gblg | R Documentation |

Estimates the gliding box lacunarity (GBL) of a stationary RACS by estimating pair-correlation from a binary map (Hingee et al., 2017). It can also calculate the GBL of a RACS from a provided pair-correlation function.

```
gblg(boxes, paircorr = NULL, xiim = NULL, integrationMethod = "cubature")
```

`boxes` |
Either a list of side lengths for square boxes or a list of |

`paircorr` |
A |

`xiim` |
An observation of a stationary RACS as an |

`integrationMethod` |
The integration method used by |

If we denote the estimated pair-correlation by `\hat{g}(v)`

then the estimate of GBL is

`\frac{1}{|B|^2}\int \gamma_B(v)\hat{g}(v)dv, `

where `B`

is each of the sets (often called a box) specified by `boxes`

,
`\gamma_B`

is the set covariance of `B`

,
`|B|`

is the area of `B`

,
`p`

is the coverage probability of a stationary RACS.
This can be used to compute the GBL from model parameters by passing `gblc`

the
covariance and coverage probability of the model.

If the `xiim`

argument to `gblg`

is used then pair correlation is estimated from `xiim`

using `paircorr`

and the `pickaH`

estimator.

The set covariance of `B`

is computed empirically using spatstat's `setcov`

function, which converts `B`

into a binary pixel mask using `as.mask`

defaults. Computation speed can be increased by setting a small default number of pixels, `npixel`

, in spatstat's global options (accessed through `spatstat.options`

), however fewer pixels also decreases the accuracy of the GBL computation.

The default integration method for this function uses `cubature::cubintegrate()`

from the cubature package.
The 'harmonisesum' integration method is known to produce numerical artefacts (Section 6.2 of (Hingee et al., 2019))

If `boxes`

is a list of numerical values then GBL is estimated for square boxes with side length given by `boxes`

.
The returned object is then an `fv`

object containing estimates of GBL.
If `boxes`

is a list of `owin`

objects then `gblg`

returns a dataframe of with columns corresponding to estimates of GBL.

Note that if any values in the `paircorr`

object needed for `gblg`

are `NA`

or `NaN`

then `gblg`

will return `NA`

or `NaN`

, respectively.

Hingee K, Baddeley A, Caccetta P, Nair G (2019). Computation of lacunarity from covariance of spatial binary maps. *Journal of Agricultural, Biological and Environmental Statistics*, 24, 264-288. DOI: 10.1007/s13253-019-00351-9.

```
xi <- as.im(heather$coarse, na.replace = 0, eps = 4 * heather$coarse$xstep)
sidelengths <- seq(0.3, 14, by = 3)
# reduce resolution in setcov() for faster (less accurate) computation
oldopt <- spatstat.options()
spatstat.options("npixel" = 2^4)
# compute GBL estimates from binary map
xiim <- as.im(xi, na.replace = 0)
gblgest <- gblg(sidelengths, xiim = xiim)
spatstat.options(oldopt)
```

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