osmgeosample (version 0.1)

osm_discrete_inhibit_sample: OSM discrete Inhibitory sampling.

Description

Draw a spatially discrete sample from a specified set of OSM spatial locations within a polygonal sampling region according to an 'inhibitory plus close pairs' specification.

Usage

osm_discrete_inhibit_sample(
  bounding_geom = NULL,
  key = NULL,
  value = NULL,
  data_return = c("osm_polygons", "osm_points", "osm_multipolygons", "multilines",
    "lines"),
  boundary = 0,
  buff_dist = 0,
  buff_epsg = 4326,
  join_type = "within",
  sample_size,
  plotit = TRUE,
  plotit_leaflet = TRUE,
  delta,
  delta.fix = FALSE,
  k = 0,
  cp.criterion = NULL,
  zeta,
  ntries = 10000,
  boundary_or_feature = "boundary",
  join_features_to_osm = FALSE,
  feature_geom = NULL
)

Arguments

bounding_geom

A sf or sp with each line corresponding to one spatial location. It should contain values of 2D coordinates. This argument must be provided when sampling from a 'discrete' set of locations defined in OSM.

key

A feature key as defined in OSM. An example is 'building'.

value

A value for a feature key (key); can be negated with an initial exclamation mark, value = '!this', and can also be a vector, value = c ('this', 'that'). More details at https://wiki.openstreetmap.org/wiki/Map_Features.

data_return

A list which specifies what data types (as specified in OSM) you want returned. More than one can be selected. The options are 'osm_polygons', 'osm_points', 'osm_multipolygons','osm_multilines','osm_lines'. ##'@param data_return specifies what data types (as specified in OSM) you want returned. More than one can be selected. The options are 'osm_polygons', 'osm_points', 'osm_multipolygons','osm_multilines','osm_lines'.

boundary

A categorical variable to determine whether the exact boundary (boundary = 0), the bounding box (boundary = 1) or a buffer around the boundary (boundary = 2) is used for sampling. The default is boundary = 0.

buff_dist

If boundary = 2 then this value determines the size of the buffer by distance. The default is buff_dist is NULL).

buff_epsg

If boundary = 2 then this value determines the local geographic grid reference so that the buffer can be calculated in meters. The default is buff_epsg = 4326 which will use decimal degrees instead of meters. As an example, 27700 relates to the British National Grid.

join_type

A text value to determine how to spatially join all features with the boundary. The options are 'within' or 'intersect'.

sample_size

A non-negative integer giving the total number of locations to be sampled.

plotit

A 'logical' input specifying if a graphical output is required. Default is plotit = TRUE.

plotit_leaflet

A 'logical' input specifying if leaflet (html) graphical output is required. This is prioritised over plotit if both are selected. Default is plotit_leaflet = TRUE.

delta

The minimum permissible distance between any two locations in preliminary sample. This can be allowed to vary with number of 'close pairs' if a simple inhibitory design is compared to one of the inhibitory plus close pairs design.

delta.fix

A 'logical' input which specifies whether 'delta' is fixed or allowed to vary with number of close pairs \(k\). Default is delta.fix = FALSE.

k

The number of close-pair locations in the sample. It must be an integer between 0 and size/2.

cp.criterion

The criterion for choosing close pairs \(k\). The 'cp.zeta' criterion chooses locations not included in the initial sample, from the uniform distribution of a disk with radius 'zeta' (NB: zeta argument must be provided for this criterion). The 'cp.neighb' criterion chooses nearest neighbours amongst locations not included in the initial sample ('zeta' becomes trivial for 'cp.neighb' criterion).

zeta

The maximum permissible distance (radius of a disk with center \(x^{*}_{j}, j = 1, \ldots, k\)) within which a close-pair point is placed. See Details.

ntries

The number of rejected proposals after which the algorithm terminates.

boundary_or_feature

specifies whether the user inputs a boundary or a set of user-inputted features. For example if the user selects 'boundary', they can provide a spatial data frame or OSM locality which will query the osm features within that boundary or locality. If the user select 'feature' then they can provide a data frame of features that they want to sample

join_features_to_osm

is a TRUE or FALSE variable which allows the user to specify whether they want their feature geom to be spatially joined to OSM features. The output sampling data frame will have an additional column showing the joined OSM id.

feature_geom

is a user inputted data frame of features that are required to be sampled.

Value

a list with the following four components:

unique.locs: the number of unique sampled locations.

delta: the value of \(\delta\) after taking into account the number of close pairs \(k\). If delta.fix = TRUE, this will be \(\delta\) input by the user.

\(k:\) the number of close pairs included in the sample (for inhibitory plus close pairs design).

sample.locs: a sf or sp object containing the final sampled locations and any associated values.

Details

To draw a sample of size \(n\) from a population of spatial locations \(X_{i} : i = 1,\ldots,N\), with the property that the distance between any two sampled locations is at least \(\delta\), the function implements the following algorithm.

• Step 1. Draw an initial sample of size \(n\) completely at random and call this \(x_{i} : i = 1,\dots, n\).

• Step 2. Set \(i = 1\).

• Step 3. Calculate the smallest distance, \(d_{\min}\), from \(x_{i}\) to all other \(x_{j}\) in the initial sample.

• Step 4. If \(d_{\min} \ge \delta\), increase \(i\) by 1 and return to step 2 if \(i \le n\), otherwise stop.

• Step 5. If \(d_{\min} < \delta\), draw an integer \(j\) at random from \(1, 2,\ldots,N\), set \(x_{i} = X_{j}\) and return to step 3.

Samples generated in this way exhibit more regular spatial arrangements than would random samples of the same size. The degree of regularity achievable will be influenced by the spatial arrangement of the population \(X_{i} : i = 1,\ldots,N\), the specified value of \(\delta\) and the sample size \(n\). For any given population, if \(n\) and/or \(\delta\) is too large, a sample of the required size with the distance between any two sampled locations at least \(\delta\) will not be achievable; the algorithm will then find \(n_{s} < n\) points that can be placed for the given parameters.

Sampling close pairs of points.

For some purposes, typically when using the same sample for parameter estimation and spatial prediction, it is desirable that a spatial sampling scheme include pairs of closely spaced points \(x\). The function offers two ways of specifying close pairs, either as the closest available unsampled point to an existing sampled point (cp.critetrion = cp.neighb), or as a random choice from amongst all available unsampled points within distance \(zeta\) of an existing sampled point (cp.criterion = cp.zeta). The algorithm proceeds as follows.

Let \(k\) be the required number of close pairs.

• Step 1. Construct a simple inhibitory design SI\((n - k, \delta)\).

• Step 2. Sample \(k\) from \(x_{1}, \ldots, x_{n - k}\) without replacement and call this set \(x_{j} : j = 1, \ldots, k\).

• Step 3. For each \(x_{j}: j = 1, \ldots, k\), select a close pair \(x_{n-k+j}\) according to the specified criterion.

Note: Depending on the spatial configuration of potential sampling locations and, when the selection criterion cp.criterion = cp.zeta, the specified value of \(zeta\), it is possible that one or more of the selected points \(x_{j}\) in Step 2 will not have an eligible ``close pair''. In this case, the algorithm will try find an alternative \(x_{j}\) and report a warning if it fails to do so.

References

Chipeta M G, Terlouw D J, Phiri K S and Diggle P J. (2016). Inhibitory geostatistical designs for spatial prediction taking account of uncertain covariance structure, Enviromentrics, pp. 1-11. Diggle P J. (2014). Statistical Analysis of Spatial and Spatio-Temporal Point Patterns. 3rd ed., Boca Raton: CRC Press Diggle P J and Lophaven S. (2006). Bayesian geostatistical design, Scandinavian Journal of Statistics 33(1) pp. 53 - 64. Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655

Examples

# NOT RUN {
library(sp)
bounding_geom<-
SpatialPolygonsDataFrame(
   SpatialPolygons(list(Polygons(list(Polygon(
       cbind(
           c(3.888959,3.888744,3.888585,3.888355,3.887893,3.887504,3.886955,
           3.886565,3.886303,3.886159,3.885650,3.885650,3.885595,3.885404,
           3.885444,3.885897,3.886692,3.887241,3.888068,3.888323,3.888697,
           3.889150,3.889548,3.889890,3.890184,3.890828,3.891258,3.891807,
           3.892061,3.892292,3.892689,3.893294,3.893008,3.893676,3.888959),
           c(7.379483,7.379785,7.380024,7.380294,7.380629,7.380986,7.381448,
           7.381861,7.382243,7.382474,7.383277,7.383468,7.383890,7.384263,
           7.384669,7.385258,7.385313,7.385194,7.384868,7.384900,7.385051,
           7.385067,7.384955,7.384749,7.384526,7.384120,7.384009,7.384080,
           7.384430,7.384478,7.384629,7.384772,7.383269,7.380963,
           7.379483)))), ID=1))),
   data.frame( ID=1))
proj4string(bounding_geom) <- CRS('+proj=longlat +datum=WGS84')

set.seed(15892)
xy.sample <- osm_discrete_inhibit_sample(bounding_geom=bounding_geom,
 data_return=c('osm_polygons'),boundary=0, buff_dist=NULL, buff_epsg=NULL,
 join_type='within', sample_size=70, plotit=TRUE, plotit_leaflet = TRUE,
 delta = 5, key ='building', value=NULL, delta.fix = TRUE, k = 0,
 cp.criterion = 'cp.neighb', zeta = 0.025, ntries = 5)
# }
# NOT RUN {
# }