Currently, there are 8 functions associated with the
calculate verb in the
calculate_representation() - compare the
representation of strata in existing samples
calculate_distance() - per pixel distance to the
calculate_pcomp()- principal components of the input
calculate_sampsize() - determines appropriate
estimated sample sizes based on relative standard error
calculate_allocation() - sample allocation algorithm
- proportional / optimal / equal / manual sampling
calculate_coobs() - determine how
existing samples are distributed among
calculate_pop() - generate population level
information (PCA / quantile matrix / covariance matrix) of input
calculate_lhsOpt() - testing to determine optimal
Latin hypercube sampling parameters including sample number
calculate_* functions serve as intermediary helper
functions. In this section we outline and demonstrate how these
functions can be used.
calculate_representation() function allows the users to
verify how well the stratification is represented in their
existing sample networks. Users input an
sraster and their
existing samples to the
calculate_representation() function, which will result in
tabular and graphical (if
plot = TRUE) outputs that compare
strata coverage frequency and sampling frequency.
#--- quantile sraster ---# <- strat_quantiles(mraster = mraster$zq90, quantiles nStrata = 8) #--- random samples ---# <- sample_srs(raster = sraster, srs nSamp = 50) #--- calculate representation ---# calculate_representation(sraster = quantiles, existing = srs, plot = TRUE)
#> # A tibble: 8 × 6 #> strata srasterFreq sampleFreq diffFreq nSamp need #> <dbl> <dbl> <dbl> <dbl> <int> <dbl> #> 1 1 0.13 0.18 0.05 9 -2 #> 2 2 0.13 0.12 -0.0100 6 1 #> 3 3 0.13 0.1 -0.03 5 2 #> 4 4 0.12 0.06 -0.06 3 3 #> 5 5 0.12 0.16 0.04 8 -2 #> 6 6 0.12 0.1 -0.0200 5 1 #> 7 7 0.12 0.1 -0.0200 5 1 #> 8 8 0.12 0.18 0.06 9 -3
The tabular output presents the frequency of coverage for each strata
srasterFreq) (what % of the landscape does the strata
cover) and the sampling frequency within each strata
sampleFreq) (what % of total
are in the strata). The difference (
coverage frequency and sampling frequency determines whether the values
are over-represented (positive numbers) or under-represented (negative
numbers). This value translates to a discrete
attribute that defines whether there is a need to add or remove samples
to meet the number of samples necessary to be considered representative
of the strata inputted in
Performing the algorithm on a sample set derived using
sample_strat() exhibits proportional sampling to strata
calculate_representation(sraster = sraster, existing = existing, plot = TRUE)
#> # A tibble: 4 × 6 #> strata srasterFreq sampleFreq diffFreq nSamp need #> <dbl> <dbl> <dbl> <dbl> <int> <dbl> #> 1 1 0.25 0.25 0 50 0 #> 2 2 0.25 0.25 0 50 0 #> 3 3 0.25 0.25 0 50 0 #> 4 4 0.25 0.25 0 50 0
Presence of very small (negligible) differences between
sampleFreq is common.
In these situations, it is important for the user to determine
whether to add or remove the samples.
calculate_distance() function takes the input
access data and outputs the per
pixel distance to the nearest access point. This function has a specific
value for constraining the sampling protocols, such as the
sample_clhs() function, where the output raster layer can
be used as the
cost for the constraint. The output raster
consists of the input appended with the calculated distance layer
calculate_distance(raster = sraster, # input access = access, # define access road network plot = TRUE) # plot
#> class : SpatRaster #> dimensions : 277, 373, 2 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> sources : memory #> memory #> names : strata, dist2access #> min values : 1, 6.621213e-03 #> max values : 4, 1.061660e+03
Access network polygons with a large number of features and/or large spatial extent could result in slow processing times.
calculate_pcomp() function takes
the input and performs principal component analysis. The number of
components defined by the
nComp parameter specifies the
number of components that will be rasterized onto the output.
calculate_pcomp(mraster = mraster, # input nComp = 3, # number of components to output plot = TRUE, # plot details = TRUE) # details about the principal component analysis appended
#> $pca #> Standard deviations (1, .., p=3): #>  1.5479878 0.7359109 0.2493371 #> #> Rotation (n x k) = (3 x 3): #> PC1 PC2 PC3 #> zq90 0.6286296 -0.1795433 -0.7566961 #> pzabove2 0.5104140 0.8293596 0.2272450 #> zsd 0.5867729 -0.5290812 0.6130014 #> #> $raster #> class : SpatRaster #> dimensions : 277, 373, 3 (nrow, ncol, nlyr) #> resolution : 20, 20 (x, y) #> extent : 431100, 438560, 5337700, 5343240 (xmin, xmax, ymin, ymax) #> coord. ref. : UTM Zone 17, Northern Hemisphere #> sources : memory #> memory #> memory #> names : PC1, PC2, PC3 #> min values : -4.402269, -5.357801, -1.446156 #> max values : 5.282663, 2.155242, 1.510955
calculate_sampsize() function allows the user to
estimate an appropriate sample size using the relative standard error
rse) of input metrics. If the input
contains multiple layers, the sample sizes will be determined for all
plot = TRUE and
rse is defined, a
rse values will be visualized with the
indicators and the values for the matching sample size.
#--- determine sample size based on relative standard error (rse) of 1% ---# calculate_sampsize(mraster = mraster, rse = 0.01) #> nSamp rse var #> 1 1394 0.01 zq90 #> 2 1341 0.01 pzabove2 #> 3 1859 0.01 zsd
#--- change default threshold sequence values ---# #--- if increment and rse are not divisible the closest value will be taken ---# <- calculate_sampsize(mraster = mraster, p rse = 0.025, start = 0.01, end = 0.08, increment = 0.01, plot = TRUE) #> 'rse' not perfectly divisible by 'increment'. Selecting closest sample size (rse = 0.03) based on values. p#> $nSamp #> # A tibble: 3 × 3 #> # Groups: var  #> nSamp rse var #> <dbl> <dbl> <chr> #> 1 157 0.03 zq90 #> 2 151 0.03 pzabove2 #> 3 211 0.03 zsd #> #> $plot
calculate_allocation() function determines how to
allocate samples based on the desired number of samples
nSamp) and the input
sraster. This function
is used internally in a number of functions, including
sample_strat. Currently, there are three
methods for allocations included: proportional (
default), optimal (
optim), equal (
nSamp) are allocated to each strata.
weightsis provided allowing users to manually assign weights to strata.
#--- perform grid sampling ---# calculate_allocation(sraster = sraster, nSamp = 200) #> strata total #> 1 1 50 #> 2 2 50 #> 3 3 50 #> 4 4 50
#--- calculate existing samples to include ---# <- extract_strata(sraster = sraster, e.sr existing = existing) calculate_allocation(sraster = sraster, nSamp = 200, existing = e.sr) #> strata total need #> 1 1 0 50 #> 2 2 0 50 #> 3 3 0 50 #> 4 4 0 50
Notice that some of the values under
total from the
result above are negative. The negative value indicates that the
existing samples over represent those strata and that some
of the samples could removed to prevent over-representation.
$total indicates the number of samples that could be added
Optimal allocation method uses the variation within the strata metric
to allocate samples. This means that in addition to providing and
sraster, that a specific metric (
be provided to calculate variation to optimally allocate samples.
calculate_allocation(sraster = sraster, # stratified raster nSamp = 200, # desired sample number existing = e.sr, #existing samples allocation = "optim", # optimal allocation mraster = mraster$zq90, # metric raster force = TRUE) # force nSamp number #> # A tibble: 4 × 3 #> # Rowwise: #> strata total need #> <dbl> <dbl> <dbl> #> 1 1 27 77 #> 2 2 -14 36 #> 3 3 -26 25 #> 4 4 13 63
There may be situations where the user wants to have the same number
of samples allocated to each strata. In these situations use
allocation = equal. In this case,
to the total number of samples per strata, instead of the overall total
number of samples.
calculate_allocation(sraster = sraster, # stratified raster nSamp = 20, # desired sample number allocation = "equal") # optimal allocation #> Implementing equal allocation of samples. #> # A tibble: 4 × 2 #> strata total #> <dbl> <dbl> #> 1 1 20 #> 2 2 20 #> 3 3 20 #> 4 4 20
The code in the demonstration above yields a total of 80 samples (20
nSamp for each of the 4 strata in
The user may wish to manually assign weights to strata. In this case,
allocation = manual can be used and
must be provided as a numeric vector
weights = c(0.2, 0.2, 0.2, 0.4) where
sum(weights) == 1). In this case,
be allocated based on
<- c(0.2, 0.2, 0.2, 0.4) weights calculate_allocation(sraster = sraster, # stratified raster nSamp = 20, # desired sample number allocation = "manual", # manual allocation weights = weights) # weights adding to 1 #> Implementing allocation of samples based on user-defined weights. #> strata total #> 1 1 4 #> 2 2 4 #> 3 3 4 #> 4 4 8
The code in the demonstration above yields a total of 20 samples with
plots being allocated based on the
weights provided in
ascending strata order.
The following algorithms were initially developed by Dr. Brendan Malone from the University of Sydney. Dr. Brendan Malone and his colleagues graciously supplied an in depth description of the functionality of these algorithms, which were originally developed to improve soil sampling strategies. These functions were modified and implemented to be used for structurally guided sampling approaches. Many thanks to Dr. Malone for his excellent collaboration and being a proponent of open source algorithms.
Please consult the original reference for these scripts and ideas as their paper holds extremely helpful and valuable information to understand their rationale for sampling and algorithm development.
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
calculate_coobs() function performs the COunt of
OBServations (coobs) algorithm using
existing sample data
mraster covariates. This algorithm helps the user
understand how the
existing sample data set is distributed
among the landscape in relation to the
The output coobs raster can be used to constrain clhs sampling using the
sample_clhs() function to the areas that are
The coobs raster determines how many observations are similar in terms of the covariate space at every pixel. This function takes advantage of parallel processing routines.
calculate_coobs(mraster = mraster, # input existing = existing, # existing samples cores = 4, # parallel cores to use details = TRUE, # provide details from algorithm output plot = TRUE) # plot
The following 2 algorithms presents the means to maximize the effectiveness of the latin hypercube sampling protocols.
calculate_pop() function calculates population level
statistics of the
mraster covariates that are being used,
which includes calculating the principal components, quantile &
covariate distributions, and Kullback-Leibler divergence testing. The
outputs produced from this functions are required to use the
calculate_lhsOpt() function described in the following
section. Additionally, this algorithm can be pre-emptively used to
MatCov, two values that are
used for the
sample_ahels() function. This will save
processing time during sampling.
#--- by default all statistical data are calculated ---# calculate_pop(mraster = mraster) # input
The output list contains the following:
$values - Pixel values from
$pcaLoad - PCA loadings
$matQ - Quantile matrix
$matCov - Covariate matrix
#--- statistical analyses can be chosen by setting their parameter to `FALSE` ---# <- calculate_pop(mraster = mraster, # input mat nQuant = 10) # desired number of quantiles #--- use matrix output within sample ahels algorithm ---# sample_ahels(mraster = mraster, existing = existing, nQuant = 10, nSamp = 50, matCov = mat)
calculate_lhsOpt() function performs a bootstrapped
latin hypercube sampling approach where population level analysis of
mraster data is performed to determine the optimal latin
hypercube sample size.
Using data calculated using the
varying sample sizes defined by
protocols are conducted and statistical effectiveness of those sampling
outcomes are evaluated to determine where sample size is minimized and
statistical representation is maximized.
#--- calculate lhsPop details ---# <- calculate_pop(mraster = mr) poplhs calculate_lhsOpt(popLHS = poplhs)
calculate_lhsOpt(popLHS = poplhs, PCA = FALSE, iter = 200)