Package 'paar'

Barley grain yield

Description

A dataset containing Barley grain yield using calibrated commercial yield monitors mounted on combines equipped with DGPS.

Usage

barley

Format

A data frame with 7395 rows and 3 variables:

X

X coordinate, in meters

Y

Y coordinate, in meters

Yield

grain yield, in ton per hectare

Details

Coordinate reference system is "WGS 84 / UTM zone 20S", epsg:32720

---

Bind outlier condition to an object.

Description

Bind outlier condition to an object.

Usage

## S3 method for class 'paar'
cbind(..., deparse.level = 1)

Arguments

...	objects to bind.
deparse.level	integer controlling the construction of labels in the case of non-matrix-like arguments (for the default method): deparse.level = 0 constructs no labels; the default deparse.level = 1 typically and deparse.level = 2 always construct labels from the argument names, see the ‘Value’ section below.

Value

cbind called with m.

---

Compare means between spatial zones

Description

Compares variable means across spatial zones using a spatially-adjusted least significant difference (LSD) approach based on kriging variance.

The function accounts for spatial variability by estimating semivariograms and deriving a spatial variance component, which is then used to assess differences between zone means.

Usage

compare_zone(
  data,
  variable,
  zonesCol,
  alpha = 0.05,
  join = sf::st_nearest_feature,
  returnLSD = FALSE,
  grid_dim
)

Arguments

data	an sf object containing the spatial zones
variable	either: a character vector with column names in data, or an sf object with external variables to be compared. In this case, values are spatially joined to data.
zonesCol	character. Column name in data defining zones
alpha	numeric. Significance level for mean comparison
join	function used in sf::st_join when variable is an external sf object (default: sf::st_nearest_feature)
returnLSD	logical. If TRUE, returns the LSD value used for comparisons
grid_dim	numeric. Grid resolution used to estimate spatial variance when interpolating external variables. If missing, it is automatically determined.

Details

When variable is an external sf object, values are interpolated using ordinary kriging before comparison. Otherwise, cross-validation of the variogram model is used to estimate spatial variance.

Pairwise comparisons between zones are evaluated using a spatially-adjusted LSD criterion:

$LSD = z_{1-\alpha/2} \times \sigma_{spatial}$

where $\sigma_{spatial}$ is derived from kriging variance.

Results are presented using compact letter displays to indicate groups of zones that are not significantly different.

Value

A list with:

differences

list of data frames with mean comparisons per variable

descriptive_stat

data frame with descriptive statistics and spatial variance

References

Paccioretti, P., Córdoba, M., & Balzarini, M. (2020). FastMapping: Software to create field maps and identify management zones in precision agriculture. Computers and Electronics in Agriculture, 175, 105556. doi:10.1016/j.compag.2020.105556

Examples

library(sf)
data(wheat, package = "paar")

##Convert to an sf object
wheat <- sf::st_as_sf(wheat, coords = c("x", "y"), crs = 32720)

clusters <- paar::kmspc(
  wheat,
  variables = c('CE30', 'CE90', 'Elev', 'Pe', 'Tg'),
  number_cluster = 3:4
)

data_clusters <- cbind(wheat, clusters$cluster)

compare_zone(data_clusters, "Elev", "Cluster_3")

---

Spatial data depuration (error removal)

Description

Filters spatial point data by removing erroneous observations based on geometric, statistical, and spatial criteria. The function implements a sequential depuration workflow commonly used in precision agriculture.

Usage

depurate(
  x,
  y,
  toremove = c("edges", "outlier", "inlier"),
  crs = NULL,
  buffer = -10,
  ylimitmax = NA,
  ylimitmin = 0,
  sdout = 3,
  ldist = 0,
  udist = 40,
  criteria = c("LM", "MP"),
  zero.policy = NULL,
  poly_border = NULL
)

Arguments

x	An sf object with POINT geometries.
y	A character string indicating the variable name used for filtering. If missing and only one attribute column is present, it is used by default.
toremove	A character vector specifying which procedures to apply. Options are "edges", "outlier", and "inlier". The order of execution is fixed and cannot be modified.
crs	Coordinate reference system used when transforming longitude/latitude data. Can be an EPSG code or proj4string.
buffer	A numeric value indicating the distance (in meters) for edge removal. Negative values are recommended to shrink boundaries.
ylimitmax	Numeric upper bound for y. If NA, Inf is used.
ylimitmin	Numeric lower bound for y. If NA, -Inf is used.
sdout	Numeric multiplier for standard deviation used to detect global outliers.
ldist	Numeric lower distance bound for neighborhood definition.
udist	Numeric upper distance bound for neighborhood definition.
criteria	Character vector specifying spatial outlier detection methods: "LM" (Local Moran) and/or "MP" (Moran Plot).
zero.policy	Logical. If TRUE, allows empty neighbor sets; if FALSE, stops with an error.
poly_border	Optional sf polygon defining field boundaries. If NULL, a hull is computed automatically.

Details

The depuration process is applied in a fixed sequence:

1. Edge removal ("edges")

2. Global outlier removal ("outlier")

3. Spatial outlier removal ("inlier")

The toremove argument controls which of these steps are applied, but **does not modify the order of execution**.

Available procedures are:

edges

Removes points located within a specified buffer distance from the field boundary. The boundary is computed using a concave hull (concaveman) or a convex hull if the package is not available.

outlier

Removes global outliers based on:

• user-defined limits (ylimitmin, ylimitmax)

• statistical thresholds defined as $mean \pm sdout \times sd$

inlier

Identifies and removes spatial outliers using:

• Local Moran's I statistic ("LM")

• Moran scatterplot influence ("MP")

Default parameter values are tuned for precision agriculture datasets (e.g., yield maps).

Value

An object of class paar (list) with:

depurated_data

Filtered sf object

condition

Character vector indicating the reason each observation was removed (or NA if retained)

References

Vega, A., Córdoba, M., Castro-Franco, M. et al. (2019). Protocol for automating error removal from yield maps. Precision Agriculture, 20, 1030–1044. doi:10.1007/s11119-018-09632-8

Examples

library(sf)
data(barley, package = 'paar')
#Convert to an sf object
barley <- st_as_sf(barley, coords = c("X", "Y"), crs = 32720)

depurated <-
  depurate(barley, "Yield")

# Summary of depurated data
summary(depurated)

# Keep only depurate data
depurated_data <- depurated$depurated_data
# Combine the condition for all data
all_data_condition <- cbind(depurated, barley)

---

Fuzzy k-means clustering (non-spatial)

Description

Performs fuzzy k-means clustering on tabular data (non-spatial). This function is a lightweight wrapper around e1071::cmeans, providing a vectorized workflow and clustering quality indices.

It is primarily intended as a fallback method when spatial clustering (e.g., kmspc) cannot be applied, such as when only one variable is available.

Usage

fuzzy_k_means(
  data,
  variables,
  number_cluster = 3:5,
  fuzzyness = 1.2,
  distance = "euclidean"
)

Arguments

data	an sf object with point geometries
variables	character vector with variable names used for clustering. If missing, all numeric variables in data are used.
number_cluster	numeric vector indicating the number of clusters to evaluate (e.g., 3:5)
fuzzyness	numeric value greater than 1 controlling the degree of fuzziness in clustering (see e1071::cmeans)
distance	character distance metric for clustering. One of "euclidean" or "manhattan" (abbreviations allowed)

Details

Missing values are removed prior to clustering. Observations with missing values are reintroduced in the output with NA cluster assignments.

Clustering is performed for each value in number_cluster, and several indices are returned to assist in selecting the optimal number of clusters:

• Xie-Beni index

• Partition coefficient

• Partition entropy

• Summary index

Value

A list with:

cluster

data.frame with cluster assignments for each evaluated number of clusters

indices

data.frame with clustering validity indices

summaryResults

data.frame with clustering metrics

See Also

kmspc

Examples

library(sf)
data(wheat, package = 'paar')

# Transform the data.frame into a sf object
wheat_sf <- st_as_sf(wheat, coords = c('x', 'y'), crs = 32720)

# Run the fuzzy_k_means function
fuzzy_k_means_results <- fuzzy_k_means(
  wheat_sf,
  variables = 'Tg',
  number_cluster = 2:4
)

# Print the summaryResults
fuzzy_k_means_results$summaryResults

# Print the indices
fuzzy_k_means_results$indices

# Print the cluster
head(fuzzy_k_means_results$cluster, 5)

# Combine the results in a single object
wheat_clustered <- cbind(wheat_sf, fuzzy_k_means_results$cluster)

# Plot the results
plot(wheat_clustered[, "Cluster_2"])

---

Spatial PCA-based fuzzy clustering (MULTISPATI-PCA)

Description

Performs clustering of spatial data using a combination of spatial Principal Component Analysis (PCA), and fuzzy k-means clustering.

The workflow consists of:

1. Dimensionality reduction using spatial PCA

2. Selection of components based on explained spatial variance

3. Fuzzy clustering over selected components

Usage

kmspc(
  data,
  variables,
  number_cluster = 3:5,
  explainedVariance = 70,
  ldist = 0,
  udist = 40,
  center = TRUE,
  fuzzyness = 1.2,
  distance = "euclidean",
  zero.policy = FALSE,
  only_spca_results = TRUE,
  all_results = FALSE
)

Arguments

data	an sf object with point geometries
variables	character vector with variable names used for clustering. If missing, all numeric variables in data are used.
number_cluster	numeric vector indicating the number of clusters to evaluate (e.g., 3:5)
explainedVariance	numeric. Percentage (0–100) of cumulative explained spatial variance used to select spatial principal components. Values between 0 and 1 are interpreted as proportions.
ldist, udist	numeric. Lower and upper distance thresholds used to define spatial neighbors.
center	centering option passed to PCA: TRUE center variables by their mean FALSE no centering numeric custom centering vector
fuzzyness	numeric value greater than 1 controlling the degree of fuzziness in clustering (see e1071::cmeans)
distance	character distance metric for clustering. One of "euclidean" or "manhattan" (abbreviations allowed)
zero.policy	Logical. If TRUE, allows empty neighbor sets; if FALSE, stops with an error.
only_spca_results	logical. If TRUE, only spatial PCA results are returned. If FALSE, both PCA and spatial PCA summaries are included.
all_results	logical. If TRUE, full PCA and spatial PCA objects are returned (can increase computation time and memory use).

Details

Spatial relationships are defined using distance-based neighbors (spdep::dnearneigh). These relationships are incorporated into the spatial PCA analysis to extract spatially structured components.

Clustering is performed using fuzzy c-means over selected spatial components. Several indices are computed to help determine the optimal number of clusters:

• Xie-Beni index

• Partition coefficient

• Partition entropy

• Summary index (normalized combination)

Value

A list with the following elements:

cluster

data.frame with cluster assignments for each evaluated number of clusters

indices

data.frame with clustering validity indices

summaryResults

data.frame with clustering metrics (iterations, SSDW)

pca_results

a list with the spatial PCA results, always present: spca_summary_results (eigenvalues, spatial variance, explained percentage of the total inertia, cumulative percentage and Moran index per axis), eigenvectors_used (variable loadings on the retained axes) and scores (site coordinates on the retained axes, the input of the clustering step). If only_spca_results = FALSE it also contains pca_results with the classical PCA summary, and if all_results = TRUE, the complete pca_results_all and spca_results_all objects.

See Also

[spca_biplot()] to display 'eigenvectors_used' and 'scores' together in a biplot.

Examples

library(sf)
data(wheat, package = 'paar')

# Transform the data.frame into a sf object
wheat_sf <- st_as_sf(wheat, coords = c('x', 'y'), crs = 32720)

# Run the kmspc function
kmspc_results <- kmspc(wheat_sf, number_cluster = 2:4)

# Print the summaryResults
kmspc_results$summaryResults

# Print the indices
kmspc_results$indices

# Print the cluster
head(kmspc_results$cluster, 5)

# Combine the results in a single object
wheat_clustered <- cbind(wheat_sf, kmspc_results$cluster)

# Plot the results
plot(wheat_clustered[, "Cluster_2"])

---

Print paar objects

Description

Print paar objects

Usage

## S3 method for class 'paar'
print(x, n = 3, ...)

Arguments

x	an object used to select a method.
n	an integer vector specifying maximum number of rows or elements to print.
...	further arguments passed to or from other methods.

Value

invisible object x

---

Print summarized paar object

Description

Print summarized paar object

Usage

## S3 method for class 'summary.paar'
print(x, digits, ...)

Arguments

x	an object used to select a method.
digits	minimal number of significant digits, see print.default.
...	further arguments passed to or from other methods.

Value

A data.frame with the summarized condition of the object.

---

Modified t test

Description

Performs a modified t-test to assess the correlation between variables while accounting for spatial autocorrelation. This implementation wraps SpatialPack::modified.ttest.

Usage

spatial_t_test(data, variables)

Arguments

data	An sf object containing geometry and variables, or a matrix/data.frame with two columns representing spatial coordinates (e.g., X and Y).
variables	A character vector with the names of the variables to be tested. If data is not an sf object, this should be a matrix or data.frame of variables to test.

Details

The function computes pairwise correlations between the specified variables and adjusts the significance test to account for spatial dependence using coordinates. If data is an sf object, coordinates are extracted automatically. Otherwise, coordinates must be provided as an object with two columns.

Value

A data.frame with the following columns:

Var1

Name of the first variable

Var2

Name of the second variable

corr

Estimated correlation coefficient

p.value

P-value adjusted for spatial autocorrelation

See Also

modified.ttest

Examples

if (requireNamespace("SpatialPack", quietly = TRUE)) {
  library(sf)
  data(wheat, package = 'paar')

  # Transform the data.frame into a sf object
  wheat_sf <- st_as_sf(wheat, coords = c('x', 'y'), crs = 32720)

  # Run spatial t test
  t_test_results <-
    spatial_t_test(
      wheat_sf,
      variables = c('CE30', 'CE90')
    )

  # Print the t_test_results
  t_test_results
}

---

Biplot of a spatial PCA

Description

Builds a biplot from the spatial principal component analysis computed by [kmspc()]. Sites are drawn as points using their coordinates on the retained spatial components, and variables as arrows from the origin using their loadings.

The biplot complements the clustering output: the angles between arrows approximate the correlations among the original variables, the length of an arrow indicates how well the plotted plane represents that variable, and the position of a site relative to an arrow indicates its relative value for that variable. When management zones are mapped onto the points, it also shows which variables drive the separation between zones.

Usage

spca_biplot(
  x,
  axes = c(1, 2),
  cluster = NULL,
  arrow_scale = NULL,
  point_size = 1,
  point_alpha = 0.6,
  label_size = 3.2
)

Arguments

x	a list returned by [kmspc()].
axes	numeric vector of length two with the spatial components to be plotted.
cluster	optional. Either a character with the name of one of the columns of x$cluster (for example "Cluster_3"), or a vector with one value per site. Points are coloured according to it.
arrow_scale	numeric. Factor applied to the loadings so that the arrows are legible next to the cloud of sites. If NULL (default) it is computed so that the longest arrow spans about 85% of the point cloud. Because the same factor is applied to every arrow, it does not alter their interpretation.
point_size, point_alpha	numeric. Size and opacity of the points.
label_size	numeric. Size of the variable labels.

Details

Note that the sign of a component is arbitrary: the eigendecomposition fixes the direction of each axis but not its orientation, so two runs may produce mirrored biplots without any change in the conclusions. Interpretations should therefore be phrased in terms of relative positions, that is, which variables oppose each other and which go together, rather than in terms of absolute signs.

The correlations suggested by the angles between arrows are computed treating the sites as independent observations. With spatially autocorrelated layers that assumption does not hold, so the magnitudes remain a valid description of the observed association but their statistical significance is misleading. See [spatial_t_test()] for a test that corrects the degrees of freedom by the effective sample size.

Value

A ggplot object, which can be further modified with the usual ggplot2 functions.

See Also

[kmspc()], [spatial_t_test()]

Examples

library(sf)
data(wheat, package = 'paar')

# Transform the data.frame into a sf object
wheat_sf <- st_as_sf(wheat, coords = c('x', 'y'), crs = 32720)

# Run the kmspc function
kmspc_results <- kmspc(wheat_sf, number_cluster = 2:4)

# Biplot of the first two spatial components
spca_biplot(kmspc_results)

# Colouring the sites by the three-zone classification shows which variables
# drive the separation between management zones
spca_biplot(kmspc_results, cluster = "Cluster_3")

---

Summarizing paar objects

Description

Summarizing paar objects

Usage

## S3 method for class 'paar'
summary(object, ...)

Arguments

object	an object for which a summary is desired.
...	additional arguments affecting the summary produced.

Value

An object of class summary.paar (data.frame) with the following columns:

• condition a character vector with the final condition.

• n a numeric vector with the number of rows for each condition.

• percentage a numeric vector with the percentage of rows for each condition.

---

Database from a production field under continuous agriculture

Description

A database from a wheat (Triticum aestivum L.) production field (60 ha) under continuous agriculture, located in south-eastern Pampas, Argentina.

Usage

wheat

Format

A data frame with 5982 rows and 7 variables:

x

X coordinate, in meters

y

Y coordinate, in meters

CE30

apparent electrical conductivity taken at 0–30 cm

CE90

apparent electrical conductivity taken at 0–90 cm

Elev

elevation, in meters

Pe

soil depth, in centimeters

Tg

wheat grain yield

Details

Coordinate reference system is "WGS 84 / UTM zone 20S", epsg:32720 Wheat grain yield was recorded in 2009 using calibrated commercial yield monitors mounted on combines equipped with DGPS. Soil ECa measurements were taken using Veris 3100 (VERIS technologies enr., Salina, KS, USA). Soil depth was measured using a hydraulic penetrometer on a 30 × 30 m regular grid (Peralta et al., 2015). Re-gridding was performed to obtain values of all variables at each intersection point of a 10 × 10 m grid.

References

N.R. Peralta, J.L. Costa, M. Balzarini, M. Castro Franco, M. Córdoba, D. Bullock Delineation of management zones to improve nitrogen management of wheat Comput. Electron. Agric., 110 (2015), pp. 103-113, 10.1016/j.compag.2014.10.017

Paccioretti, P., Córdoba, M., & Balzarini, M. (2020). FastMapping: Software to create field maps and identify management zones in precision agriculture. Computers and Electronics in Agriculture, 175, 105556.

---