gblc | R Documentation |

Can be used to estimate the gliding box lacunarity (GBL) of a stationary RACS from a binary map using the plug-in moment covariance covariance estimator (Hingee et al., 2019). It can also calculate the GBL of a RACS from a given covariance function and coverage probability.

```
gblc(
boxes,
covariance = NULL,
p = NULL,
xiim = NULL,
integrationMethod = "cubature"
)
```

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

`covariance` |
A |

`p` |
The coverage probability. Typically estimated by the fraction of the observation window covered by the set of interest. |

`xiim` |
A binary coverage map as an |

`integrationMethod` |
The integration method used by |

Computes a numerical approximation of

`\int \gamma_B(v) C(v) dv / (p^2 |B|^2).`

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, and
`C(v)`

is the covariance 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.

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 method of integration for the above integral is `cubature::cubintegrate()`

from the cubature package.
The '`harmonisesum`

' method is known to produce numerical artefacts (Section 6.2 of (Hingee et al., 2019))

If a binary map is supplied then `p`

and `C(v)`

are estimated using
the usual coverage probability estimator and the plug-in moment covariance estimator, respectively
(see `coverageprob`

and `plugincvc`

).

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,
box mass variance and box mass mean.
If `boxes`

is a list of `owin`

objects then `gblc`

returns a
dataframe with columns corresponding to estimates of GBL, box mass variance and box mass mean.

Note if `NA`

or `NaN`

values in the `covariance`

object are used then `gblc`

will return `NA`

or `NaN`

.

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 <- heather$coarse
# reduce resolution in setcov() for faster (less accurate) computation
oldopt <- spatstat.options()
spatstat.options("npixel" = 2^5)
covar <- plugincvc(xi, Frame(xi))
p <- area(xi) / area(Frame(xi))
sidelengths <- seq(0.3, 14, by = 1)
# compute GBL estimate for square boxes from estimated covariance
gblest <- gblc(sidelengths, covar, p)
# compute GBL estimate for boxes that are discs
discboxes <- lapply(sidelengths / 2, disc)
discgbls <- gblc(discboxes, covar, p)
# compute GBL estimates from binary map
xiim <- as.im(xi, na.replace = 0)
gblest <- gblc(sidelengths, xiim = xiim)
spatstat.options(oldopt)
```

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