Type: Package
Title: Multivariate and Functional Spatial Scan Statistics
Version: 1.0.5
Description: Allows to detect spatial clusters of abnormal values on multivariate or functional data (Frévent et al. (2022) <doi:10.32614/RJ-2022-045>). See also: Frévent et al. (2023) <doi:10.1093/jrsssc/qlad017>, Smida et al. (2022) <doi:10.1016/j.csda.2021.107378>, Frévent et al. (2021) <doi:10.1016/j.spasta.2021.100550>. Cucala et al. (2019) <doi:10.1016/j.spasta.2018.10.002>, Cucala et al. (2017) <doi:10.1016/j.spasta.2017.06.001>, Jung and Cho (2015) <doi:10.1186/s12942-015-0024-6>, Kulldorff et al. (2009) <doi:10.1186/1476-072X-8-58>.
Depends: R (≥ 3.5.0)
License: GPL-3
Encoding: UTF-8
LazyData: true
Imports: Rcpp, parallel, pbapply, purrr, matrixStats, SpatialNP, sp, sf, DT, TeachingDemos, plotrix, fmsb, swfscMisc, raster, graphics, stats, grDevices, methods
LinkingTo: RcppArmadillo, Rcpp
Collate: 'documentation_page.R' 'clusters.R' 'permutations.R' 'gaussian_multi.R' 'wmw_multi.R' 'wmw_fonc.R' 'scan_fonc.R' 'scan_multi.R' 'plot_map.R' 'RcppExports.R' 'dfree_index_multi.R' 'pointwise_dfree.R' 'pointwise_wmw_multi.R' 'pointwise_wmw_uni.R' 'transform_data.R' 'data_fmulti_data.R' 'data_funi_data.R' 'data_multi_data.R' 'data_map_sites.R' 'posteriori_filtering.R' 'non_overlap.R' 'scan_uni.R' 'wmw_uni.R' 'dfree.R' 'finalizing_scan_procedure.R' 'HDSpatialScan_plot.R' 'HDSpatialScan_Classes.R' 'HDSpatialScan_plotCurves.R' 'HDSpatialScan_plotSummary.R' 'HDSpatialScan_print.R' 'HDSpatialScan_summary.R' 'InitScan.R' 'SpatialScan.R'
RoxygenNote: 7.3.1
Suggests: knitr, rmarkdown
NeedsCompilation: yes
Packaged: 2025-06-05 13:55:52 UTC; cfrevent
Author: Camille FREVENT [aut, cre, cph], Mohamed-Salem AHMED [aut], Julien SOULA [aut], Zaineb SMIDA [aut], Lionel CUCALA [aut], Sophie DABO-NIANG [aut], Michaël GENIN [aut]
Maintainer: Camille FREVENT <camille.frevent@univ-lille.fr>
Repository: CRAN
Date/Publication: 2025-06-05 16:10:10 UTC

Multivariate and Functional Spatial Scan Statistics

Description

Allows to detect spatial clusters of abnormal values on multivariate or functional data.

Details

Package: HDSpatialScan
Type: Package
Version: 1.0.5
Date: 2025-06-05
License: GPL-3
LazyLoad: yes

Author(s)

FREVENT Camille, AHMED Mohamed-Salem, SOULA Julien, SMIDA Zaineb, CUCALA Lionel, DABO-NIANG Sophie and GENIN Michaël. Maintainer: FREVENT Camille <camille.frevent@univ-lille.fr>

References

Martin Kulldorff and Lan Huang and Kevin Konty (2009). A Scan Statistic for Continuous Data Based on the Normal Probability Model. International Journal of Health Geographics, 8 (58).

Inkyung Jung and Ho Jin Cho (2015). A Nonparametric Spatial Scan Statistic for Continuous Data. International Journal of Health Geographics, 14.

Lionel Cucala and Michaël Genin and Caroline Lanier and Florent Occelli (2017). A Multivariate Gaussian Scan Statistic for Spatial Data. Spatial Statistics, 21, 66-74.

Lionel Cucala and Michaël Genin and Florent Occelli and Julien Soula (2019). A Multivariate Nonparametric Scan Statistic for Spatial Data. Spatial statistics, 29, 1-14.

Camille Frévent and Mohamed-Salem Ahmed and Matthieu Marbac and Michaël Genin (2021). Detecting Spatial Clusters in Functional Data: New Scan Statistic Approaches. Spatial Statistics, 46.

Zaineb Smida and Lionel Cucala and Ali Gannoun and Ghislain Durif (2022). A Wilcoxon-Mann-Whitney spatial scan statistic for functional data. Computational Statistics & Data Analysis, 167.

Camille Frévent and Mohamed-Salem Ahmed and Sophie Dabo-Niang and Michaël Genin (2023). Investigating Spatial Scan Statistics for Multivariate Functional Data. Journal of the Royal Statistical Society Series C: Applied Statistics, 72(2), 450-475.

DFFSS scan procedure

Description

This function computes the DFFSS (Distribution-Free Functional scan statistic).

Usage

DFFSS(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

matrix. Matrix of the data, the rows correspond to the sites (or to the individuals if the observations are by individuals and not by sites) and each column represents an observation time. The times must be the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputUniFunct.

References

Camille Frévent and Mohamed-Salem Ahmed and Matthieu Marbac and Michaël Genin (2021). Detecting Spatial Clusters in Functional Data: New Scan Statistic Approaches. Spatial Statistics, 46.

Finalization of the scan procedures

Description

This function finalizes the scan procedures.

Usage

FinScan(
  index_clusters_temp,
  index,
  filtering_post,
  type_minimaxi_post,
  mini_post,
  maxi_post,
  nb_sites,
  matrix_clusters,
  radius,
  areas,
  centres,
  pvals,
  maximize = TRUE
)

Arguments

index_clusters_temp

numeric vector. Indices of the significant clusters.

index

numeric vector. Index of concentration for each potential cluster.

filtering_post

logical. Is there an a posteriori filtering?

type_minimaxi_post

character. Type of minimum and maximum a posteriori: by default "sites/indiv": the mini_post and maxi_post are on the number of sites or individuals in the significant clusters. Other possible values are "area": the minimum and maximum area of the clusters, or "radius": the minimum and maximum radius.

mini_post

numeric. A minimum to filter the significant clusters a posteriori (see type_minimaxi_post). The default NULL is for no filtering with a a posteriori minimum.

maxi_post

numeric. A maximum to filter the significant clusters a posteriori (see type_minimaxi_post). The default NULL is for no filtering with a a posteriori maximum.

nb_sites

numeric. The number of considered sites or individuals.

matrix_clusters

matrix. The matrix of potential clusters taking the value 1 at lign i and column j if the cluster j contains the site i, 0 otherwise.

radius

numeric vector. The radius of the potential clusters.

areas

numeric vector. The areas of the potential clusters.

centres

numeric matrix. The coordinates of the centres of each potential cluster.

pvals

numeric vector. The pvalue of each potential cluster.

maximize

logical. Should the index be maximized? By default TRUE. If FALSE it will be minimized.

Value

The list of the following elements:

Initalization of the scan procedures by creating the matrix of potential clusters

Description

This function initializes the scan procedures by creating the matrix of potential clusters.

Usage

InitScan(
  mini_post,
  maxi_post,
  type_minimaxi_post,
  sites_areas,
  sites_coord,
  system,
  mini,
  maxi,
  type_minimaxi
)

Arguments

mini_post

numeric. A minimum to filter the significant clusters a posteriori (see type_minimaxi_post). The default NULL is for no filtering with a a posteriori minimum.

maxi_post

numeric. A maximum to filter the significant clusters a posteriori (see type_minimaxi_post). The default NULL is for no filtering with a a posteriori maximum.

type_minimaxi_post

character. Type of minimum and maximum a posteriori: by default "sites/indiv": the mini_post and maxi_post are on the number of sites or individuals in the significant clusters. Other possible values are "area": the minimum and maximum area of the clusters, or "radius": the minimum and maximum radius.

sites_areas

numeric vector. Areas of the sites. It must contain the same number of elements than the rows of sites_coord. If the data is on individuals and not on sites, there can be duplicated values. By default: NULL

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

mini

integer. A minimum for the clusters (see type_minimaxi). Changing the default value may bias the inference.

maxi

integer. A Maximum for the clusters (see type_minimaxi). Changing the default value may bias the inference.

type_minimaxi

character. Type of minimum and maximum: by default "sites/indiv": the mini and maxi are on the number of sites or individuals in the potential clusters. Other possible values are "area": the minimum and maximum area of the clusters, or "radius": the minimum and maximum radius.

Value

The list of the following elements:

MDFFSS scan procedure

Description

This function computes the MDFFSS (Multivariate Distribution-Free Functional scan statistic).

Usage

MDFFSS(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  variable_names = NULL,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

list of numeric matrices. List of nb_sites (or nb_individuals if the observations are by individuals and not by sites) matrices of the data, the rows correspond to the variables and each column represents an observation time. The times must be the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

variable_names

character. Names of the variables. By default NULL.

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputMultiFunct.

References

Camille Frévent and Mohamed-Salem Ahmed and Sophie Dabo-Niang and Michaël Genin (2023). Investigating Spatial Scan Statistics for Multivariate Functional Data. Journal of the Royal Statistical Society Series C: Applied Statistics, 72(2), 450-475.

MG scan procedure

Description

This function computes the MG (Multivariate Gaussian scan statistic).

Usage

MG(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  variable_names = NULL,
  initialization,
  permutations
)

Arguments

data

matrix. Matrix of the data, the rows correspond to the sites (or the individuals if the observations are by individuals and not by sites) and each column represents a variable.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

variable_names

character. Names of the variables. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputMulti.

References

Lionel Cucala and Michaël Genin and Caroline Lanier and Florent Occelli (2017). A Multivariate Gaussian Scan Statistic for Spatial Data. Spatial Statistics, 21, 66-74.

MNP scan procedure

Description

This function computes the MNP (Multivariate Nonparametric scan statistic).

Usage

MNP(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  variable_names = NULL,
  initialization,
  permutations
)

Arguments

data

matrix. Matrix of the data, the rows correspond to the sites (or the individuals if the observations are by individuals and not by sites) and each column represents a variable.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

variable_names

character. Names of the variables. By default NULL

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputMulti.

References

Lionel Cucala and Michaël Genin and Florent Occelli and Julien Soula (2019). A Multivariate Nonparametric Scan Statistic for Spatial Data. Spatial statistics, 29, 1-14.

MPFSS scan procedure

Description

This function computes the MPFSS (Parametric Multivariate Functional scan statistic).

Usage

MPFSS(
  data,
  MC = 999,
  typeI = 0.05,
  method = c("LH", "W", "P", "R"),
  nbCPU = 1,
  variable_names = NULL,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

list of numeric matrices. List of nb_sites (or nb_individuals if the observations are by individuals and not by sites) matrices of the data, the rows correspond to the variables and each column represents an observation time. The times must be equally spaced and the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

method

character vector. The methods to compute the significant clusters. Options: "LH", "W", "P", "R" for respectively the Lawley-Hotelling trace test statistic, The Wilks lambda test statistic, the Pillai trace test statistic and the Roy's maximum root test statistic. By default all are computed.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

variable_names

character. Names of the variables. By default NULL.

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

List of objects of class ResScanOutputMultiFunct (one element by method)

References

Camille Frévent and Mohamed-Salem Ahmed and Sophie Dabo-Niang and Michaël Genin (2023). Investigating Spatial Scan Statistics for Multivariate Functional Data. Journal of the Royal Statistical Society Series C: Applied Statistics, 72(2), 450-475.

MRBFSS scan procedure

Description

This function computes the MRBFSS (Multivariate Rank-Based Functional scan statistic).

Usage

MRBFSS(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  variable_names = NULL,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

list of numeric matrices. List of nb_sites (or nb_individuals if the observations are by individuals and not by sites) matrices of the data, the rows correspond to the variables and each column represents an observation time. The times must be the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

variable_names

character. Names of the variables. By default NULL.

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputMultiFunct

References

Camille Frévent and Mohamed-Salem Ahmed and Sophie Dabo-Niang and Michaël Genin (2023). Investigating Spatial Scan Statistics for Multivariate Functional Data. Journal of the Royal Statistical Society Series C: Applied Statistics, 72(2), 450-475.

NPFSS scan procedure (univariate functional or multivariate functional)

Description

This function computes the NPFSS (Nonparametric Functional scan statistic for multivariate or univariate functional data).

Usage

NPFSS(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  variable_names = NULL,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

list of numeric matrices or a matrix. List of nb_sites (or nb_individuals if the observations are by individuals and not by site) matrices of the data, the rows correspond to the variables and each column represents an observation time (multivariate case) ; or Matrix of the data, the rows correspond to the sites (or to the individuals) and each column represents an observation time (univariate case). The times must be equally spaced and the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

variable_names

character. Names of the variables. By default NULL. Ignored if the data is a matrix (univariate functional case).

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputUniFunct or ResScanOutputMultiFunct depending on the data

References

Zaineb Smida and Lionel Cucala and Ali Gannoun and Ghislain Durif (2022). A Wilcoxon-Mann-Whitney spatial scan statistic for functional data. Computational Statistics & Data Analysis, 167.

PFSS scan procedure

Description

This function computes the PFSS (Parametric Functional scan statistic).

Usage

PFSS(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

matrix. Matrix of the data, the rows correspond to the sites (or to the individuals if the observations are by individuals and not by sites) and each column represents an observation time. The times must be equally spaced and the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputUniFunct.

References

Camille Frévent and Mohamed-Salem Ahmed and Matthieu Marbac and Michaël Genin (2021). Detecting Spatial Clusters in Functional Data: New Scan Statistic Approaches. Spatial Statistics, 46.

Constructor function for objects of the ResScanOutput class

Description

This is the constructor function for objects of the ResScanOutput class.

Usage

ResScanOutput(
  sites_clusters,
  pval_clusters,
  centres_clusters,
  radius_clusters,
  areas_clusters,
  system,
  sites_coord,
  data,
  method
)

Arguments

sites_clusters

list. List of the indices of the sites of the selected clusters.

pval_clusters

numeric vector. The pvalues of the selected clusters.

centres_clusters

numeric matrix. Coordinates of the centres of the selected clusters.

radius_clusters

numeric vector. Radius of the selected clusters.

areas_clusters

numeric vector. Areas of the selected clusters.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

data

list of numeric matrices or a matrix or a vector. List of nb_sites (or nb_individuals if the observations are by individuals and not by site) matrices of the data, the rows correspond to the variables and each column represents an observation time (multivariate functional case) ; or Matrix of the data, the rows correspond to the sites (or to the individuals) and each column represents an observation time (univariate functional case) or a variable (multivariate case) ; or Vector of the data, the elements correspond to the sites (or to the individuals) (univariate case).

method

character. The scan procedure used.

Value

An object of class ResScanOutput which is a list of the following elements:

Constructor function for objects of the ResScanOutputMulti class

Description

This is the constructor function for objects of the ResScanOutputMulti class which inherits from class ResScanOutput.

Usage

ResScanOutputMulti(
  sites_clusters,
  pval_clusters,
  centres_clusters,
  radius_clusters,
  areas_clusters,
  system,
  variable_names = NULL,
  sites_coord,
  data,
  method
)

Arguments

sites_clusters

list. List of the indices of the sites of the selected clusters.

pval_clusters

numeric vector. The pvalues of the selected clusters.

centres_clusters

numeric matrix. Coordinates of the centres of the selected clusters.

radius_clusters

numeric vector. Radius of the selected clusters.

areas_clusters

numeric vector. Areas of the selected clusters.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

variable_names

character. Names of the variables. By default NULL.

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

data

matrix. Matrix of the data, the rows correspond to the sites (or to the individuals) and each column represents a variable.

method

character. The scan procedure used.

Value

An object of class ResScanOutputMulti which is a list of the following elements:

Constructor function for objects of the ResScanOutputMultiFunct class

Description

This is the constructor function for objects of the ResScanOutputMultiFunct class which inherits from class ResScanOutput.

Usage

ResScanOutputMultiFunct(
  sites_clusters,
  pval_clusters,
  centres_clusters,
  radius_clusters,
  areas_clusters,
  system,
  times = NULL,
  variable_names = NULL,
  sites_coord,
  data,
  method
)

Arguments

sites_clusters

list. List of the indices of the sites of the selected clusters.

pval_clusters

numeric vector. The pvalues of the selected clusters.

centres_clusters

numeric matrix. Coordinates of the centres of the selected clusters.

radius_clusters

numeric vector. Radius of the selected clusters.

areas_clusters

numeric vector. Areas of the selected clusters.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

times

numeric. Times of observation of the data. By default NULL.

variable_names

character. Names of the variables. By default NULL.

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

data

list of numeric matrices. List of nb_sites (or nb_individuals if the observations are by individuals and not by site) matrices of the data, the rows correspond to the variables and each column represents an observation time.

method

character. The scan procedure used.

Value

An object of class ResScanOutputMultiFunct which is a list of the following elements:

Constructor function for objects of the ResScanOutputUni class

Description

This is the constructor function for objects of the ResScanOutputUni class which inherits from class ResScanOutput.

Usage

ResScanOutputUni(
  sites_clusters,
  pval_clusters,
  centres_clusters,
  radius_clusters,
  areas_clusters,
  system,
  sites_coord,
  data,
  method
)

Arguments

sites_clusters

list. List of the indices of the sites of the selected clusters.

pval_clusters

numeric vector. The pvalues of the selected clusters.

centres_clusters

numeric matrix. Coordinates of the centres of the selected clusters.

radius_clusters

numeric vector. Radius of the selected clusters.

areas_clusters

numeric vector. Areas of the selected clusters.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

data

vector. Vector of the data, the elements correspond to the sites (or to the individuals).

method

character. The scan procedure used.

Value

An object of class ResScanOutputUni which is a list of the following elements:

Constructor function for objects of the ResScanOutputUniFunct class

Description

This is the constructor function for objects of the ResScanOutputUniFunct class which inherits from class ResScanOutput.

Usage

ResScanOutputUniFunct(
  sites_clusters,
  pval_clusters,
  centres_clusters,
  radius_clusters,
  areas_clusters,
  system,
  times = NULL,
  sites_coord,
  data,
  method
)

Arguments

sites_clusters

list. List of the indices of the sites of the selected clusters.

pval_clusters

numeric vector. The pvalues of the selected clusters.

centres_clusters

numeric matrix. Coordinates of the centres of the selected clusters.

radius_clusters

numeric vector. Radius of the selected clusters.

areas_clusters

numeric vector. Areas of the selected clusters.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

times

numeric. Times of observation of the data. By default NULL.

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

data

matrix. Matrix of the data, the rows correspond to the sites (or to the individuals) and each column represents an observation time.

method

character. The scan procedure used.

Value

An object of class ResScanOutputUniFunct which is a list of the following elements:

Spatial scan procedure

Description

This function computes the different scan procedures available in the package.

Usage

SpatialScan(
  method,
  data,
  sites_coord = NULL,
  system = NULL,
  mini = 1,
  maxi = nrow(sites_coord)/2,
  type_minimaxi = "sites/indiv",
  mini_post = NULL,
  maxi_post = NULL,
  type_minimaxi_post = "sites/indiv",
  sites_areas = NULL,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  variable_names = NULL,
  times = NULL
)

Arguments

method

character vector. The scan procedures to apply on the data. Possible values are:

  • Univariate scan procedures: "UG" (univariate gaussian, see UG), "UNP" (univariate nonparametric, see UNP)

  • Multivariate scan procedures: "MG" (multivariate gaussian, see MG), "MNP" (multivariate nonparametric, see MNP)

  • Univariate functional scan procedures: "NPFSS" (nonparametric functional scan statistic, see NPFSS), "PFSS" (parametric functional scan statistic, see PFSS), "DFFSS" (distribution-free functional scan statistic, see DFFSS), "URBFSS" (univariate rank-based functional scan statistic, see URBFSS)

  • Multivariate functional scan procedures: "NPFSS" (nonparametric functional scan statistic, see NPFSS), "MDFFSS" (multivariate distribution-free functional scan statistic, see MDFFSS), "MRBFSS" (multivariate rank-based functional scan statistic, see MRBFSS), "MPFSS", "MPFSS-LH", "MPFSS-W", "MPFSS-P" and "MPFSS-R" (parametric multivariate functional scan statistic ; "LH", "W", "P", "R" correspond respectively to the Lawley-Hotelling trace test statistic, The Wilks lambda test statistic, the Pillai trace test statistic and the Roy's maximum root test statistic, see MPFSS). Note that "MPFSS" computes "MPFSS-LH", "MPFSS-W", "MPFSS-P" and "MPFSS-R".

data

list of numeric matrices or a matrix or a vector:

  • Univariate case: Vector of the data, each element corresponds to a site (or an individual if the observations are by individuals and not by sites).

  • Multivariate case: Matrix of the data, the rows correspond to the sites (or the individuals if the observations are by individuals and not by sites) and each column represents a variable.

  • Univariate functional case: Matrix of the data, the rows correspond to the sites (or to the individuals if the observations are by individuals and not by sites) and each column represents an observation time. The times must be the same for each site/individual. Depending on the scan procedure they also need to be equally-spaced.

  • Multivariate functional case: List of nb_sites (or nb_individuals if the observations are by individuals and not by sites) matrices of the data, the rows correspond to the variables and each column represents an observation time. The times must be the same for each site/individual. Depending on the scan procedure they also need to be equally-spaced.

sites_coord

numeric matrix. Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

mini

numeric. A minimum for the clusters (see type_minimaxi). Changing the default value may bias the inference.

maxi

numeric. A Maximum for the clusters (see type_minimaxi). Changing the default value may bias the inference.

type_minimaxi

character. Type of minimum and maximum: by default "sites/indiv": the mini and maxi are on the number of sites or individuals in the potential clusters. Other possible values are "area": the minimum and maximum area of the clusters, or "radius": the minimum and maximum radius.

mini_post

numeric. A minimum to filter the significant clusters a posteriori (see type_minimaxi_post). The default NULL is for no filtering with a a posteriori minimum.

maxi_post

numeric. A maximum to filter the significant clusters a posteriori (see type_minimaxi_post). The default NULL is for no filtering with a a posteriori maximum.

type_minimaxi_post

character. Type of minimum and maximum a posteriori: by default "sites/indiv": the mini_post and maxi_post are on the number of sites or individuals in the significant clusters. Other possible values are "area": the minimum and maximum area of the clusters, or "radius": the minimum and maximum radius.

sites_areas

numeric vector. Areas of the sites. It must contain the same number of elements than the rows of sites_coord. If the data is on individuals and not on sites, there can be duplicated values. By default: NULL

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1. Ignored for "UG" and "UNP"

variable_names

character. Names of the variables. By default NULL. Ignored for the univariate and univariate functional scan procedures.

times

numeric. Times of observation of the data. By default NULL. Ignored for the univariate and multivariate scan procedures.

Value

A list of objects of class ResScanOutput:

References

For univariate scan statistics:

For multivariate scan statistics:

For functional scan statistics:

See Also

ResScanOutput, ResScanOutputUni, ResScanOutputMulti, ResScanOutputUniFunct and ResScanOutputMultiFunct

Examples

# Univariate scan statistics

library(sp)
data("map_sites")
data("multi_data")
uni_data <- multi_data[,1]
coords <- coordinates(map_sites)
res <- SpatialScan(method = c("UG", "UNP"), data = uni_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)

# Multivariate scan statistics

library(sp)
data("map_sites")
data("multi_data")
coords <- coordinates(map_sites)
res <- SpatialScan(method = c("MG", "MNP"), data = multi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)

# Univariate functional scan statistics

library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)
res <- SpatialScan(method = c("NPFSS", "PFSS", "DFFSS", "URBFSS"), data = funi_data,
sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)

# Multivariate functional

library(sp)
data("map_sites")
data("fmulti_data")
coords <- coordinates(map_sites)
res <- SpatialScan(method = c("NPFSS", "MPFSS", "MDFFSS", "MRBFSS"), data = fmulti_data,
sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)

UG scan procedure

Description

This function computes the UG (Univariate Gaussian scan statistic).

Usage

UG(data, MC = 999, typeI = 0.05, initialization, permutations)

Arguments

data

vector. Vector of the data, each element corresponds to a site (or an individual if the observations are by individuals and not by sites).

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputUni.

References

Martin Kulldorff and Lan Huang and Kevin Konty (2009). A Scan Statistic for Continuous Data Based on the Normal Probability Model. International Journal of Health Geographics, 8 (58).

UNP scan procedure

Description

This function computes the UNP (Univariate Nonparametric scan statistic).

Usage

UNP(data, MC = 999, typeI = 0.05, initialization, permutations)

Arguments

data

vector. Vector of the data, each element corresponds to a site (or an individual if the observations are by individuals and not by sites).

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputUni.

References

Inkyung Jung and Ho Jin Cho (2015). A Nonparametric Spatial Scan Statistic for Continuous Data. International Journal of Health Geographics, 14.

URBFSS scan procedure

Description

This function computes the URBFSS (Univariate Rank-Based Functional scan statistic).

Usage

URBFSS(
  data,
  MC = 999,
  typeI = 0.05,
  nbCPU = 1,
  times = NULL,
  initialization,
  permutations
)

Arguments

data

matrix. Matrix of the data, the rows correspond to the sites (or to the individuals if the observations are by individuals and not by sites) and each column represents an observation time. The times must be the same for each site/individual.

MC

numeric. Number of Monte-Carlo permutations to evaluate the statistical significance of the clusters. By default: 999.

typeI

numeric. The desired type I error. A cluster will be evaluated as significant if its associated p-value is less than typeI. By default 0.05.

nbCPU

numeric. Number of CPU. If nbCPU > 1 parallelization is done. By default: 1.

times

numeric. Times of observation of the data. By default NULL.

initialization

list. Initialization for the scan procedure (see InitScan for more details).

permutations

matrix. Indices of permutations of the data.

Value

An object of class ResScanOutputUniFunct.

See Also

MRBFSS which is the multivariate version of the URBFSS

Creation of the matrix of potential clusters

Description

This function creates the matrix in which each column corresponds to a potential clusters, taking the value 1 when a site (or an individual) is in the potential cluster and 0 otherwise.

Usage

clusters(sites_coord, system, mini, maxi, type_minimaxi, sites_areas)

Arguments

sites_coord

numeric matrix. Matrix of the coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates). It has the same number of rows as the number of sites or individuals and 2 columns.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

mini

numeric. Minimum for the clusters (see type_minimaxi).

maxi

numeric. Maximum for the clusters (see type_minimaxi).

type_minimaxi

character. Type of minimum and maximum: "area": the minimum and maximum area of the clusters, "radius": the minimum and maximum radius, or "sites/indiv": the minimum and maximum number of sites or individuals in the clusters.

sites_areas

numeric vector. Areas of the sites. It must contain the same number of elements than the rows of sites_coord. If the data is on individuals and not on sites, there can be duplicated values. By default: NULL

Value

The list of the following elements:

Index for the UG scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster and each permutation

Usage

dfree(data, matrix_clusters)

Arguments

data

numeric matrix. Matrix of the data. The rows correspond to the sites (or the individuals) and each column represents a permutation.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric matrix.

Index for the MDFFSS scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

dfree_index_multi(data, matrix_clusters)

Arguments

data

List. List of the data, each element of the list corresponds to a site (or an individual), for each element each row corresponds to a variable and each column represents an observation time.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

Multivariate functional data

Description

Concentrations over the time of NO2, O3, PM10 and PM2.5 from 2020/05/01 to 2020/06/25 in each canton (administrative subdivision) of Nord-Pas-de-Calais (a region from France).

Usage

data("fmulti_data")

Format

A list of 169 elements. Each element corresponds to a canton and is a matrix of 56 columns (for the 56 days of observation) and 4 rows (4 variables, in the order NO2, O3, PM10 and PM2.5).

References

Data from the National Air Quality Forecasting Platform www.prevair.org

Univariate functional data

Description

Concentration over the time of the pollutant NO2 from 2020/05/01 to 2020/06/25 in each canton (administrative subdivision) of Nord-Pas-de-Calais (a region from France).

Usage

data("funi_data")

Format

A matrix of 169 rows and 56 columns. Each row corresponds to a canton, and each column is an observation time (a day). The 56 observation times are thus equally spaced times.

References

Data from the National Air Quality Forecasting Platform www.prevair.org

Spatial object corresponding to the sites of the data of the package HDSpatialScan

Description

Spatial object corresponding to the sites (169 cantons) of the data of the package HDSpatialScan.

Usage

data("map_sites")

Format

A SpatialPolygonsDataFrame.

Index for the MNP scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

multi_WMW(rank_data, matrix_clusters)

Arguments

rank_data

numeric matrix. Matrix of the ranks of the initial data, the rows correspond to the sites (or the individuals) and each column represents a variable.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

Multivariate non-functional data

Description

Average concentrations over the time of NO2, O3, PM10 and PM2.5 from 2020/05/01 to 2020/06/25 in each canton (administrative subdivision) of Nord-Pas-de-Calais (a region from France).

Usage

data("multi_data")

Format

A matrix of 169 rows and 4 columns. Each row corresponds to a canton, and each column is a concentration mean in the order NO2, O3, PM10 and PM2.5.

References

Data from the National Air Quality Forecasting Platform www.prevair.org

Index for the NPFSS scan procedure (multivariate functional case)

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

multi_fWMW(signs, matrix_clusters)

Arguments

signs

list of numeric matrices. List of nb_sites (or nb_individuals) sign matrices, the rows correspond to the variables and each column represents an observation time.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

Index for the MG scan procedure

Description

This function returns the index we want to minimize on the set of potential clusters, for each potential cluster

Usage

multi_gaussian(data, matrix_clusters)

Arguments

data

numeric matrix. Matrix of the data, the rows correspond to the sites (or individuals) and each column represents a variable.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

List of matrix of signs (multivariate functional data)

Description

This function returns the list of matrix of signs for the multivariate functional data

Usage

multi_signs_matrix(data)

Arguments

data

list of numeric matrices. List of nb_sites (or nb_individuals) matrices of the data, the rows correspond to the variables and each column represents an observation time.

Value

list of numeric matrices.

Return only the detected clusters with no overlapping in their order of detection

Description

This function allows to return only the detected clusters with no overlapping in their order of detection.

Usage

non_overlap(index_clusters, matrix_clusters)

Arguments

index_clusters

numeric vector. The indices of the detected clusters.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. A value of 1 indicate that the site (or the individual) is in the cluster, 0 otherwise.

Value

The detecting clusters with no overlapping, in their order of detection.

Permutates the data

Description

This function will permit to permute the data for the MC simulations

Usage

permutate(to_permute, nb_permu)

Arguments

to_permute

vector. Vector of indices we want to permute.

nb_permu

numeric. Number of permutations.

Value

matrix. Matrix of nb_permu rows and length(to_permute) columns.

Schema or map of the clusters

Description

This function plots a schema or a map of the sites and the clusters

Usage

## S3 method for class 'ResScanOutput'
plot(
  x,
  type,
  spobject = NULL,
  system_conv = NULL,
  colors = "red",
  only.MLC = FALSE,
  ...
)

Arguments

x

ResScanOutput. Output of a scan function (UG, UNP, MG, MNP, PFSS, DFFSS, URBFSS, NPFSS, MPFSS, MDFFSS or MRBFSS)

type

character. Type of plot: "schema", "map" (the clusters are represented by circles) or "map2" (the clusters are colored on the map)

spobject

SpObject. SpatialObject with the same coordinates system the one used for the scan. Only considered if type is "map" or "map2"

system_conv

character. System to convert the coordinates for the plot. Only considered if the system used in the scan was "WGS84" and if type is "schema". Else it will be ignored. Must be entered as in the PROJ.4 documentation

colors

character. Colors of the clusters. If length(colors)=1 all the clusters will be in this color. Else it should be a vector of length the number of clusters to plot.

only.MLC

logical. Should we plot only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, plots a schema or a map of the sites and the clusters.

Examples


library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

plot(x = res_npfss, type = "schema", system_conv = "+init=epsg:2154")
plot(x = res_npfss, type = "map", spobject = map_sites)
plot(x = res_npfss, type = "map2", spobject = map_sites)

Generic function to plot curves

Description

This function is a generic function to plot curves.

Usage

plotCurves(x, ...)

Arguments

x

An object for which the curves are to be plotted.

...

Additional arguments affecting the output.

Value

No value returned, plots the curves.

See Also

plotCurves.ResScanOutputUniFunct and plotCurves.ResScanOutputMultiFunct

Examples


library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84",
mini = 1, maxi = nrow(coords)/2)$NPFSS

plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)

Plots the curves in the clusters detected by the multivariate functional scan functions (MPFSS, NPFSS, MDFFSS or MRBFSS)

Description

This function plot the curves in the clusters detected by the multivariate functional scan functions (MPFSS, NPFSS, MDFFSS or MRBFSS).

Usage

## S3 method for class 'ResScanOutputMultiFunct'
plotCurves(
  x,
  add_mean = FALSE,
  add_median = FALSE,
  colors = "red",
  only.MLC = FALSE,
  ...
)

Arguments

x

ResScanOutputMultiFunct. Output of a multivariate functional scan function (MPFSS, NPFSS, MDFFSS or MRBFSS).

add_mean

boolean. If TRUE it adds the global mean curve in black.

add_median

boolean. If TRUE it adds the global median curve in blue.

colors

character. The colors to plot the clusters' curves. If length(colors)==1 then all the clusters will be plotted in this color. Else there must be the same number of elements in colors than the number of clusters

only.MLC

logical. Should we plot only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, plots the curves.

Examples


library(sp)
data("map_sites")
data("fmulti_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = fmulti_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)

Plots the curves in the clusters detected by the univariate functional scan functions (PFSS, NPFSS, DFFSS or URBFSS)

Description

This function plot the curves in the clusters detected by the univariate functional scan functions (PFSS, NPFSS, DFFSS or URBFSS).

Usage

## S3 method for class 'ResScanOutputUniFunct'
plotCurves(
  x,
  add_mean = FALSE,
  add_median = FALSE,
  colors = "red",
  only.MLC = FALSE,
  ...
)

Arguments

x

ResScanOutputUniFunct. Output of a univariate functional scan function (PFSS, NPFSS, DFFSS or URBFSS).

add_mean

boolean. If TRUE it adds the global mean curve in black.

add_median

boolean. If TRUE it adds the global median curve in blue.

colors

character. The colors to plot the clusters' curves. If length(colors)==1 then all the clusters will be plotted in this color. Else there must be the same number of elements in colors than the number of clusters

only.MLC

logical. Should we plot only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, plots the curves.

Examples


library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)

Generic function to plot a summary

Description

This function is a generic function to plot a summary.

Usage

plotSummary(x, ...)

Arguments

x

An object for which the summary is to be plotted.

...

Additional arguments affecting the summary produced.

Value

No value returned, plots the summary.

See Also

plotSummary.ResScanOutputMulti, plotSummary.ResScanOutputUniFunct and plotSummary.ResScanOutputMultiFunct

Examples


library(sp)
data("map_sites")
data("multi_data")
coords <- coordinates(map_sites)

res_mnp <- SpatialScan(method = "MNP", data = multi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2,
variable_names = c("NO2", "O3", "PM10", "PM2.5"))$MNP

plotSummary(x = res_mnp, type = "mean")

Plots the mean or median spider chart of the clusters detected by a multivariate scan function (MG or MNP)

Description

This function plots the mean or median spider chart of the clusters detected by a multivariate scan function (MG or MNP).

Usage

## S3 method for class 'ResScanOutputMulti'
plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)

Arguments

x

ResScanOutputMulti. Output of a multivariate scan function (MG or MNP).

type

character. "mean" or "median". If "mean": the means in the clusters are plotted in solid lines, outside the cluster in dots, the global mean is in black. If "median": the medians in the clusters are plotted in solid lines, outside the cluster in dots, the global median is in black.

colors

character. The colors to plot the clusters' summaries. If length(colors)==1 then all the clusters will be plotted in this color. Else there must be the same number of elements in colors than the number of clusters

only.MLC

logical. Should we plot only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, plots the spider chart.

Examples


library(sp)
data("map_sites")
data("multi_data")
coords <- coordinates(map_sites)

res_mnp <- SpatialScan(method = "MNP", data=multi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2,
variable_names = c("NO2", "O3", "PM10", "PM2.5"))$MNP

plotSummary(x = res_mnp, type = "mean")

Plots the mean or median curves in the clusters detected by a multivariate functional scan procedure (MPFSS, NPFSS, MDFFSS or MRBFSS)

Description

This function plots the mean or median curves in the clusters detected by a multivariate functional scan procedure (MPFSS, NPFSS, MDFFSS or MRBFSS).

Usage

## S3 method for class 'ResScanOutputMultiFunct'
plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)

Arguments

x

ResScanOutputMultiFunct. Output of a multivariate functional scan function (MPFSS, NPFSS, MDFFSS or MRBFSS).

type

character. "mean" or "median". If "mean": the mean curves in the clusters are plotted in solid lines, outside the cluster in dots, the global mean curve is in black. If "median": the median curves in the clusters are plotted in solid lines, outside the cluster in dots, the global median curve is in black.

colors

character. The colors to plot the clusters' summary curves. If length(colors)==1 then all the clusters will be plotted in this color. Else there must be the same number of elements in colors than the number of clusters

only.MLC

logical. Should we plot only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, plots the curves.

Examples


library(sp)
data("map_sites")
data("fmulti_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = fmulti_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

plotSummary(x = res_npfss, type = "median")

Plots the mean or median curves in the clusters detected by a univariate functional scan procedure (PFSS, NPFSS, DFFSS or URBFSS)

Description

This function plots the mean or median curves in the clusters detected by a univariate functional scan procedure (PFSS, NPFSS, DFFSS or URBFSS).

Usage

## S3 method for class 'ResScanOutputUniFunct'
plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)

Arguments

x

ResScanOutputUniFunct. Output of a univariate functional scan function (PFSS, NPFSS, DFFSS or URBFSS).

type

character. "mean" or "median". If "mean": the mean curves in the clusters are plotted in solid lines, outside the cluster in dots, the global mean curve is in black. If "median": the median curves in the clusters are plotted in solid lines, outside the cluster in dots, the global median curve is in black.

colors

character. The colors to plot the clusters' summary curves. If length(colors)==1 then all the clusters will be plotted in this color. Else there must be the same number of elements in colors than the number of clusters

only.MLC

logical. Should we plot only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, plots the curves.

Examples


library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

plotSummary(x = res_npfss, type = "median")

Map of circular clusters

Description

This function plots a map of the sites and the circular clusters.

Usage

plot_map(spobject, centres, radius, system, colors = "red")

Arguments

spobject

SpObject. SpatialObject with the same coordinates system that centres (the same that sites_coord in the scan functions)

centres

numeric matrix or vector if only one cluster was detected. Coordinates of the centres of each cluster.

radius

numeric vector. Radius of each cluster in the user units if system = "Euclidean", or in km if system = "WGS84" (in the output of the scan functions)

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

colors

character. Colors of the clusters. If length(colors)=1 all the clusters will be in this color. Else it should be a vector of length the number of clusters to plot.

Value

No value returned, plots a map of the sites and the circular clusters.

Map of the clusters

Description

This function plots a map of the sites and the clusters

Usage

plot_map2(spobject, sites_coord, output_clusters, system, colors = "red")

Arguments

spobject

SpObject. SpatialObject corresponding the sites.

sites_coord

numeric matrix. Coordinates of the sites or the individuals, in the same order that the data for the cluster detection.

output_clusters

list. List of the sites in the clusters: it is the sites_clusters of the output of NPFSS, PFSS, DFFSS, URBFSS, MDFFSS, MRBFSS, MG, MNP, UG or UNP, or the sites_clusters_LH/sites_clusters_W/sites_clusters_P/sites_clusters_R of the MPFSS.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

colors

character. Colors of the clusters. If length(colors)=1 all the clusters will be in this color. Else it should be a vector of length the number of clusters to plot.

Value

No value returned, plots a map of the sites and the clusters.

Schema of the clusters

Description

This function plots a schema of the sites and the clusters

Usage

plot_schema(
  output_clusters,
  sites_coord,
  system,
  system_conv = NULL,
  colors = "red"
)

Arguments

output_clusters

list. List of the sites in the clusters: it is the sites_clusters of the output of NPFSS, PFSS, DFFSS, URBFSS, MDFFSS, MRBFSS, MG, MNP, UG or UNP, or the sites_clusters_LH/sites_clusters_W/sites_clusters_P/sites_clusters_R of the MPFSS.

sites_coord

numeric matrix. Coordinates of the sites, in the same order that the data for the cluster detection.

system

character. System in which the coordinates are expressed: "Euclidean" or "WGS84".

system_conv

character. System to convert the coordinates for the plot. Only considered if system is "WGS84". Must be entered as in the PROJ.4 documentation

colors

character. Colors of the clusters. If length(colors)=1 all the clusters will be in this color. Else it should be a vector of length the number of clusters to plot.

Value

No value returned, plots a schema of the sites and the clusters.

Index for the DFFSS scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

pointwise_dfree(data, matrix_clusters)

Arguments

data

numeric matrix. Matrix of the data. The rows correspond to the sites (or the individuals) and each column represents an observation time.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

Index for the MRBFSS scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

pointwise_wmw_multi(transform_data, matrix_clusters)

Arguments

transform_data

List. List of the data transformed with the function transform_data, each element of the list corresponds to an observation time. Each row of each element is a site (or an individual), and each column represents a variable.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

Index for the URBFSS scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

pointwise_wmw_uni(rank_data, matrix_clusters)

Arguments

rank_data

matrix. Matrix of the ranks of the data for each time. Each column corresponds to an observation time and each row corresponds to a site or an individual.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

A posteriori filtering on the area

Description

This function allows the a posteriori filtering on the area.

Usage

post_filt_area(mini_post, maxi_post, areas_clusters, index_clusters_temp)

Arguments

mini_post

numeric. A minimum to filter the significant clusters a posteriori. The default NULL is for no filtering with a a posteriori minimum.

maxi_post

numeric. A maximum to filter the significant clusters a posteriori. The default NULL is for no filtering with a a posteriori maximum.

areas_clusters

numeric vector. The areas of the clusters.

index_clusters_temp

numeric vector. The indices of the detected clusters.

Value

The detecting clusters with the a posteriori filtering.

A posteriori filtering on the number of sites/individuals

Description

This function allows the a posteriori filtering on the number of sites/individuals.

Usage

post_filt_nb_sites(
  mini_post,
  maxi_post,
  nb_sites,
  index_clusters_temp,
  matrix_clusters
)

Arguments

mini_post

numeric. A minimum to filter the significant clusters a posteriori. The default NULL is for no filtering with a a posteriori minimum.

maxi_post

numeric. A maximum to filter the significant clusters a posteriori. The default NULL is for no filtering with a a posteriori maximum.

nb_sites

numeric. The number of sites/individuals.

index_clusters_temp

numeric vector. The indices of the detected clusters.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. A value of 1 indicate that the site (or the individual) is in the cluster, 0 otherwise.

Value

The detecting clusters with the a posteriori filtering.

A posteriori filtering on the radius

Description

This function allows the a posteriori filtering on the radius.

Usage

post_filt_radius(mini_post, maxi_post, radius, index_clusters_temp)

Arguments

mini_post

numeric. A minimum to filter the significant clusters a posteriori. The default NULL is for no filtering with a a posteriori minimum.

maxi_post

numeric. A maximum to filter the significant clusters a posteriori. The default NULL is for no filtering with a a posteriori maximum.

radius

numeric vector. The radius of each cluster.

index_clusters_temp

numeric vector. The indices of the detected clusters.

Value

The detecting clusters with the a posteriori filtering.

Prints a result of a scan procedure

Description

This function prints a result of a scan procedure.

Usage

## S3 method for class 'ResScanOutput'
print(x, ...)

Arguments

x

ResScanOutput. Output of a scan function (UG, UNP, MG, MNP, PFSS, DFFSS, URBFSS, NPFSS, MPFSS, MDFFSS or MRBFSS)

...

Further arguments to be passed to or from methods.

Value

No value returned, print the ResScanOutput object.

Examples


library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

print(x = res_npfss)

Summary of the clusters obtained with a multivariate scan function (MG or MNP).

Description

This function gives a summary of the clusters in a table

Usage

## S3 method for class 'ResScanOutputMulti'
summary(
  object,
  type_summ = "param",
  digits = 3,
  quantile.type = 7,
  only.MLC = FALSE,
  ...
)

Arguments

object

ResScanOutputMulti. Output of a multivariate scan function (MG or MNP).

type_summ

character. "param" or "nparam". "param" gives the mean and the sd for each variable in the clusters, outside, and globally and "nparam" gives the Q25, Q50 and Q75 quantiles for each variables in the clusters, outside, and globally.

digits

integer. Number of decimals in output.

quantile.type

An integer between 1 and 9 (see function quantile). Ignored if type_summ is "param"

only.MLC

logical. Should we summarize only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, displays the results in the console

Examples


library(sp)
data("map_sites")
data("multi_data")
coords <- coordinates(map_sites)
res_mg <- SpatialScan(method = "MG", data=multi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$MG
summary(object = res_mg)

Summary of the clusters obtained with a multivariate functional scan function (MPFSS, NPFSS, MDFFSS or MRBFSS).

Description

This function gives a summary of the clusters in a table

Usage

## S3 method for class 'ResScanOutputMultiFunct'
summary(
  object,
  type_summ = "param",
  digits = 3,
  quantile.type = 7,
  only.MLC = FALSE,
  ...
)

Arguments

object

ResScanOutputMultiFunct. Output of an multivariate functional scan function (MPFSS, NPFSS, MDFFSS or MRBFSS).

type_summ

character. "param" or "nparam". "param" gives the mean and the sd for each variable in the clusters, outside, and globally and "nparam" gives the Q25, Q50 and Q75 quantiles for each variables in the clusters, outside, and globally.

digits

integer. Number of decimals in the output.

quantile.type

An integer between 1 and 9 (see function quantile). Ignored if type_summ is "param"

only.MLC

logical. Should we summarize only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, displays the results in the console

Examples


library(sp)
data("map_sites")
data("fmulti_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = fmulti_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

summary(object = res_npfss, type_summ = "nparam")

Summary of the clusters obtained with a univariate scan function (UG or UNP).

Description

This function gives a summary of the clusters in a table

Usage

## S3 method for class 'ResScanOutputUni'
summary(
  object,
  type_summ = "param",
  digits = 3,
  quantile.type = 7,
  only.MLC = FALSE,
  ...
)

Arguments

object

ResScanOutputUni. Output of a univariate scan function (UG or UNP).

type_summ

character. "param" or "nparam". "param" gives the mean and the sd for each variable in the clusters, outside, and globally and "nparam" gives the Q25, Q50 and Q75 quantiles for each variables in the clusters, outside, and globally.

digits

integer. Number of decimals in the output.

quantile.type

An integer between 1 and 9 (see function quantile). Ignored if type_summ is "param"

only.MLC

logical. Should we summarize only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, displays the results in the console

Examples


library(sp)
data("map_sites")
data("multi_data")
uni_data <- multi_data[,1]
coords <- coordinates(map_sites)
res_unp <- SpatialScan(method = "UNP", data=uni_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$UNP

summary(object = res_unp, type_summ = "nparam")

Summary of the clusters obtained with a univariate functional scan function (PFSS, NPFSS, DFFSS or URBFSS).

Description

This function gives a summary of the clusters in a table

Usage

## S3 method for class 'ResScanOutputUniFunct'
summary(
  object,
  type_summ = "param",
  digits = 3,
  quantile.type = 7,
  only.MLC = FALSE,
  ...
)

Arguments

object

ResScanOutputUniFunct. Output of a univariate functional scan function (PFSS, NPFSS, DFFSS or URBFSS).

type_summ

character. "param" or "nparam". "param" gives the mean and the sd for each variable in the clusters, outside, and globally and "nparam" gives the Q25, Q50 and Q75 quantiles for each variables in the clusters, outside, and globally.

digits

integer. Number of decimals in the output.

quantile.type

An integer between 1 and 9 (see function quantile). Ignored if type_summ is "param"

only.MLC

logical. Should we summarize only the MLC or all the significant clusters?

...

Further arguments to be passed to or from methods.

Value

No value returned, displays the results in the console

Examples


library(sp)
data("map_sites")
data("funi_data")
coords <- coordinates(map_sites)

res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords,
system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS

summary(object = res_npfss, type_summ = "nparam")

Computation of the multivariate functional ranks

Description

This function computes the multivariate ranks of the data for each observation time

Usage

transform_data(data)

Arguments

data

List. List of the data, each element of the list corresponds to a site (or an individual), each row corresponds to a variable and each column represents an observation time.

Value

List

Index for the NPFSS scan procedure (univariate functional case)

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster

Usage

uni_fWMW(signs, matrix_clusters)

Arguments

signs

numeric matrix. Matrix of signs of the data, the rows correspond to the sites (or the individuals) and each column represents an observation time.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric vector.

Computation of the matrix of signs

Description

This function returns the matrix of signs of the data.

Usage

uni_signs_matrix(data)

Arguments

data

numeric matrix. Matrix of the data, the rows correspond to the sites (or the individuals) and each column represents an observation time.

Value

numeric matrix.

Index for the UNP scan procedure

Description

This function returns the index we want to maximize on the set of potential clusters, for each potential cluster, and each permutation

Usage

wmw_uni(rank_data, matrix_clusters)

Arguments

rank_data

matrix. Matrix of the ranks of the data for all permutations. Each column corresponds to a permutation and each row corresponds to a site or an individual.

matrix_clusters

numeric matrix. Matrix in which each column represents a potential cluster. It is the result of the "clusters" function.

Value

numeric matrix.