, lambdaI=lam[I], lambdaJ=lam[J], lambdamin=lmin),
           main="")

[Package spatstat version 1.63-3 Index]