| Title: | Multivariate and Functional Spatial Scan Statistics |
|---|---|
| Description: | Allows to detect spatial clusters of abnormal values on multivariate or functional data. Martin KULLDORFF and Lan HUANG and Kevin KONTY (2009) <doi:10.1186/1476-072X-8-58>, Inkyung JUNG and Ho Jin CHO (2015) <doi:10.1186/s12942-015-0024-6>, Lionel CUCALA and Michael GENIN and Caroline LANIER and Florent OCCELLI (2017) <doi:10.1016/j.spasta.2017.06.001>, Lionel CUCALA and Michael GENIN and Florent OCCELLI and Julien SOULA (2019) <doi:10.1016/j.spasta.2018.10.002>, Camille FREVENT and Mohamed-Salem AHMED and Matthieu MARBAC and Michael GENIN (2021) <doi:10.1016/j.spasta.2021.100550>, Zaineb SMIDA and Lionel CUCALA and Ali GANNOUN and Ghislain Durif (2022) <doi:10.1016/j.csda.2021.107378>, Camille FREVENT and Mohamed-Salem AHMED and Sophie DABO-NIANG and Michael GENIN (2023) <doi:10.1093/jrsssc/qlad017>. |
| Authors: | 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 <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.4 |
| Built: | 2024-11-13 06:43:36 UTC |
| Source: | CRAN |
Allows to detect spatial clusters of abnormal values on multivariate or functional data.
| Package: | HDSpatialScan |
| Type: | Package |
| Version: | 1.0.4 |
| Date: | 2023-05-24 |
| License: | GPL-3 |
| LazyLoad: | yes |
FREVENT Camille, AHMED Mohamed-Salem, SOULA Julien, SMIDA Zaineb, CUCALA Lionel, DABO-NIANG Sophie and GENIN Michaël. Maintainer: FREVENT Camille <[email protected]>
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.
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.
clusters(sites_coord, system, mini, maxi, type_minimaxi, sites_areas)clusters(sites_coord, system, mini, maxi, type_minimaxi, sites_areas)
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 |
The list of the following elements:
matrix_clusters: numeric matrix of 0 and 1
centres: the coordinates of the centres of each cluster (numeric matrix)
radius: the radius of the clusters in km if system = "WGS84" or in the coordinates unit otherwise (numeric vector)
areas: the areas of the clusters (in same units as in sites_areas). Provided only if sites_areas is not NULL. Numeric vector
system: the system of coordinates (character)
This function computes the DFFSS (Distribution-Free Functional scan statistic).
DFFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, times = NULL, initialization, permutations )DFFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputUniFunct.
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.
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster and each permutation
dfree(data, matrix_clusters)dfree(data, matrix_clusters)
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. |
numeric matrix.
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
dfree_index_multi(data, matrix_clusters)dfree_index_multi(data, matrix_clusters)
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. |
numeric vector.
This function finalizes the scan procedures.
FinScan( index_clusters_temp, index, filtering_post, type_minimaxi_post, mini_post, maxi_post, nb_sites, matrix_clusters, radius, areas, centres, pvals, maximize = TRUE )FinScan( index_clusters_temp, index, filtering_post, type_minimaxi_post, mini_post, maxi_post, nb_sites, matrix_clusters, radius, areas, centres, pvals, maximize = TRUE )
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. |
The list of the following elements:
pval_clusters: pvalues of the selected clusters.
sites_clusters: the indices of the sites of the selected clusters.
centres_clusters: the coordinates of the centres of each selected cluster.
radius_clusters: the radius of the selected clusters.
areas_clusters: the areas of the selected clusters.
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).
data("fmulti_data")data("fmulti_data")
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).
Data from the National Air Quality Forecasting Platform www.prevair.org
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).
data("funi_data")data("funi_data")
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.
Data from the National Air Quality Forecasting Platform www.prevair.org
This function initializes the scan procedures by creating the matrix of potential clusters.
InitScan( mini_post, maxi_post, type_minimaxi_post, sites_areas, sites_coord, system, mini, maxi, type_minimaxi )InitScan( mini_post, maxi_post, type_minimaxi_post, sites_areas, sites_coord, system, mini, maxi, type_minimaxi )
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. |
The list of the following elements:
filtering_post: logical, is there an a posteriori filtering?
matrix_clusters: the matrix of potential clusters
centres: the coordinates of the centres of each potential cluster
radius: the radius of the potential clusters in km if system = WGS84 or in the user units
areas: the areas of the potential clusters (in the same units as sites_areas).
sites_coord: coordinates of the sites
system: system in which the coordinates are expressed
mini_post: a minimum to filter the significant clusters a posteriori
maxi_post: a maximum to filter the significant clusters a posteriori
type_minimaxi_post: type of minimum and maximum a posteriori
Spatial object corresponding to the sites (169 cantons) of the data of the package HDSpatialScan.
data("map_sites")data("map_sites")
A SpatialPolygonsDataFrame.
This function computes the MDFFSS (Multivariate Distribution-Free Functional scan statistic).
MDFFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )MDFFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputMultiFunct.
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.
This function computes the MG (Multivariate Gaussian scan statistic).
MG( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, initialization, permutations )MG( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputMulti.
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.
This function computes the MNP (Multivariate Nonparametric scan statistic).
MNP( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, initialization, permutations )MNP( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputMulti.
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.
This function computes the MPFSS (Parametric Multivariate Functional scan statistic).
MPFSS( data, MC = 999, typeI = 0.05, method = c("LH", "W", "P", "R"), nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )MPFSS( data, MC = 999, typeI = 0.05, method = c("LH", "W", "P", "R"), nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
List of objects of class ResScanOutputMultiFunct (one element by method)
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.
This function computes the MRBFSS (Multivariate Rank-Based Functional scan statistic).
MRBFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )MRBFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputMultiFunct
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.
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).
data("multi_data")data("multi_data")
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.
Data from the National Air Quality Forecasting Platform www.prevair.org
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
multi_fWMW(signs, matrix_clusters)multi_fWMW(signs, matrix_clusters)
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. |
numeric vector.
This function returns the index we want to minimize on the set of potential clusters, for each potential cluster
multi_gaussian(data, matrix_clusters)multi_gaussian(data, matrix_clusters)
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. |
numeric vector.
This function returns the list of matrix of signs for the multivariate functional data
multi_signs_matrix(data)multi_signs_matrix(data)
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. |
list of numeric matrices.
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
multi_WMW(rank_data, matrix_clusters)multi_WMW(rank_data, matrix_clusters)
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. |
numeric vector.
This function allows to return only the detected clusters with no overlapping in their order of detection.
non_overlap(index_clusters, matrix_clusters)non_overlap(index_clusters, matrix_clusters)
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. |
The detecting clusters with no overlapping, in their order of detection.
This function computes the NPFSS (Nonparametric Functional scan statistic for multivariate or univariate functional data).
NPFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )NPFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, variable_names = NULL, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputUniFunct or ResScanOutputMultiFunct depending on the data
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.
This function will permit to permute the data for the MC simulations
permutate(to_permute, nb_permu)permutate(to_permute, nb_permu)
to_permute |
vector. Vector of indices we want to permute. |
nb_permu |
numeric. Number of permutations. |
matrix. Matrix of nb_permu rows and length(to_permute) columns.
This function computes the PFSS (Parametric Functional scan statistic).
PFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, times = NULL, initialization, permutations )PFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputUniFunct.
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.
This function plots a map of the sites and the circular clusters.
plot_map(spobject, centres, radius, system, colors = "red")plot_map(spobject, centres, radius, system, colors = "red")
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. |
No value returned, plots a map of the sites and the circular clusters.
This function plots a map of the sites and the clusters
plot_map2(spobject, sites_coord, output_clusters, system, colors = "red")plot_map2(spobject, sites_coord, output_clusters, system, colors = "red")
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. |
No value returned, plots a map of the sites and the clusters.
This function plots a schema of the sites and the clusters
plot_schema( output_clusters, sites_coord, system, system_conv = NULL, colors = "red" )plot_schema( output_clusters, sites_coord, system, system_conv = NULL, colors = "red" )
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. |
No value returned, plots a schema of the sites and the clusters.
This function plots a schema or a map of the sites and the clusters
## S3 method for class 'ResScanOutput' plot( x, type, spobject = NULL, system_conv = NULL, colors = "red", only.MLC = FALSE, ... )## S3 method for class 'ResScanOutput' plot( x, type, spobject = NULL, system_conv = NULL, colors = "red", only.MLC = FALSE, ... )
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. |
No value returned, plots a schema or a map of the sites and the clusters.
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)$NPFSS plot(x = res_npfss, type = "schema", system_conv = "+init=epsg:2154") plot(x = res_npfss, type = "map", spobject = map_sites) plot(x = res_npfss, type = "map2", spobject = map_sites)library(sp) data("map_sites") data("funi_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$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)
This function is a generic function to plot curves.
plotCurves(x, ...)plotCurves(x, ...)
x |
An object for which the curves are to be plotted. |
... |
Additional arguments affecting the output. |
No value returned, plots the curves.
plotCurves.ResScanOutputUniFunct and plotCurves.ResScanOutputMultiFunct
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)$NPFSS plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)library(sp) data("map_sites") data("funi_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)
This function plot the curves in the clusters detected by the multivariate functional scan functions (MPFSS, NPFSS, MDFFSS or MRBFSS).
## S3 method for class 'ResScanOutputMultiFunct' plotCurves( x, add_mean = FALSE, add_median = FALSE, colors = "red", only.MLC = FALSE, ... )## S3 method for class 'ResScanOutputMultiFunct' plotCurves( x, add_mean = FALSE, add_median = FALSE, colors = "red", only.MLC = FALSE, ... )
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. |
No value returned, plots the curves.
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)$NPFSS plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)library(sp) data("map_sites") data("fmulti_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = fmulti_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)
This function plot the curves in the clusters detected by the univariate functional scan functions (PFSS, NPFSS, DFFSS or URBFSS).
## S3 method for class 'ResScanOutputUniFunct' plotCurves( x, add_mean = FALSE, add_median = FALSE, colors = "red", only.MLC = FALSE, ... )## S3 method for class 'ResScanOutputUniFunct' plotCurves( x, add_mean = FALSE, add_median = FALSE, colors = "red", only.MLC = FALSE, ... )
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. |
No value returned, plots the curves.
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)$NPFSS plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)library(sp) data("map_sites") data("funi_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS plotCurves(x = res_npfss, add_mean = TRUE, add_median = TRUE)
This function is a generic function to plot a summary.
plotSummary(x, ...)plotSummary(x, ...)
x |
An object for which the summary is to be plotted. |
... |
Additional arguments affecting the summary produced. |
No value returned, plots the summary.
plotSummary.ResScanOutputMulti, plotSummary.ResScanOutputUniFunct and plotSummary.ResScanOutputMultiFunct
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"))$MNP plotSummary(x = res_mnp, type = "mean")library(sp) data("map_sites") data("multi_data") coords <- coordinates(map_sites) res_mnp <- SpatialScan(method = "MNP", data = multi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2, variable_names = c("NO2", "O3", "PM10", "PM2.5"))$MNP plotSummary(x = res_mnp, type = "mean")
This function plots the mean or median spider chart of the clusters detected by a multivariate scan function (MG or MNP).
## S3 method for class 'ResScanOutputMulti' plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)## S3 method for class 'ResScanOutputMulti' plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)
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. |
No value returned, plots the spider chart.
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"))$MNP plotSummary(x = res_mnp, type = "mean")library(sp) data("map_sites") data("multi_data") coords <- coordinates(map_sites) res_mnp <- SpatialScan(method = "MNP", data=multi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2, variable_names = c("NO2", "O3", "PM10", "PM2.5"))$MNP plotSummary(x = res_mnp, type = "mean")
This function plots the mean or median curves in the clusters detected by a multivariate functional scan procedure (MPFSS, NPFSS, MDFFSS or MRBFSS).
## S3 method for class 'ResScanOutputMultiFunct' plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)## S3 method for class 'ResScanOutputMultiFunct' plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)
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. |
No value returned, plots the curves.
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)$NPFSS plotSummary(x = res_npfss, type = "median")library(sp) data("map_sites") data("fmulti_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = fmulti_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS plotSummary(x = res_npfss, type = "median")
This function plots the mean or median curves in the clusters detected by a univariate functional scan procedure (PFSS, NPFSS, DFFSS or URBFSS).
## S3 method for class 'ResScanOutputUniFunct' plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)## S3 method for class 'ResScanOutputUniFunct' plotSummary(x, type = "mean", colors = "red", only.MLC = FALSE, ...)
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. |
No value returned, plots the curves.
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)$NPFSS plotSummary(x = res_npfss, type = "median")library(sp) data("map_sites") data("funi_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS plotSummary(x = res_npfss, type = "median")
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
pointwise_dfree(data, matrix_clusters)pointwise_dfree(data, matrix_clusters)
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. |
numeric vector.
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
pointwise_wmw_multi(transform_data, matrix_clusters)pointwise_wmw_multi(transform_data, matrix_clusters)
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. |
numeric vector.
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
pointwise_wmw_uni(rank_data, matrix_clusters)pointwise_wmw_uni(rank_data, matrix_clusters)
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. |
numeric vector.
This function allows the a posteriori filtering on the area.
post_filt_area(mini_post, maxi_post, areas_clusters, index_clusters_temp)post_filt_area(mini_post, maxi_post, areas_clusters, index_clusters_temp)
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. |
The detecting clusters with the a posteriori filtering.
This function allows the a posteriori filtering on the number of sites/individuals.
post_filt_nb_sites( mini_post, maxi_post, nb_sites, index_clusters_temp, matrix_clusters )post_filt_nb_sites( mini_post, maxi_post, nb_sites, index_clusters_temp, matrix_clusters )
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. |
The detecting clusters with the a posteriori filtering.
This function allows the a posteriori filtering on the radius.
post_filt_radius(mini_post, maxi_post, radius, index_clusters_temp)post_filt_radius(mini_post, maxi_post, radius, index_clusters_temp)
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. |
The detecting clusters with the a posteriori filtering.
This function prints a result of a scan procedure.
## S3 method for class 'ResScanOutput' print(x, ...)## S3 method for class 'ResScanOutput' print(x, ...)
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. |
No value returned, print the ResScanOutput object.
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)$NPFSS print(x = res_npfss)library(sp) data("map_sites") data("funi_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS print(x = res_npfss)
This is the constructor function for objects of the ResScanOutput class.
ResScanOutput( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, sites_coord, data, method )ResScanOutput( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, sites_coord, data, method )
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. |
An object of class ResScanOutput which is a list of the following elements:
sites_clusters: List of the indices of the sites of the selected clusters.
pval_clusters: The pvalues of the selected clusters.
centres_clusters: Coordinates of the centres of the selected clusters.
radius_clusters: Radius of the selected clusters.
areas_clusters: Areas of the selected clusters.
system: System in which the coordinates are expressed: "Euclidean" or "WGS84".
sites_coord: 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.
method: The scan procedure used.
This is the constructor function for objects of the ResScanOutputMulti class which inherits from class ResScanOutput.
ResScanOutputMulti( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, variable_names = NULL, sites_coord, data, method )ResScanOutputMulti( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, variable_names = NULL, sites_coord, data, method )
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. |
An object of class ResScanOutputMulti which is a list of the following elements:
sites_clusters: List of the indices of the sites of the selected clusters.
pval_clusters: The pvalues of the selected clusters.
centres_clusters: Coordinates of the centres of the selected clusters.
radius_clusters: Radius of the selected clusters.
areas_clusters: Areas of the selected clusters.
system: System in which the coordinates are expressed: "Euclidean" or "WGS84".
sites_coord: Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).
data: Matrix.
variable_names: names of the variables.
method: The scan procedure used.
This is the constructor function for objects of the ResScanOutputMultiFunct class which inherits from class ResScanOutput.
ResScanOutputMultiFunct( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, times = NULL, variable_names = NULL, sites_coord, data, method )ResScanOutputMultiFunct( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, times = NULL, variable_names = NULL, sites_coord, data, method )
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. |
An object of class ResScanOutputMultiFunct which is a list of the following elements:
sites_clusters: List of the indices of the sites of the selected clusters.
pval_clusters: The pvalues of the selected clusters.
centres_clusters: Coordinates of the centres of the selected clusters.
radius_clusters: Radius of the selected clusters.
areas_clusters: Areas of the selected clusters.
system: System in which the coordinates are expressed: "Euclidean" or "WGS84".
sites_coord: Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).
data: list of numeric matrices.
times: times of observation of the data.
variable_names: names of the variables.
method: the scan procedure used.
This is the constructor function for objects of the ResScanOutputUni class which inherits from class ResScanOutput.
ResScanOutputUni( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, sites_coord, data, method )ResScanOutputUni( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, sites_coord, data, method )
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. |
An object of class ResScanOutputUni which is a list of the following elements:
sites_clusters: List of the indices of the sites of the selected clusters.
pval_clusters: The pvalues of the selected clusters.
centres_clusters: Coordinates of the centres of the selected clusters.
radius_clusters: Radius of the selected clusters.
areas_clusters: Areas of the selected clusters.
system: System in which the coordinates are expressed: "Euclidean" or "WGS84".
sites_coord: Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).
data: Vector.
method: The scan procedure used.
This is the constructor function for objects of the ResScanOutputUniFunct class which inherits from class ResScanOutput.
ResScanOutputUniFunct( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, times = NULL, sites_coord, data, method )ResScanOutputUniFunct( sites_clusters, pval_clusters, centres_clusters, radius_clusters, areas_clusters, system, times = NULL, sites_coord, data, method )
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. |
An object of class ResScanOutputUniFunct which is a list of the following elements:
sites_clusters: List of the indices of the sites of the selected clusters.
pval_clusters: The pvalues of the selected clusters.
centres_clusters: Coordinates of the centres of the selected clusters.
radius_clusters: Radius of the selected clusters.
areas_clusters: Areas of the selected clusters.
system: System in which the coordinates are expressed: "Euclidean" or "WGS84".
sites_coord: Coordinates of the sites (or the individuals, in that case there can be many individuals with the same coordinates).
data: Matrix.
times: times of observation of the data.
method : the scan procedure used
This function computes the different scan procedures available in the package.
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 )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 )
method |
character vector. The scan procedures to apply on the data. Possible values are:
|
data |
list of numeric matrices or a matrix or a vector:
|
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. |
A list of objects of class ResScanOutput:
Univariate case (UG, UNP): A list of objects of class ResScanOutputUni
Multivariate case (MG, MNP): A list of objects of class ResScanOutputMulti
Univariate functional case (NPFSS, PFSS, DFFSS, URBFSS): A list of objects of class ResScanOutputUniFunct
Multivariate functional case (NPFSS, MPFSS, MDFFSS, MRBFSS): A list of objects of class ResScanOutputMultiFunct
For univariate scan statistics:
Inkyung Jung and Ho Jin Cho (2015). A Nonparametric Spatial Scan Statistic for Continuous Data. International Journal of Health Geographics, 14.
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).
For multivariate scan statistics:
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.
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.
For functional scan statistics:
Zaineb Smida and Lionel Cucala and Ali Gannoun. A Nonparametric Spatial Scan Statistic for Functional Data. Pre-print <https://hal.archives-ouvertes.fr/hal-02908496>.
Camille Frévent and Mohamed-Salem Ahmed and Matthieu Marbac and Michaël Genin. Detecting Spatial Clusters in Functional Data: New Scan Statistic Approaches. Pre-print <arXiv:2011.03482>.
Camille Frévent and Mohamed-Salem Ahmed and Sophie Dabo-Niang and Michaël Genin. Investigating Spatial Scan Statistics for Multivariate Functional Data. Pre-print <arXiv:2103.14401>.
ResScanOutput, ResScanOutputUni, ResScanOutputMulti, ResScanOutputUniFunct and ResScanOutputMultiFunct
# 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)# 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)
This function gives a summary of the clusters in a table
## S3 method for class 'ResScanOutputMulti' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )## S3 method for class 'ResScanOutputMulti' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )
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. |
No value returned, displays the results in the console
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)$MG summary(object = res_mg)library(sp) data("map_sites") data("multi_data") coords <- coordinates(map_sites) res_mg <- SpatialScan(method = "MG", data=multi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$MG summary(object = res_mg)
This function gives a summary of the clusters in a table
## S3 method for class 'ResScanOutputMultiFunct' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )## S3 method for class 'ResScanOutputMultiFunct' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )
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. |
No value returned, displays the results in the console
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)$NPFSS summary(object = res_npfss, type_summ = "nparam")library(sp) data("map_sites") data("fmulti_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = fmulti_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS summary(object = res_npfss, type_summ = "nparam")
This function gives a summary of the clusters in a table
## S3 method for class 'ResScanOutputUni' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )## S3 method for class 'ResScanOutputUni' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )
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. |
No value returned, displays the results in the console
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)$UNP summary(object = res_unp, type_summ = "nparam")library(sp) data("map_sites") data("multi_data") uni_data <- multi_data[,1] coords <- coordinates(map_sites) res_unp <- SpatialScan(method = "UNP", data=uni_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$UNP summary(object = res_unp, type_summ = "nparam")
This function gives a summary of the clusters in a table
## S3 method for class 'ResScanOutputUniFunct' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )## S3 method for class 'ResScanOutputUniFunct' summary( object, type_summ = "param", digits = 3, quantile.type = 7, only.MLC = FALSE, ... )
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. |
No value returned, displays the results in the console
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)$NPFSS summary(object = res_npfss, type_summ = "nparam")library(sp) data("map_sites") data("funi_data") coords <- coordinates(map_sites) res_npfss <- SpatialScan(method = "NPFSS", data = funi_data, sites_coord = coords, system = "WGS84", mini = 1, maxi = nrow(coords)/2)$NPFSS summary(object = res_npfss, type_summ = "nparam")
This function computes the multivariate ranks of the data for each observation time
transform_data(data)transform_data(data)
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. |
List
This function computes the UG (Univariate Gaussian scan statistic).
UG(data, MC = 999, typeI = 0.05, initialization, permutations)UG(data, MC = 999, typeI = 0.05, initialization, permutations)
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputUni.
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).
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster
uni_fWMW(signs, matrix_clusters)uni_fWMW(signs, matrix_clusters)
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. |
numeric vector.
This function returns the matrix of signs of the data.
uni_signs_matrix(data)uni_signs_matrix(data)
data |
numeric matrix. Matrix of the data, the rows correspond to the sites (or the individuals) and each column represents an observation time. |
numeric matrix.
This function computes the UNP (Univariate Nonparametric scan statistic).
UNP(data, MC = 999, typeI = 0.05, initialization, permutations)UNP(data, MC = 999, typeI = 0.05, initialization, permutations)
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputUni.
Inkyung Jung and Ho Jin Cho (2015). A Nonparametric Spatial Scan Statistic for Continuous Data. International Journal of Health Geographics, 14.
This function computes the URBFSS (Univariate Rank-Based Functional scan statistic).
URBFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, times = NULL, initialization, permutations )URBFSS( data, MC = 999, typeI = 0.05, nbCPU = 1, times = NULL, initialization, permutations )
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 |
permutations |
matrix. Indices of permutations of the data. |
An object of class ResScanOutputUniFunct.
MRBFSS which is the multivariate version of the URBFSS
This function returns the index we want to maximize on the set of potential clusters, for each potential cluster, and each permutation
wmw_uni(rank_data, matrix_clusters)wmw_uni(rank_data, matrix_clusters)
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. |
numeric matrix.