R: Inhomogeneous Multitype Pair Correlation Function (Dot-type)...

linearpcfdot.inhom {spatstat.linnet} | R Documentation

## Inhomogeneous Multitype Pair Correlation Function (Dot-type) for Linear Point Pattern

### Description

For a multitype point pattern on a linear network, estimate the inhomogeneous multitype pair correlation function from points of type i to points of any type.

### Usage

    linearpcfdot.inhom(X, i, lambdaI, lambdadot, r=NULL, ...,
                       correction="Ang", normalise=TRUE)

### Arguments

`X` | The observed point pattern, from which an estimate of the i-to-any pair correlation function g[i.](r) will be computed. An object of class `"lpp"` which must be a multitype point pattern (a marked point pattern whose marks are a factor).
`i` | Number or character string identifying the type (mark value) of the points in `X` from which distances are measured. Defaults to the first level of `marks(X)`.
`lambdaI` | Intensity values for the points of type `i`. Either a numeric vector, a `function`, a pixel image (object of class `"im"` or `"linim"`) or a fitted point process model (object of class `"ppm"` or `"lppm"`).
`lambdadot` | Intensity values for all points of `X`. Either a numeric vector, a `function`, a pixel image (object of class `"im"` or `"linim"`) or a fitted point process model (object of class `"ppm"` or `"lppm"`).
`r` | numeric vector. The values of the argument r at which the function g[i.](r) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on r.
`correction` | Geometry correction. Either `"none"` or `"Ang"`. See Details.
`...` | Arguments passed to `density.default` to control the kernel smoothing.
`normalise` | Logical. If `TRUE` (the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the points of type `i`), which reduces the sampling variability. If `FALSE`, the denominator is the length of the network.

### Details

This is a counterpart of the function `pcfdot.inhom` for a point pattern on a linear network (object of class `"lpp"`).

The argument `i` will be interpreted as levels of the factor `marks(X)`. If `i` is missing, it defaults to the first level of the marks factor.

The argument `r` is the vector of values for the distance r at which g[i.](r) should be evaluated. The values of r must be increasing nonnegative numbers and the maximum r value must not exceed the radius of the largest disc contained in the window.

If `lambdaI` or `lambdadot` is a fitted point process model, the default behaviour is to update the model by re-fitting it to the data, before computing the fitted intensity. This can be disabled by setting `update=FALSE`.

### Value

An object of class `"fv"` (see `fv.object`).

### Warnings

The argument `i` is interpreted as a level of the factor `marks(X)`. Beware of the usual trap with factors: numerical values are not interpreted in the same way as character values.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

### References

Baddeley, A, Jammalamadaka, A. and Nair, G. (to appear) Multitype point process analysis of spines on the dendrite network of a neuron. Applied Statistics (Journal of the Royal Statistical Society, Series C), 63, 673–694.

### See Also

`linearpcfcross.inhom`, `linearpcfcross`, `pcfcross.inhom`.

### Examples

       lam <- table(marks(chicago))/(summary(chicago)$totlength)
       lamI <- function(x,y,const=lam[["assault"]]){ rep(const, length(x)) }
       lam. <- function(x,y,const=sum(lam)){ rep(const, length(x)) }

       g <- linearpcfdot.inhom(chicago, "assault", lamI, lam.)

       # using fitted models for the intensity
       # fit <- lppm(chicago, ~marks + x)
       # linearpcfdot.inhom(chicago, "assault", fit, fit)

[Package spatstat.linnet version 2.0-0 Index]