STATIS and STATIS Dual Multivariate Methods

Description

STATIS is a multivariate technique developed in France in the 1970s by L'Hermier des Plantes and Escoufier, designed to analyze multiple data tables. This package provides an implementation of methods for the joint analysis of multiple data tables sharing the same set of observations. Includes functions for performing inter-structure and intra-structure analyses, as well as graphical representations of compromise structures and the shared variability across different groups of variables.

Details

Author(s)

Oldemar Rodriguez Rojas
Maintainer: Oldemar Rodriguez Rojas oldemar.rodriguez@ucr.ac.cr

References

Abdi, H., & Valentin, D. (2007). The STATIS method. Encyclopedia of measurement and statistics, 955-962.

González, J., & Rodrıguez, O. (1995). Algoritmo e implementación del método Statis. In IX Simposio Métodos Matemáticos Aplicados a las Ciencias. UCR-ITCR, Turrialba.

Elizondo, W. C., & Varela, J. G. (1998). Stadis dual: software y análisis de datos reales. Revista de Matemática: Teoría y Aplicaciones, 5(2), 149-162.

Abdi, H. (2007). RV coefficient and congruence coefficient. Encyclopedia of measurement and statistics, 849(853), 92.

Abdi, H. (2007). Singular value decomposition (SVD) and generalized singular value decomposition. Encyclopedia of measurement and statistics, 907(912), 44.

Xiang, G. (2007). Fast algorithms for computing statistics under interval uncertainty, with applications to computer science and to electrical and computer engineering. The University of Texas at El Paso.

McHale, D., & Lavit, C. (1990). Analyse Conjointe de Tableaux Quantitatifs. Biometrics, 46(2), 542.

Physicochemical Variables Dataset for STATIS Analysis

Description

This dataset belongs to a project called “Development and application of effective, low-cost methods for the biological monitoring of Costa Rican rivers” by the National University, and contains measurements of various physicochemical variables collected across several sampling sites. It is intended to be used in the examples and demonstrations of the main functions of the package, particularly those related to multivariate analysis and STATIS methodology.

Usage

data(STATIS_TABLE1)

Format

A data frame with 14 columns and multiple rows (one per sampling site):

NIT

Total nitrogen level.

FOS

Phosphorus level.

CAL

Calcium level.

STO

Sodium level.

PH

pH measurement.

MN

Manganese concentration.

ZN

Zinc concentration.

SS

Suspended solids.

ALC

Alkalinity.

CL

Chlorine level.

CAU

Exchangeable calcium or equivalent measurement.

DBO

Biological oxygen demand.

POR

Porosity or related percentage.

Examples

data(STATIS_TABLE1)
head(STATIS_TABLE1)

Physicochemical Variables Dataset for STATIS Analysis

Description

This dataset belongs to a project called “Development and application of effective, low-cost methods for the biological monitoring of Costa Rican rivers” by the National University, and contains measurements of various physicochemical variables collected across several sampling sites. It is intended to be used in the examples and demonstrations of the main functions of the package, particularly those related to multivariate analysis and STATIS methodology.

Usage

data(STATIS_TABLE1)

Format

A data frame with 14 columns and multiple rows (one per sampling site):

NIT

Total nitrogen level.

FOS

Phosphorus level.

CAL

Calcium level.

STO

Sodium level.

PH

pH measurement.

MN

Manganese concentration.

ZN

Zinc concentration.

SS

Suspended solids.

ALC

Alkalinity.

CL

Chlorine level.

CAU

Exchangeable calcium or equivalent measurement.

DBO

Biological oxygen demand.

POR

Porosity or related percentage.

Examples

data(STATIS_TABLE2)
head(STATIS_TABLE2)

Physicochemical Variables Dataset for STATIS Analysis

Description

This dataset belongs to a project called “Development and application of effective, low-cost methods for the biological monitoring of Costa Rican rivers” by the National University, and contains measurements of various physicochemical variables collected across several sampling sites. It is intended to be used in the examples and demonstrations of the main functions of the package, particularly those related to multivariate analysis and STATIS methodology.

Usage

data(STATIS_TABLE3)

Format

A data frame with 14 columns and multiple rows (one per sampling site):

NIT

Total nitrogen level.

FOS

Phosphorus level.

CAL

Calcium level.

STO

Sodium level.

PH

pH measurement.

MN

Manganese concentration.

ZN

Zinc concentration.

SS

Suspended solids.

ALC

Alkalinity.

CL

Chlorine level.

CAU

Exchangeable calcium or equivalent measurement.

DBO

Biological oxygen demand.

POR

Porosity or related percentage.

Examples

data(STATIS_TABLE3)
head(STATIS_TABLE3)

Physicochemical Variables Dataset for STATIS Analysis

Description

This dataset belongs to a project called “Development and application of effective, low-cost methods for the biological monitoring of Costa Rican rivers” by the National University, and contains measurements of various physicochemical variables collected across several sampling sites. It is intended to be used in the examples and demonstrations of the main functions of the package, particularly those related to multivariate analysis and STATIS methodology.

Usage

data(STATIS_TABLE4)

Format

A data frame with 14 columns and multiple rows (one per sampling site):

NIT

Total nitrogen level.

FOS

Phosphorus level.

CAL

Calcium level.

STO

Sodium level.

PH

pH measurement.

MN

Manganese concentration.

ZN

Zinc concentration.

SS

Suspended solids.

ALC

Alkalinity.

CL

Chlorine level.

CAU

Exchangeable calcium or equivalent measurement.

DBO

Biological oxygen demand.

POR

Porosity or related percentage.

Examples

data(STATIS_TABLE4)
head(STATIS_TABLE4)

Physicochemical Quality Data (Tuis5_95)

Description

This dataset contains physicochemical measurements collected from a Sugarcane Fertilizer experiment in Costa Rica. The values represent indicators measured during a monitoring campaign. The dataset is useful for illustrating multivariate methods, STATIS analyses, or environmental data exploration workflows.

Usage

data(Tuis5_95)

Format

A data frame with 10 observations and 19 variables:

Ph

pH value of the sample.

Temp

Temperature (°C).

Na

Sodium concentration.

Ka

Potassium concentration.

Ca

Calcium concentration.

Mg

Magnesium concentration.

Si02

Silica concentration.

OD

Dissolved oxygen.

DBO

Biochemical oxygen demand (BOD).

SD

Dissolved solids.

ST

Total solids.

PO4

Phosphate concentration.

Cl

Chloride concentration.

NO3

Nitrate concentration.

SO45

Sulfate concentration.

HC03

Bicarbonate concentration.

DT

Total hardness or related measurement.

POD

Dissolved oxygen percentage or related measure.

Cal

Calcium-related parameter (likely residual hardness).

Examples

data(Tuis5_95)
head(Tuis5_95)

Physicochemical Quality Data (Tuis5_96)

Description

This dataset contains physicochemical measurements collected from a Sugarcane Fertilizer experiment in Costa Rica. The values represent indicators measured during a monitoring campaign. The dataset is useful for illustrating multivariate methods, STATIS analyses, or environmental data exploration workflows.

Usage

data(Tuis5_96)

Format

A data frame with 12 observations and 19 variables:

Ph

pH value of the water sample.

Temp

Temperature (°C).

Na

Sodium concentration.

Ka

Potassium concentration.

Ca

Calcium concentration.

Mg

Magnesium concentration.

Si02

Silica concentration.

OD

Dissolved oxygen.

DBO

Biochemical oxygen demand (BOD).

SD

Dissolved solids.

ST

Total solids.

PO4

Phosphate concentration.

Cl

Chloride concentration.

NO3

Nitrate concentration.

SO45

Sulfate concentration.

HC03

Bicarbonate concentration.

DT

Total hardness or related parameter.

POD

Dissolved oxygen percentage or related measurement.

Cal

Calcium-related parameter (e.g., residual hardness).

Examples

data(Tuis5_96)
head(Tuis5_96)

Physicochemical Quality Data (Tuis5_97)

Description

This dataset contains physicochemical measurements collected from a Sugarcane Fertilizer experiment in Costa Rica. The values represent indicators measured during a monitoring campaign. The dataset is useful for illustrating multivariate methods, STATIS analyses, or environmental data exploration workflows.

Usage

data(Tuis5_97)

Format

A data frame with 12 observations and 19 variables:

Ph

pH value of the water sample.

Temp

Temperature (°C).

Na

Sodium concentration.

Ka

Potassium concentration.

Ca

Calcium concentration.

Mg

Magnesium concentration.

Si02

Silica concentration.

OD

Dissolved oxygen.

DBO

Biochemical oxygen demand (BOD).

SD

Dissolved solids.

ST

Total solids.

PO4

Phosphate concentration.

Cl

Chloride concentration.

NO3

Nitrate concentration.

SO45

Sulfate concentration.

HC03

Bicarbonate concentration.

DT

Total hardness or related parameter.

POD

Dissolved oxygen percentage or related measure.

Cal

Calcium-related parameter (e.g., residual hardness).

Examples

data(Tuis5_97)
head(Tuis5_97)

Physicochemical Quality Data (Tuis5_98)

Description

This dataset contains physicochemical measurements collected from a Sugarcane Fertilizer experiment in Costa Rica. The values represent indicators measured during a monitoring campaign. The dataset is useful for illustrating multivariate methods, STATIS analyses, or environmental data exploration workflows.

Usage

data(Tuis5_98)

Format

A data frame with 12 observations and 19 variables:

Ph

pH value of the water sample.

Temp

Temperature (°C).

Na

Sodium concentration.

Ka

Potassium concentration.

Ca

Calcium concentration.

Mg

Magnesium concentration.

Si02

Silica concentration.

OD

Dissolved oxygen.

DBO

Biochemical oxygen demand (BOD).

SD

Dissolved solids.

ST

Total solids.

PO4

Phosphate concentration.

Cl

Chloride concentration.

NO3

Nitrate concentration.

SO45

Sulfate concentration.

HC03

Bicarbonate concentration.

DT

Total hardness or related parameter.

POD

Dissolved oxygen percentage or related measurement.

Cal

Calcium-related parameter (e.g., residual hardness).

Examples

data(Tuis5_98)
head(Tuis5_98)

Sensory Evaluation Data from Expert 1

Description

This dataset contains the ratings provided by Expert 1 for six wine samples. Each wine is evaluated according to three sensory attributes commonly used in descriptive analysis: fruity, woody, and coffee. The dataset is typically used in STATIS and multitable analyses to illustrate how different experts evaluate the same set of products.

Usage

data(expert1)

Format

A data frame with 6 rows (Wine1–Wine6) and 3 sensory attributes:

fruity

Intensity of fruity aromas.

woody

Intensity of woody/aged aromas.

coffee

Perceived coffee-like notes.

References

Abdi, H., & Valentin, D. (2007). The STATIS method. Encyclopedia of measurement and statistics, 955-962.

Examples

data(expert1)
expert1

Sensory Evaluation Data from Expert 2

Description

This dataset contains the evaluations provided by Expert 2 for the same six wine samples. Unlike Expert 1, this expert uses four sensory descriptors: red_fruit, roasted, vanillin, and woody. The dataset demonstrates how experts may differ in terminology and profiling, and it is commonly used in STATIS, MFA, and other multitable comparison techniques.

Usage

data(expert2)

Format

A data frame with 6 rows (Wine1–Wine6) and 4 sensory attributes:

red_fruit

Intensity of red fruit aromas.

roasted

Intensity of roasted or toasted notes.

vanillin

Perceived vanilla-related notes.

woody

Intensity of woody/aged aromas.

References

Abdi, H., & Valentin, D. (2007). The STATIS method. Encyclopedia of measurement and statistics, 955-962.

Examples

data(expert2)
expert2

Sensory Evaluation Data from Expert 3

Description

This dataset contains the ratings given by Expert 3 for the same set of six wine samples. This expert evaluates wines using three sensory attributes: fruity, butter, and woody. The dataset is often used in multivariate and STATIS examples to highlight both agreement and divergence across panels of experts.

Usage

data(expert3)

Format

A data frame with 6 rows (Wine1–Wine6) and 3 sensory attributes:

fruity

Intensity of fruity aromas.

butter

Presence of buttery or lactic notes.

woody

Intensity of woody/aged aromas.

References

Abdi, H., & Valentin, D. (2007). The STATIS method. Encyclopedia of measurement and statistics, 955-962.

Examples

data(expert3)
expert3

Plot a Correlation Circle (Unit Circle)

Description

This function generates a correlation circle plot from two-dimensional coordinates, commonly used in principal component analysis (PCA) or other multivariate methods.

Usage

## S3 method for class 'statis.circle'
plot(points, inertia = 100, labels = NULL, title = "")

Arguments

Details

Arrows are drawn from the origin to each point specified in points. A reference circle with radius 1 is displayed. You can also show the percentage of explained inertia and point labels.

The inertia argument is flexible and can be passed as the second or third parameter if argument names are omitted.

Value

A ggplot object with the generated plot.

See Also

statis

Examples

data(expert1, expert2, expert3)

labels <- c("Expert 1", "Expert 2", "Expert 3")

# If you want to select an specific table or row just set the parameters in the statis function.

res <- statis(list(expert1, expert2, expert3), table.labels = labels)

# Circle of correlations of all the tables
inter <- res$circle.inter
plot.statis.circle(inter$points, inter$inertia, inter$labels, inter$title)

# Circle of correlations of all variables evolution
intra <- res$circle.intra
plot.statis.circle(intra$points, intra$inertia, intra$labels, intra$title)

Bivariate PCA-style Scatter Plot

Description

This function generates a 2D scatter plot with support for multiple groups, labels, arrows from the origin, reference circles, cross axes, and full style customization using ggplot2.

Usage

## S3 method for class 'statis.dual.circle'
plot(
  points.list,
  style.points = list(list(size = 3)),
  style.circle = list(),
  radius.circle = 1,
  labels = "auto",
  labels.style = NULL,
  draw.labels = TRUE,
  vars.direction = NULL,
  style.vars = list(),
  radius.vars = c(0.5, 1),
  join.dots = FALSE,
  style.join = list(),
  base.colors = .base.colors,
  axes = TRUE,
  frame = TRUE,
  hide.ticks = TRUE,
  proportion = 1,
  xlim = NULL,
  ylim = NULL,
  axes.xy = TRUE,
  style.axes.xy = list(linewidth = 0.35, linetype = "dashed", color = "gray40"),
  arrows.points = TRUE,
  factor.arrow = 0.95,
  style.arrows = list(color = "red", linewidth = 0.6, arrow = grid::arrow(length =
    grid::unit(0.2, "cm")))
)

Arguments

Value

A ggplot object with the generated plot.

See Also

statis.dual

Examples

data(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98)
labels <- c("95","96","97","98")

res <- statis.dual(list(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98), labels.tables = labels)

# Interstructure
t <- ggplot2::ggtitle("Interstructure")
plot.statis.dual.circle(points.list = list(res$interstructure), labels = res$labels.tables) + t

# Circle of correlations (all variables)
t <- ggplot2::ggtitle("Correlation (all variables)")
plot.statis.dual.circle(list(res$supervariables), labels = row.names(res$supervariables)) + t

# Circle of correlations (variables selected)
selected.variables <- c("Ph", "Temp", "DBO", "ST", "PO4", "NO3", "POD", "Cal")
superv.sel.df <- select.super.variables(res$supervariables, res$vars.names, selected.variables)

t <- ggplot2::ggtitle("Correlation (selected variables)")
plot.statis.dual.circle(list(superv.sel.df), labels = row.names(superv.sel.df)) + t

Plot Variable Trajectories in STATIS DUAL

Description

Visualizes the evolution of one or more variables across the different tables in a STATIS DUAL analysis. Each trajectory represents the sequence of positions of a variable in the compromise space.

Usage

## S3 method for class 'statis.dual.trajectories'
plot(
  vars,
  trajectories,
  labels.tables,
  .range = NULL,
  style.line = list(linetype = 2, linewidth = 0.5, color = "orange"),
  point.size = 3,
  base.colors = c("red", "blue", "brown", "darkgreen", "purple", "orange", "cyan4",
    "gold3", "black")
)

Arguments

Value

A ggplot object showing the trajectories of the selected variables.

See Also

plot.statis.dual.circle, statis.dual

Examples

data(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98)
labels = c("95","96","97","98")

res <- statis.dual(list(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98), labels.tables = labels)

# If you want to select some variables
vars.A <- c("Ph","ST","NO3")
t <- ggplot2::ggtitle(sprintf("Trayectorias (%s)", paste(vars.A, collapse = ", ")))

plot.statis.dual.trajectories(vars.A, res$trajectories, res$labels.tables) + t

# If you want to select an specific variable
vars.1 <- "Temp"
t <- ggplot2::ggtitle(sprintf("Trajectory (%s)", vars.1))

plot.statis.dual.trajectories(vars.1, res$trajectories, res$labels.tables) + t

# All variables
t <- ggplot2::ggtitle("Trajectories (all variables)")
plot.statis.dual.trajectories(res$vars.names, res$trajectories, res$labels.tables) + t

Plot a Plane of Observations or 2D Projections

Description

This function generates a two-dimensional scatter plot with centered axes, useful for representing the results of multivariate analyses.

Usage

## S3 method for class 'statis.plane'
plot(points, inertia = 100, labels = NULL, title = "")

Arguments

Details

The plot includes points, optional labels, Cartesian axes (centered at 0), and a title indicating the percentage of explained inertia.

Value

A ggplot object with the generated plot.

See Also

statis

Examples

data(expert1, expert2, expert3)

labels <- c("Expert 1", "Expert 2", "Expert 3")

# If you want to select an specific table or row just set the parameters in the statis function.

res <- statis(list(expert1, expert2, expert3), table.labels = labels)

# Main Plane of Average Individuals
individuals <- res$plane.individuals
plot.statis.plane(individuals$points, individuals$inertia, individuals$labels, individuals$title)

# Main Plane of the Evolution of individuals
evolution <- res$plane.evolution
plot.statis.plane(evolution$points, evolution$inertia, evolution$labels, evolution$title)

Select and prepare a subset of variables from a supervision matrix

Description

This function selects a predefined subset of variables (ETCal) from a supervision matrix (superv), checks dimension consistency, verifies missing variables, and constructs a clean data frame containing the first two coordinates typically used for PCA or STATIS correlation plots.

Usage

select.super.variables(superv, ET, ETCal)

Arguments

Details

The function performs the following steps:

1. Checks that the number of rows in superv matches the length of ET.

2. Assigns the row names of superv using ET.

3. Identifies whether any variables in ETCal are missing in superv; missing variables trigger a warning.

4. Creates an ordered list of valid variables (ETCal_ok) based on their presence in superv.

5. Extracts the corresponding rows from superv and constructs a data frame with columns x and y.

Value

A data frame with two columns:

• x: first coordinate (e.g., PC1)

• y: second coordinate (e.g., PC2)

Row names correspond to the selected variables defined in ETCal.

Examples

data(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98)
labels <- c("95","96","97","98")

res <- statis.dual(list(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98), labels.tables = labels)

ETCal <- c("Ph","Temp","DBO","ST","PO4","NO3","POD","Cal")

df_selected <- select.super.variables(res$supervariables, res$vars.names, ETCal)

STATIS Method

Description

Applies the STATIS method to a set of matrices (data tables) with the same rows. Is a multivariate analysis technique that allows studying the common structure and the evolution of individuals and variables across multiple tables.

Usage

statis(
  matrices,
  selected.tables = NULL,
  selected.rows = NULL,
  table.labels = NULL
)

Arguments

Value

A list with the following elements:

See Also

plot.statis.circle, plot.statis.plane

Examples

data(expert1, expert2, expert3)

labels <- c("Expert 1", "Expert 2", "Expert 3")

# If you want to select an specific table or tables
res <- statis(list(expert1, expert2, expert3), selected.tables = c(1, 3), table.labels = labels)

# If you want to select an specific row or rows
res <- statis(list(expert1, expert2, expert3), selected.rows = c(1, 5), table.labels = labels)

# If you want to select some tables and rows at the same time
res <- statis(list(expert1,expert2,expert3), selected.tables=c(1, 3), selected.rows=c(1, 4), labels)

# All tables and rows selected
res <- statis(list(expert1, expert2, expert3), table.labels = labels)

# How to use res
inter <- res$circle.inter
plot.statis.circle(inter$points, inter$inertia, inter$labels, inter$title)

evolution <- res$plane.evolution
plot.statis.plane(evolution$points, evolution$inertia, evolution$labels, evolution$title)

STATIS DUAL Analysis

Description

Implementation of the STATIS DUAL method for the joint analysis of multiple tables that share the same variables. This approach allows evaluating the common structure between tables (interstructure), building a compromise (weighted average of structures), and analyzing the trajectories of variables across the tables.

Usage

statis.dual(tables, labels.tables = NULL)

Arguments

Details

The STATIS DUAL method allows:

• Evaluating structural coherence across multiple tables using the interstructure

• Constructing a representative compromise of the set of tables

• Analyzing the behavior of the variables across the set (trajectories)

Internally, the tables are centered and normalized considering uniform observation weights. The R matrices capture the internal structure of each table. The interstructure is based on scalar products between these matrices.

Value

A list with the following elements:

See Also

plot.statis.dual.circle, plot.statis.dual.trajectories

Examples

data(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98)
labels = c("95","96","97","98")

res <- statis.dual(list(Tuis5_95, Tuis5_96, Tuis5_97, Tuis5_98), labels.tables = labels)

# How to use res
t <- ggplot2::ggtitle("Correlation (all variables)")
plot.statis.dual.circle(list(res$supervariables), labels = row.names(res$supervariables)) + t

t <- ggplot2::ggtitle("Trajectories (all variables)")
plot.statis.dual.trajectories(res$vars.names, res$trajectories, res$labels.tables) + t