In tgoodbody/sgsR: Structurally Guided Sampling

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

```{css,echo=FALSE} .infobox { padding: 1em 1em 1em 4em; margin-bottom: 10px; border: 2px solid #43602d; border-radius: 10px; background: #738e41 5px center/3em no-repeat; }

.caution { background-image: url("https://tgoodbody.github.io/sgsR/logo.png"); }

```r
library(sgsR)
library(terra)
library(dplyr)

par(mar = c(1, 1, 1, 1))

#--- Load mraster and access files ---#
r <- system.file("extdata", "mraster.tif", package = "sgsR")

#--- load the mraster using the terra package ---#
mraster <- terra::rast(r)

a <- system.file("extdata", "access.shp", package = "sgsR")

#--- load the access vector using the sf package ---#
access <- sf::st_read(a, quiet = TRUE)

#--- apply quantiles algorithm to metrics raster ---#
sraster <- strat_quantiles(
  mraster = mraster$zq90, # use mraster as input for sampling
  nStrata = 4
) # algorithm will produce 4 strata

#--- apply stratified sampling algorithm ---#
existing <- sample_strat(
  sraster = sraster, # use mraster as input for sampling
  nSamp = 200, # request 200 samples be taken
  mindist = 100
) # define that samples must be 100 m apart

sf::st_crs(existing) <- terra::crs(sraster)

#--- algorithm table ---#

a <- c("`sample_srs()`", "`sample_systematic()`", "`sample_strat()`", "`sample_sys_strat()`", "`sample_nc()`", "`sample_clhs()`", "`sample_balanced()`", "`sample_ahels()`", "`sample_existing()`")

d <- c("Simple random", "Systematic", "Stratified", "Systematic Stratified", "Nearest centroid", "Conditioned Latin hypercube", "Balanced sampling", "Adapted hypercube evaluation of a legacy sample", "Sub-sampling an `existing` sample")

s <- c("", "", "[Queinnec, White, & Coops (2021)](https://www.sciencedirect.com/science/article/pii/S0034425721002303)", "", "[Melville & Stone (2016)](https://doi.org/10.1080/00049158.2016.1218265)", "[Minasny & McBratney (2006)](https://www.sciencedirect.com/science/article/pii/S009830040500292X?via%3Dihub)", "[Grafström, A. Lisic, J (2018)](http://www.antongrafstrom.se/balancedsampling/)", "[Malone, Minasny, & Brungard (2019)](https://peerj.com/articles/6451/)", "")

urls <- c("#srs", "#systematic", "#sstrat", "#sysstrat", "#nc", "#clhs", "#balanced", "#ahels", "#samp-existing")

df <- data.frame(Algorithm = a, Description = d, Reference = s)

df$Algorithm <- paste0("[", df$Algorithm, "](", urls, ")")

Currently, there are 9 functions associated with the sample verb in the sgsR package:

knitr::kable(df, align = "c")

sample_srs {#srs .unnumbered}

We have demonstrated a simple example of using the sample_srs() function in vignette("sgsR"). We will demonstrate additional examples below.

::: {.infobox .caution data-latex="{caution}"} raster

The input required for sample_srs() is a raster. This means that sraster and mraster are supported for this function. :::

#--- perform simple random sampling ---#
sample_srs(
  raster = sraster, # input sraster
  nSamp = 200, # number of desired sample units
  plot = TRUE
) # plot

sample_srs(
  raster = mraster, # input mraster
  nSamp = 200, # number of desired sample units
  access = access, # define access road network
  mindist = 200, # minimum distance sample units must be apart from one another
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 200, # outer buffer - no sample units further than this distance from road
  plot = TRUE
) # plot

sample_systematic {#systematic .unnumbered}

The sample_systematic() function applies systematic sampling across an area with the cellsize parameter defining the resolution of the tessellation. The tessellation shape can be modified using the square parameter. Assigning TRUE (default) to the square parameter results in a regular grid and assigning FALSE results in a hexagonal grid.

The location of sample units can also be adjusted using the locations parameter, where centers takes the center, corners takes all corners, and random takes a random location within each tessellation. Random start points and translations are applied when the function is called.

#--- perform grid sampling ---#
sample_systematic(
  raster = sraster, # input sraster
  cellsize = 1000, # grid distance
  plot = TRUE
) # plot

#--- perform grid sampling ---#
sample_systematic(
  raster = sraster, # input sraster
  cellsize = 500, # grid distance
  square = FALSE, # hexagonal tessellation
  location = "random", # randomly sample within tessellation
  plot = TRUE
) # plot

sample_systematic(
  raster = sraster, # input sraster
  cellsize = 500, # grid distance
  access = access, # define access road network
  buff_outer = 200, # outer buffer - no sample units further than this distance from road
  square = FALSE, # hexagonal tessellation
  location = "corners", # take corners instead of centers
  plot = TRUE
)

sample_strat {#sstrat .unnumbered}

The sample_strat() contains two methods to perform sampling:

• "Queinnec" - Hierarchical sampling using a focal window to isolate contiguous groups of stratum pixels, which was originally developed by Martin Queinnec.

• "random" - Traditional stratified random sampling. This method ignores much of the functionality of the algorithm to allow users the capability to use standard stratified random sampling approaches without the use of a focal window to locate contiguous stratum cells.

method = "Queinnec" {#queinnec .unnumbered}

Queinnec, M., White, J. C., & Coops, N. C. (2021). Comparing airborne and spaceborne photon-counting LiDAR canopy structural estimates across different boreal forest types. Remote Sensing of Environment, 262(August 2020), 112510.

This algorithm uses moving window (wrow and wcol parameters) to filter the input sraster to prioritize sample unit allocation to where stratum pixels are spatially grouped, rather than dispersed individuals across the landscape.

Sampling is performed using 2 rules:

• Rule 1 - Sample within spatially grouped stratum pixels. Moving window defined by wrow and wcol.

• Rule 2 - If no additional sample units exist to satisfy desired sample size(nSamp), individual stratum pixels are sampled.

The rule applied to a select each sample unit is defined in the rule attribute of output samples. We give a few examples below:

#--- perform stratified sampling random sampling ---#
sample_strat(
  sraster = sraster, # input sraster
  nSamp = 200
) # desired sample size # plot

In some cases, users might want to include an existing sample within the algorithm. In order to adjust the total number of sample units needed per stratum to reflect those already present in existing, we can use the intermediate function extract_strata().

This function uses the sraster and existing sample units and extracts the stratum for each. These sample units can be included within sample_strat(), which adjusts total sample units required per class based on representation in existing.

#--- extract strata values to existing samples ---#
e.sr <- extract_strata(
  sraster = sraster, # input sraster
  existing = existing
) # existing samples to add strata value to

::: {.infobox .caution data-latex="{caution}"} TIP!

sample_strat() requires the sraster input to have an attribute named strata and will give an error if it doesn't. :::

sample_strat(
  sraster = sraster, # input sraster
  nSamp = 200, # desired sample size
  access = access, # define access road network
  existing = e.sr, # existing sample with strata values
  mindist = 200, # minimum distance sample units must be apart from one another
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 200, # outer buffer - no sample units further than this distance from road
  plot = TRUE
) # plot

The code in the example above defined the mindist parameter, which specifies the minimum euclidean distance that new sample units must be apart from one another.

Notice that the sample units have type and rule attributes which outline whether they are existing or new, and whether rule1 or rule2 were used to select them. If type is existing (a user provided existing sample), rule will be existing as well as seen above.

sample_strat(
  sraster = sraster, # input
  nSamp = 200, # desired sample size
  access = access, # define access road network
  existing = e.sr, # existing samples with strata values
  include = TRUE, # include existing sample in nSamp total
  buff_outer = 200, # outer buffer - no samples further than this distance from road
  plot = TRUE
) # plot

The include parameter determines whether existing sample units should be included in the total sample size defined by nSamp. By default, the include parameter is set as FALSE.

method = "random {#stratrandom .unnumbered}

Stratified random sampling with equal probability for all cells (using default algorithm values for mindist and no use of access functionality). In essence this method perform the sample_srs algorithm for each stratum separately to meet the specified sample size.

#--- perform stratified sampling random sampling ---#
sample_strat(
  sraster = sraster, # input sraster
  method = "random", # stratified random sampling
  nSamp = 200, # desired sample size
  plot = TRUE
) # plot

sample_sys_strat {#sysstrat .unnumbered}

sample_sys_strat() function implements systematic stratified sampling on an sraster. This function uses the same functionality as sample_systematic() but takes an sraster as input and performs sampling on each stratum iteratively.

#--- perform grid sampling on each stratum separately ---#
sample_sys_strat(
  sraster = sraster, # input sraster with 4 strata
  cellsize = 1000, # grid size
  plot = TRUE # plot output
)

Just like with sample_systematic() we can specify where we want our samples to fall within our tessellations. We specify location = "corners" below. Note that the tesselations are all saved to a list file when details = TRUE should the user want to save them.

sample_sys_strat(
  sraster = sraster, # input sraster with 4 strata
  cellsize = 500, # grid size
  square = FALSE, # hexagon tessellation
  location = "corners", # samples on tessellation corners
  plot = TRUE # plot output
)

This sampling approach could be especially useful incombination with strat_poly() to ensure consistency of sampling accross specific management units.

#--- read polygon coverage ---#
poly <- system.file("extdata", "inventory_polygons.shp", package = "sgsR")
fri <- sf::st_read(poly)

#--- stratify polygon coverage ---#
#--- specify polygon attribute to stratify ---#
attribute <- "NUTRIENTS"

#--- specify features within attribute & how they should be grouped ---#
#--- as a single vector ---#
features <- c("poor", "rich", "medium")

#--- get polygon stratification ---#
srasterpoly <- strat_poly(
  poly = fri,
  attribute = attribute,
  features = features,
  raster = sraster
)

#--- systematatic stratified sampling for each stratum ---#
sample_sys_strat(
  sraster = srasterpoly, # input sraster from strat_poly() with 3 strata
  cellsize = 500, # grid size
  square = FALSE, # hexagon tessellation
  location = "random", # randomize plot location
  plot = TRUE # plot output
)

sample_nc {#nc .unnumbered}

sample_nc() function implements the Nearest Centroid sampling algorithm described in Melville & Stone (2016). The algorithm uses kmeans clustering where the number of clusters (centroids) is equal to the desired sample size (nSamp).

Cluster centers are located, which then prompts the nearest neighbour mraster pixel for each cluster to be selected (assuming default k parameter). These nearest neighbours are the output sample units.

#--- perform simple random sampling ---#
sample_nc(
  mraster = mraster, # input
  nSamp = 25, # desired sample size
  plot = TRUE
)

Altering the k parameter leads to a multiplicative increase in output sample units where total output samples = $nSamp * k$.

#--- perform simple random sampling ---#
samples <- sample_nc(
  mraster = mraster, # input
  k = 2, # number of nearest neighbours to take for each kmeans center
  nSamp = 25, # desired sample size
  plot = TRUE
)

#--- total samples = nSamp * k (25 * 2) = 50 ---#
nrow(samples)

Visualizing what the kmeans centers and sample units looks like is possible when using details = TRUE. The $kplot output provides a quick visualization of where the centers are based on a scatter plot of the first 2 layers in mraster. Notice that the centers are well distributed in covariate space and chosen sample units are the closest pixels to each center (nearest neighbours).

#--- perform simple random sampling with details ---#
details <- sample_nc(
  mraster = mraster, # input
  nSamp = 25, # desired sample number
  details = TRUE
)

#--- plot ggplot output ---#

details$kplot

sample_clhs {#clhs .unnumbered}

sample_clhs() function implements conditioned Latin hypercube (clhs) sampling methodology from the clhs package.

::: {.infobox .caution data-latex="{caution}"} TIP!

A number of other functions in the sgsR package help to provide guidance on clhs sampling including calculate_pop() and calculate_lhsOpt(). Check out these functions to better understand how sample numbers could be optimized. :::

The syntax for this function is similar to others shown above, although parameters like iter, which define the number of iterations within the Metropolis-Hastings process are important to consider. In these examples we use a low iter value for efficiency. Default values for iter within the clhs package are 10,000.

sample_clhs(
  mraster = mraster, # input
  nSamp = 200, # desired sample size
  plot = TRUE, # plot
  iter = 100
) # number of iterations

sample_clhs(
  mraster = mraster, # input
  nSamp = 200, # desired sample size
  plot = TRUE, # plot
  iter = 100
) # number of iterations

The cost parameter defines the mraster covariate, which is used to constrain the clhs sampling. An example could be the distance a pixel is from road access (e.g. from calculate_distance() see example below), terrain slope, the output from calculate_coobs(), or many others.

#--- cost constrained examples ---#
#--- calculate distance to access layer for each pixel in mr ---#
mr.c <- calculate_distance(
  raster = mraster, # input
  access = access, # define access road network
  plot = TRUE
) # plot

sample_clhs(
  mraster = mr.c, # input
  nSamp = 250, # desired sample size
  iter = 100, # number of iterations
  cost = "dist2access", # cost parameter - name defined in calculate_distance()
  plot = TRUE
) # plot

sample_clhs(
  mraster = mr.c, # input
  nSamp = 250, # desired sample size
  iter = 100, # number of iterations
  cost = "dist2access", # cost parameter - name defined in calculate_distance()
  plot = TRUE
) # plot

sample_balanced {#balanced .unnumbered}

The sample_balanced() algorithm performs a balanced sampling methodology from the stratifyR / SamplingBigData packages.

sample_balanced(
  mraster = mraster, # input
  nSamp = 200, # desired sample size
  plot = TRUE
) # plot

sample_balanced(
  mraster = mraster, # input
  nSamp = 100, # desired sample size
  algorithm = "lcube", # algorithm type
  access = access, # define access road network
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 200
) # outer buffer - no sample units further than this distance from road

sample_ahels {#ahels .unnumbered}

The sample_ahels() function performs the adapted Hypercube Evaluation of a Legacy Sample (ahels) algorithm usingexisting sample data and an mraster. New sample units are allocated based on quantile ratios between the existing sample and mraster covariate dataset.

This algorithm was adapted from that presented in the paper below, which we highly recommend.

Malone BP, Minansy B, Brungard C. 2019. Some methods to improve the utility of conditioned Latin hypercube sampling. PeerJ 7:e6451 DOI 10.7717/peerj.6451

This algorithm:

1. Determines the quantile distributions of existing sample units and mraster covariates.

2. Determines quantiles where there is a disparity between sample units and covariates.

3. Prioritizes sampling within those quantile to improve representation.

To use this function, user must first specify the number of quantiles (nQuant) followed by either the nSamp (total number of desired sample units to be added) or the threshold (sampling ratio vs. covariate coverage ratio for quantiles - default is 0.9) parameters.

#--- remove `type` variable from existing  - causes plotting issues ---#

existing <- existing %>% select(-type)

sample_ahels(
  mraster = mraster,
  existing = existing, # existing sample
  plot = TRUE
) # plot

s <- sample_ahels(
  mraster = mraster,
  existing = existing
) # existing samples

s

::: {.infobox .caution data-latex="{caution}"} TIP!

Notice that no threshold, nSamp, or nQuant were defined. That is because the default setting for threshold = 0.9 and nQuant = 10. :::

The first matrix output shows the quantile ratios between the sample and the covariates. A value of 1.0 indicates that the sample is representative of quantile coverage. Values > 1.0 indicate over representation of sample units, while < 1.0 indicate under representation.

sample_ahels(
  mraster = mraster,
  existing = existing, # existing sample
  nQuant = 20, # define 20 quantiles
  nSamp = 300
) # desired sample size

s <- sample_ahels(
  mraster = mraster,
  existing = existing, # existing sample
  nQuant = 20, # define 20 quantiles
  nSamp = 300
) # plot

s

Notice that the total number of samples is 500. This value is the sum of existing units (200) and number of sample units defined by nSamp = 300.

sample_existing {#samp-existing .unnumbered}

Acknowledging that existing sample networks are common is important. There is significant investment into these samples, and in order to keep inventories up-to-date, we often need to collect new data for sample units. The sample_existing algorithm provides the user with methods for sub-sampling an existing sample network should the financial / logistical resources not be available to collect data at all sample units. The functions allows users to choose between algorithm types using (type = "clhs" - default, type = "balanced", type = "srs", type = "strat"). Differences in type result in calling internal sample_existing_*() functions (sample_existing_clhs() (default), sample_existing_balanced(), sample_existing_srs(), sample_existing_strat()). These functions are not exported to be used stand-alone, however they employ the same functionality as their sample_clhs() etc counterparts.

While using sample_existing(), should the user wish to specify algorithm specific parameters (e.g. algorithm = "lcube" in sample_balanced() or allocation = "equal" in sample_strat()), they can specify within sample_existing() as if calling the function directly.

I give applied examples for all methods below that are based on the following scenario:

• We have a systematic sample where sample units are 200m apart.

• We know we only have resources to sample 300 of them.

• We have some ALS data available (mraster), which we can use to improve knowledge of the metric populations.

See our existing sample for the scenario below.

#--- generate existing samples and extract metrics ---#
existing <- sample_systematic(raster = mraster, cellsize = 200, plot = TRUE)

#--- sub sample using ---#
e <- existing %>%
  extract_metrics(mraster = mraster, existing = .)

sample_existing(type = "clhs")

The algorithm is unique in that it has two fundamental approaches:

1. Sample exclusively using existing and the attributes it contains.

#--- sub sample using ---#
sample_existing(existing = e, nSamp = 300, type = "clhs")

1. Sub-sampling using raster distributions

Our systematic sample of ~900 plots is fairly comprehensive, however we can generate a true population distribution through the inclusion of the ALS metrics in the sampling process. The metrics will be included in internal latin hypercube sampling to help guide sub-sampling of existing.

#--- sub sample using ---#
sample_existing(
  existing = existing, # our existing sample
  nSamp = 300, # desired sample size
  raster = mraster, # include mraster metrics to guide sampling of existing
  plot = TRUE
) # plot

The sample distribution again mimics the population distribution quite well! Now lets try using a cost variable to constrain the sub-sample.

#--- create distance from roads metric ---#
dist <- calculate_distance(raster = mraster, access = access)

#--- sub sample using ---#
sample_existing(
  existing = existing, # our existing sample
  nSamp = 300, # desired sample size
  raster = dist, # include mraster metrics to guide sampling of existing
  cost = 4, # either provide the index (band number) or the name of the cost layer
  plot = TRUE
) # plot

Finally, should the user wish to further constrain the sample based on access like other sampling approaches in sgsR that is also possible.

#--- ensure access and existing are in the same CRS ---#

sf::st_crs(existing) <- sf::st_crs(access)

#--- sub sample using ---#
sample_existing(
  existing = existing, # our existing sample
  nSamp = 300, # desired sample size
  raster = dist, # include mraster metrics to guide sampling of existing
  cost = 4, # either provide the index (band number) or the name of the cost layer
  access = access, # roads layer
  buff_inner = 50, # inner buffer - no sample units within this distance from road
  buff_outer = 300, # outer buffer - no sample units further than this distance from road
  plot = TRUE
) # plot

::: {.infobox .caution data-latex="{caution}"} TIP!

The greater constraints we add to sampling, the less likely we will have strong correlations between the population and sample, so its always important to understand these limitations and plan accordingly. :::

sample_existing(type = "balanced")

When type = "balanced" users can define all parameters that are found within sample_balanced(). This means that one can change the algorithm, p etc.

sample_existing(existing = e, nSamp = 300, type = "balanced")

sample_existing(existing = e, nSamp = 300, type = "balanced", algorithm = "lcube")

sample_existing(type = "srs")

The simplest, type = srs, randomly selects sample units.

sample_existing(existing = e, nSamp = 300, type = "srs")

sample_existing(type = "strat")

When type = "strat", existing must have an attribute named strata (just like how sample_strat() requires a strata layer). If it doesnt exist you will get an error. Lets define an sraster so that we are compliant.

sraster <- strat_kmeans(mraster = mraster, nStrata = 4)

e_strata <- extract_strata(sraster = sraster, existing = e)

When we do have a strata attribute, the function works very much the same as sample_strat() in that is allows the user to define the allocation method ("prop" - defaults, "optim", "manual", "equal").

#--- proportional stratified sampling of existing ---#
sample_existing(existing = e_strata, nSamp = 300, type = "strat", allocation = "prop")

::: {.infobox .caution data-latex="{caution}"} TIP!

Remember that when allocation = "equal", the nSamp value will be allocated for each strata. :::

We get 400 sample units in our output below because we have 4 strata and nSamp = 100.

#--- equal stratified sampling of existing ---#
sample_existing(existing = e_strata, nSamp = 100, type = "strat", allocation = "equal")

#--- manual stratified sampling of existing with user defined weights ---#
s <- sample_existing(existing = e_strata, nSamp = 100, type = "strat", allocation = "manual", weights = c(0.2, 0.6, 0.1, 0.1))

We can check the proportion of samples from each strata with:

#--- check proportions match weights ---#
table(s$strata) / 100

Finally, type = "optim allows for the user to define a raster metric to be used to optimize within strata variances.

#--- manual stratified sampling of existing with user defined weights ---#
sample_existing(existing = e_strata, nSamp = 100, type = "strat", allocation = "optim", raster = mraster, metric = "zq90")

We see from the output that we get 300 sample units that are a sub-sample of existing. The plotted output shows cumulative frequency distributions of the population (all existing samples) and the sub-sample (the 300 samples we requested).

tgoodbody/sgsR documentation built on March 7, 2024, 2:20 a.m.