Calculate for multiple bandwidth the cross validation likelihood to select an appropriate bandwidth in a data-driven approach

bw_cv_likelihood_calc(
bw_range,
bw_step,
lines,
events,
w,
kernel_name,
method,
diggle_correction = FALSE,
study_area = NULL,
max_depth = 15,
digits = 5,
tol = 0.1,
agg = NULL,
sparse = TRUE,
grid_shape = c(1, 1),
sub_sample = 1,
zero_strat = "min_double",
verbose = TRUE,
check = TRUE
)

## Arguments

bw_range

The range of the bandwidths to consider, given as a numeric vector of two values: c(bandwidth_min, bandwidth_max)

bw_step

The step between each bandwidth to calculate given as a float

lines

A feature collection of linestrings representing the underlying network. The geometries must be simple Linestrings (may crash if some geometries are invalid) without MultiLineSring.

events

events A feature collection of points representing the events on the network. The points will be snapped on the network to their closest line.

w

A vector representing the weight of each event

kernel_name

The name of the kernel to use. Must be one of triangle, gaussian, tricube, cosine, triweight, quartic, epanechnikov or uniform.

method

The method to use when calculating the NKDE, must be one of simple / discontinuous / continuous (see nkde details for more information)

diggle_correction

A Boolean indicating if the correction factor for edge effect must be used.

study_area

A feature collection of polygons representing the limits of the study area.

max_depth

when using the continuous and discontinuous methods, the calculation time and memory use can go wild if the network has many small edges (area with many of intersections and many events). To avoid it, it is possible to set here a maximum depth. Considering that the kernel is divided at intersections, a value of 10 should yield good estimates in most cases. A larger value can be used without a problem for the discontinuous method. For the continuous method, a larger value will strongly impact calculation speed.

digits

The number of digits to retain from the spatial coordinates. It ensures that topology is good when building the network. Default is 3. Too high a precision (high number of digits) might break some connections

tol

A float indicating the minimum distance between the events and the lines' extremities when adding the point to the network. When points are closer, they are added at the extremity of the lines.

agg

A double indicating if the events must be aggregated within a distance. If NULL, the events are aggregated only by rounding the coordinates.

sparse

A Boolean indicating if sparse or regular matrices should be used by the Rcpp functions. These matrices are used to store edge indices between two nodes in a graph. Regular matrices are faster, but require more memory, in particular with multiprocessing. Sparse matrices are slower (a bit), but require much less memory.

grid_shape

A vector of two values indicating how the study area must be split when performing the calculus. Default is c(1,1) (no split). A finer grid could reduce memory usage and increase speed when a large dataset is used. When using multiprocessing, the work in each grid is dispatched between the workers.

sub_sample

A float between 0 and 1 indicating the percentage of quadra to keep in the calculus. For large datasets, it may be useful to limit the bandwidth evaluation and thus reduce calculation time.

zero_strat

A string indicating what to do when density is 0 when calculating LOO density estimate for an isolated event. "min_double" (default) replace the 0 value by the minimum double possible on the machine. "remove" will remove them from the final score. The first approach penalizes more strongly the small bandwidths.

verbose

A Boolean, indicating if the function should print messages about the process.

check

A Boolean indicating if the geometry checks must be run before the operation. This might take some times, but it will ensure that the CRS of the provided objects are valid and identical, and that geometries are valid.

## Value

A dataframe with two columns, one for the bandwidths and the second for the cross validation score (the lower the better).

## Details

The function calculates the likelihood cross validation score for several bandwidths in order to find the most appropriate one. The general idea is to find the bandwidth that would produce the most similar results if one event was removed from the dataset (leave one out cross validation). We use here the shortcut formula as described by the package spatstat (Baddeley et al. 2021) .

LCV(h) = sum[i] log(lambda[-i](x[i]))

Where the sum is taken for all events x[i] and where lambda[-i](x[i]) is the leave-one-out kernel estimate at x[i] for a bandwidth h. A higher value indicates a better bandwidth.

## References

Baddeley A, Turner R, Rubak E (2021). spatstat: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests. R package version 2.1-0, https://CRAN.R-project.org/package=spatstat.

## Examples

# \donttest{
data(mtl_network)
data(bike_accidents)
cv_scores <- bw_cv_likelihood_calc(c(200,800),50,
mtl_network, bike_accidents,
rep(1,nrow(bike_accidents)),
"quartic", "simple",
diggle_correction = FALSE, study_area = NULL,
max_depth = 8,
digits=2, tol=0.1, agg=5,
sparse=TRUE, grid_shape=c(1,1),
sub_sample = 1, verbose=TRUE, check=TRUE)
# }