Package 'dimensio'

Title:	Multivariate Data Analysis
Description:	Simple Principal Components Analysis (PCA) and (Multiple) Correspondence Analysis (CA) based on the Singular Value Decomposition (SVD). This package provides S4 classes and methods to compute, extract, summarize and visualize results of multivariate data analysis. It also includes methods for partial bootstrap validation described in Greenacre (1984, ISBN: 978-0-12-299050-2) and Lebart et al. (2006, ISBN: 978-2-10-049616-7).
Authors:	Nicolas Frerebeau [aut, cre] (<https://orcid.org/0000-0001-5759-4944>, Université Bordeaux Montaigne), Jean-Baptiste Fourvel [ctb] (<https://orcid.org/0000-0002-1061-4642>, CNRS), Brice Lebrun [ctb] (<https://orcid.org/0000-0001-7503-8685>, Logo designer), Université Bordeaux Montaigne [fnd], CNRS [fnd]
Maintainer:	Nicolas Frerebeau <[email protected]>
License:	GPL (>= 3)
Version:	0.9.0
Built:	2024-08-27 06:08:20 UTC
Source:	https://github.com/tesselle/dimensio

Benthos

Description

Abundances of Marine Species in Sea-Bed Samples

Usage

benthos
benthos

Format

A data.frame with 13 columns (sites) and 92 rows (species).

Source

http://www.carme-n.org/?sec=data7

Biplot

Description

Biplot

Usage

## S4 method for signature 'CA'
biplot(
  x,
  ...,
  axes = c(1, 2),
  type = c("symetric", "rows", "columns", "contributions"),
  active = TRUE,
  sup = TRUE,
  labels = NULL,
  col.rows = c("#E69F00", "#009E73"),
  col.columns = c("#56B4E9", "#F0E442"),
  cex.rows = graphics::par("cex"),
  cex.columns = graphics::par("cex"),
  pch.rows = 16,
  pch.columns = 17,
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'PCA'
biplot(
  x,
  ...,
  axes = c(1, 2),
  type = c("form", "covariance"),
  active = TRUE,
  sup = TRUE,
  labels = "variables",
  col.rows = c("#E69F00", "#009E73"),
  col.columns = c("#56B4E9", "#F0E442"),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  legend = list(x = "topleft")
)
## S4 method for signature 'CA'
biplot(
  x,
  ...,
  axes = c(1, 2),
  type = c("symetric", "rows", "columns", "contributions"),
  active = TRUE,
  sup = TRUE,
  labels = NULL,
  col.rows = c("#E69F00", "#009E73"),
  col.columns = c("#56B4E9", "#F0E442"),
  cex.rows = graphics::par("cex"),
  cex.columns = graphics::par("cex"),
  pch.rows = 16,
  pch.columns = 17,
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'PCA'
biplot(
  x,
  ...,
  axes = c(1, 2),
  type = c("form", "covariance"),
  active = TRUE,
  sup = TRUE,
  labels = "variables",
  col.rows = c("#E69F00", "#009E73"),
  col.columns = c("#56B4E9", "#F0E442"),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  legend = list(x = "topleft")
)

Arguments

`x`	A `CA`, `MCA` or `PCA` object.
`...`	Currently not used.
`axes`	A length-two `numeric` vector giving the dimensions to be plotted.
`type`	A `character` string specifying the biplot to be plotted (see below). It must be one of "`rows`", "`columns`", "`contribution`" (CA), "`form`" or "`covariance`" (PCA). Any unambiguous substring can be given.
`active`	A `logical` scalar: should the active observations be plotted?
`sup`	A `logical` scalar: should the supplementary observations be plotted?
`labels`	A `character` vector specifying whether "`rows`"/"`individuals`" and/or "`columns`"/"`variables`" names must be drawn. Any unambiguous substring can be given.
`col.rows`	A length-two `vector` of color specification for the active and supplementary rows.
`col.columns`	A length-two `vector` of color specification for the active and supplementary columns.
`xlim`	A length-two `numeric` vector giving the x limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`ylim`	A length-two `numeric` vector giving the y limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`main`	A `character` string giving a main title for the plot.
`sub`	A `character` string giving a subtitle for the plot.
`legend`	A `list` of additional arguments to be passed to `graphics::legend()`; names of the list are used as argument names. If `NULL`, no legend is displayed.
`pch`, `pch.rows`, `pch.columns`	A symbol specification.
`cex`, `cex.rows`, `cex.columns`	A `numeric` vector giving the amount by which plotting characters and symbols should be scaled relative to the default.

Details

A biplot is the simultaneous representation of rows and columns of a rectangular dataset. It is the generalization of a scatterplot to the case of mutlivariate data: it allows to visualize as much information as possible in a single graph (Greenacre 2010).

Biplots have the drawbacks of their advantages: they can quickly become difficult to read as they display a lot of information at once. It may then be preferable to visualize the results for individuals and variables separately.

Value

biplot() is called for its side-effects: it results in a graphic being displayed. Invisibly returns x.

PCA Biplots

form (row-metric-preserving): The form biplot favors the representation of the individuals: the distance between the individuals approximates the Euclidean distance between rows. In the form biplot the length of a vector approximates the quality of the representation of the variable.
covariance (column-metric-preserving): The covariance biplot favors the representation of the variables: the length of a vector approximates the standard deviation of the variable and the cosine of the angle formed by two vectors approximates the correlation between the two variables. In the covariance biplot the distance between the individuals approximates the Mahalanobis distance between rows.

CA Biplots

symetric (symetric biplot): Represents the row and column profiles simultaneously in a common space: rows and columns are in standard coordinates. Note that the the inter-distance between any row and column items is not meaningful.
rows (asymetric biplot): Row principal biplot (row-metric-preserving) with rows in principal coordinates and columns in standard coordinates.
columns (asymetric biplot): Column principal biplot (column-metric-preserving) with rows in standard coordinates and columns in principal coordinates.
contribution (asymetric biplot): Contribution biplot with rows in principal coordinates and columns in standard coordinates multiplied by the square roots of their masses.

Author(s)

N. Frerebeau

References

Aitchison, J. and Greenacre, M. J. (2002). Biplots of Compositional Data. Journal of the Royal Statistical Society: Series C (Applied Statistics), 51(4): 375-92. doi:10.1111/1467-9876.00275.

Greenacre, M. J. (2010). Biplots in Practice. Bilbao: Fundación BBVA.

Examples

## Replicate examples from Greenacre 2007, p. 59-68
data("countries")

## Compute principal components analysis
## All rows and all columns obtain the same weight
row_w <- rep(1 / nrow(countries), nrow(countries)) # 1/13
col_w <- rep(1 / ncol(countries), ncol(countries)) # 1/6
Y <- pca(countries, scale = FALSE, weight_row = row_w, weight_col = col_w)

## Row-metric-preserving biplot (form biplot)
biplot(Y, type = "form")

## Column-metric-preserving biplot (covariance biplot)
biplot(Y, type = "covariance", legend = list(x = "bottomright"))

## Replicate examples from Greenacre 2007, p. 79-88
data("benthos")

## Compute correspondence analysis
X <- ca(benthos)

## Symetric CA biplot
biplot(X, labels = "columns", legend = list(x = "bottomright"))

## Row principal CA biplot
biplot(X, type = "row", labels = "columns", legend = list(x = "bottomright"))

## Column principal CA biplot
biplot(X, type = "column", labels = "columns", legend = list(x = "bottomright"))

## Contribution CA biplot
biplot(X, type = "contrib", labels = NULL, legend = list(x = "bottomright"))
## Replicate examples from Greenacre 2007, p. 59-68
data("countries")

## Compute principal components analysis
## All rows and all columns obtain the same weight
row_w <- rep(1 / nrow(countries), nrow(countries)) # 1/13
col_w <- rep(1 / ncol(countries), ncol(countries)) # 1/6
Y <- pca(countries, scale = FALSE, weight_row = row_w, weight_col = col_w)

## Row-metric-preserving biplot (form biplot)
biplot(Y, type = "form")

## Column-metric-preserving biplot (covariance biplot)
biplot(Y, type = "covariance", legend = list(x = "bottomright"))

## Replicate examples from Greenacre 2007, p. 79-88
data("benthos")

## Compute correspondence analysis
X <- ca(benthos)

## Symetric CA biplot
biplot(X, labels = "columns", legend = list(x = "bottomright"))

## Row principal CA biplot
biplot(X, type = "row", labels = "columns", legend = list(x = "bottomright"))

## Column principal CA biplot
biplot(X, type = "column", labels = "columns", legend = list(x = "bottomright"))

## Contribution CA biplot
biplot(X, type = "contrib", labels = NULL, legend = list(x = "bottomright"))

Partial Bootstrap Analysis

Description

Checks analysis with partial bootstrap resampling.

Usage

## S4 method for signature 'CA'
bootstrap(object, n = 30)

## S4 method for signature 'PCA'
bootstrap(object, n = 30)
## S4 method for signature 'CA'
bootstrap(object, n = 30)

## S4 method for signature 'PCA'
bootstrap(object, n = 30)

Arguments

`object`	A `CA` or `PCA` object.
`n`	A non-negative `integer` giving the number of bootstrap replications.

Value

Returns a BootstrapCA or a BootstrapPCA object.

Author(s)

N. Frerebeau

References

Greenacre, Michael J. Theory and Applications of Correspondence Analysis. London: Academic Press, 1984.

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006.

Lockyear, K. (2013). Applying Bootstrapped Correspondence Analysis to Archaeological Data. Journal of Archaeological Science, 40(12): 4744-4753. doi:10.1016/j.jas.2012.08.035.

Ringrose, T. J. (1992). Bootstrapping and Correspondence Analysis in Archaeology. Journal of Archaeological Science, 19(6): 615-629. doi:10.1016/0305-4403(92)90032-X.

Examples

## Bootstrap on CA
## Data from Lebart et al. 2006, p. 170-172
data("colours")

## Compute correspondence analysis
X <- ca(colours)

## Bootstrap (30 replicates)
Y <- bootstrap(X, n = 30)

## Not run: 
## Get replicated coordinates
get_replications(Y, margin = 1)
get_replications(Y, margin = 2)

## End(Not run)

## Plot with ellipses
viz_rows(Y)
viz_tolerance(Y, margin = 1, level = c(0.68, 0.95))

viz_columns(Y)
viz_tolerance(Y, margin = 2, level = c(0.68, 0.95))

## Plot with convex hulls
viz_columns(Y)
viz_hull(Y, margin = 2)

## Bootstrap on PCA
## Compute principal components analysis
data("iris")
X <- pca(iris)

## Bootstrap (30 replicates)
Y <- bootstrap(X, n = 30)

## Plot with ellipses
viz_variables(Y)
viz_tolerance(Y, margin = 2, level = c(0.68, 0.95))
## Bootstrap on CA
## Data from Lebart et al. 2006, p. 170-172
data("colours")

## Compute correspondence analysis
X <- ca(colours)

## Bootstrap (30 replicates)
Y <- bootstrap(X, n = 30)

## Not run: 
## Get replicated coordinates
get_replications(Y, margin = 1)
get_replications(Y, margin = 2)

## End(Not run)

## Plot with ellipses
viz_rows(Y)
viz_tolerance(Y, margin = 1, level = c(0.68, 0.95))

viz_columns(Y)
viz_tolerance(Y, margin = 2, level = c(0.68, 0.95))

## Plot with convex hulls
viz_columns(Y)
viz_hull(Y, margin = 2)

## Bootstrap on PCA
## Compute principal components analysis
data("iris")
X <- pca(iris)

## Bootstrap (30 replicates)
Y <- bootstrap(X, n = 30)

## Plot with ellipses
viz_variables(Y)
viz_tolerance(Y, margin = 2, level = c(0.68, 0.95))

Burt Table

Description

Computes the burt table of a factor table.

Usage

burt(object, ...)

## S4 method for signature 'data.frame'
burt(object, exclude = NULL, abbrev = TRUE)
burt(object, ...)

## S4 method for signature 'data.frame'
burt(object, exclude = NULL, abbrev = TRUE)

Arguments

`object`	A `data.frame`.
`...`	Currently not used.
`exclude`	A `vector` of values to be excluded when forming the set of levels (see `factor()`). If `NULL` (the default), will make `NA` an extra level.
`abbrev`	A `logical` scalar: should the column names be abbreviated? If `FALSE`, these are of the form 'factor_level' but if `abbrev = TRUE` they are just 'level' which will suffice if the factors have distinct levels.

Value

A symetric matrix.

Author(s)

N. Frerebeau

Examples

## Create a factor table
x <- data.frame(
  A = c("a", "b", "a"),
  B = c("x", "y", "z")
)

## Complete disjunctive table
cdt(x)

## Burt table
burt(x)
## Create a factor table
x <- data.frame(
  A = c("a", "b", "a"),
  B = c("x", "y", "z")
)

## Complete disjunctive table
cdt(x)

## Burt table
burt(x)

Correspondence Analysis

Description

Computes a simple correspondence analysis based on the singular value decomposition.

Usage

ca(object, ...)

## S4 method for signature 'data.frame'
ca(object, rank = NULL, sup_row = NULL, sup_col = NULL)

## S4 method for signature 'matrix'
ca(object, rank = NULL, sup_row = NULL, sup_col = NULL)
ca(object, ...)

## S4 method for signature 'data.frame'
ca(object, rank = NULL, sup_row = NULL, sup_col = NULL)

## S4 method for signature 'matrix'
ca(object, rank = NULL, sup_row = NULL, sup_col = NULL)

Arguments

`object`	A $m \times p$ numeric `matrix` or a `data.frame`.
`...`	Currently not used.
`rank`	An `integer` value specifying the maximal number of components to be kept in the results. If `NULL` (the default), $min(m, p) - 1$ components will be returned.
`sup_row`	A `vector` specifying the indices of the supplementary rows.
`sup_col`	A `vector` specifying the indices of the supplementary columns.

Value

A CA object.

Author(s)

N. Frerebeau

References

Greenacre, M. J. Theory and Applications of Correspondence Analysis. London: Academic Press, 1984.

Greenacre, M. J. Correspondence Analysis in Practice. Seconde edition. Interdisciplinary Statistics Series. Boca Raton: Chapman & Hall/CRC, 2007.

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006.

Examples

## Data from Lebart et al. 2006, p. 170-172
data("colours")

## The chi square of independence between the two variables
stats::chisq.test(colours)

## Compute correspondence analysis
X <- ca(colours)

## Plot rows
viz_rows(X, labels = TRUE)

## Plot columns
viz_columns(X, labels = TRUE)

## Get row coordinates
get_coordinates(X, margin = 1)

## Get column coordinates
get_coordinates(X, margin = 2)

## Get total inertia
sum(get_inertia(X))

## Get row contributions
get_contributions(X, margin = 1)
## Data from Lebart et al. 2006, p. 170-172
data("colours")

## The chi square of independence between the two variables
stats::chisq.test(colours)

## Compute correspondence analysis
X <- ca(colours)

## Plot rows
viz_rows(X, labels = TRUE)

## Plot columns
viz_columns(X, labels = TRUE)

## Get row coordinates
get_coordinates(X, margin = 1)

## Get column coordinates
get_coordinates(X, margin = 2)

## Get total inertia
sum(get_inertia(X))

## Get row contributions
get_contributions(X, margin = 1)

Complete Disjunctive Table

Description

Computes the complete disjunctive table of a factor table.

Usage

cdt(object, ...)

## S4 method for signature 'matrix'
cdt(object, exclude = NULL, abbrev = TRUE)

## S4 method for signature 'data.frame'
cdt(object, exclude = NULL, abbrev = TRUE)
cdt(object, ...)

## S4 method for signature 'matrix'
cdt(object, exclude = NULL, abbrev = TRUE)

## S4 method for signature 'data.frame'
cdt(object, exclude = NULL, abbrev = TRUE)

Arguments

`object`	A `data.frame`.
`...`	Currently not used.
`exclude`	A `vector` of values to be excluded when forming the set of levels (see `factor()`). If `NULL` (the default), will make `NA` an extra level.
`abbrev`	A `logical` scalar: should the column names be abbreviated? If `FALSE`, these are of the form 'factor_level' but if `abbrev = TRUE` they are just 'level' which will suffice if the factors have distinct levels.

Value

A data.frame.

Author(s)

N. Frerebeau

Examples

## Create a factor table
x <- data.frame(
  A = c("a", "b", "a"),
  B = c("x", "y", "z")
)

## Complete disjunctive table
cdt(x)

## Burt table
burt(x)
## Create a factor table
x <- data.frame(
  A = c("a", "b", "a"),
  B = c("x", "y", "z")
)

## Complete disjunctive table
cdt(x)

## Burt table
burt(x)

Colours

Description

Contingency table of eye and hair colours of different individuals.

Usage

colours
colours

Format

A data.frame with 4 columns (hair colours) and 4 rows (eye colours).

Source

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006, p. 170-172

Countries

Description

Student ratings of 13 countries on six attributes.

Usage

countries
countries

Format

A data.frame with 6 columns (attributes) and 13 rows (countries).

Source

Greenacre, M. J. Biplots in Practice. Bilbao: Fundación BBVA, 2010.

Dimnames of an Object

Description

Retrieve or set the dimnames of an object.

Usage

## S4 method for signature 'MultivariateAnalysis'
dim(x)

## S4 method for signature 'MultivariateAnalysis'
rownames(x, do.NULL = TRUE, prefix = "row")

## S4 method for signature 'MultivariateAnalysis'
colnames(x, do.NULL = TRUE, prefix = "col")

## S4 method for signature 'MultivariateAnalysis'
dimnames(x)
## S4 method for signature 'MultivariateAnalysis'
dim(x)

## S4 method for signature 'MultivariateAnalysis'
rownames(x, do.NULL = TRUE, prefix = "row")

## S4 method for signature 'MultivariateAnalysis'
colnames(x, do.NULL = TRUE, prefix = "col")

## S4 method for signature 'MultivariateAnalysis'
dimnames(x)

Arguments

`x`	An object from which to retrieve the row or column names (a `CA` or `PCA` object).
`do.NULL`	A `logical` scalar. If `FALSE` and names are `NULL`, names are created.
`prefix`	A `character` string specifying the prefix for created names.

Author(s)

N. Frerebeau

Get Contributions

Description

Get Contributions

Usage

get_contributions(x, ...)

get_correlations(x, ...)

get_cos2(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_contributions(x, margin = 1)

## S4 method for signature 'PCA'
get_correlations(x, sup_name = ".sup")

## S4 method for signature 'MultivariateAnalysis'
get_cos2(x, margin = 1, sup_name = ".sup")
get_contributions(x, ...)

get_correlations(x, ...)

get_cos2(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_contributions(x, margin = 1)

## S4 method for signature 'PCA'
get_correlations(x, sup_name = ".sup")

## S4 method for signature 'MultivariateAnalysis'
get_cos2(x, margin = 1, sup_name = ".sup")

Arguments

`x`	An object from which to get element(s) (a `CA`, `MCA` or `PCA` object).
`...`	Currently not used.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`sup_name`	A `character` string specifying the name of the column to create for supplementary points attribution (see below).

Value

get_contributions() returns a data.frame of contributions to the definition of the principal dimensions.
get_correlations() returns a data.frame of correlations between variables and dimensions. An extra column (named after sup_name) is added specifying whether an observation is a supplementary point or not.
get_cos2() returns a data.frame of $cos^2$ values (i.e. quality of the representation of the points on the factor map). An extra column (named after sup_name) is added specifying whether an observation is a supplementary point or not.

Author(s)

N. Frerebeau

Get Coordinates

Description

Get Coordinates

Usage

get_coordinates(x, ...)

get_replications(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_coordinates(x, margin = 1, principal = TRUE, sup_name = ".sup")

## S4 method for signature 'PCOA'
get_coordinates(x)

## S4 method for signature 'MultivariateBootstrap'
get_replications(x, margin = 1)

## S4 method for signature 'BootstrapPCA'
get_replications(x)
get_coordinates(x, ...)

get_replications(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_coordinates(x, margin = 1, principal = TRUE, sup_name = ".sup")

## S4 method for signature 'PCOA'
get_coordinates(x)

## S4 method for signature 'MultivariateBootstrap'
get_replications(x, margin = 1)

## S4 method for signature 'BootstrapPCA'
get_replications(x)

Arguments

`x`	An object from which to get element(s) (a `CA`, `MCA` or `PCA` object).
`...`	Currently not used.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`principal`	A `logical` scalar: should principal coordinates be returned? If `FALSE`, standard coordinates are returned.
`sup_name`	A `character` string specifying the name of the column to create for supplementary points attribution (see below).

Value

get_coordinates() returns a data.frame of coordinates. An extra column (named after sup_name) is added specifying whether an observation is a supplementary point or not.
get_replications() returns an array of coordinates.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_row = 5:10)

## Get row principal coordinates
head(get_coordinates(X, margin = 1, principal = TRUE))

## Get row standard coordinates
head(get_coordinates(X, margin = 1, principal = FALSE))

## Tidy principal coordinates
head(tidy(X, margin = 1))
head(tidy(X, margin = 2))

head(augment(X, margin = 1, axes = c(1, 2)))
head(augment(X, margin = 2, axes = c(1, 2)))
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_row = 5:10)

## Get row principal coordinates
head(get_coordinates(X, margin = 1, principal = TRUE))

## Get row standard coordinates
head(get_coordinates(X, margin = 1, principal = FALSE))

## Tidy principal coordinates
head(tidy(X, margin = 1))
head(tidy(X, margin = 2))

head(augment(X, margin = 1, axes = c(1, 2)))
head(augment(X, margin = 2, axes = c(1, 2)))

Get Original Data

Description

Get Original Data

Usage

get_data(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_data(x)
get_data(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_data(x)

Arguments

`x`	An object from which to get element(s) (a `CA`, `MCA` or `PCA` object).
`...`	Currently not used.

Value

Returns a data.frame of original data.

Author(s)

N. Frerebeau

Get Eigenvalues

Description

Get Eigenvalues

Usage

get_eigenvalues(x)

get_variance(x, ...)

get_distances(x, ...)

get_inertia(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_distances(x, margin = 1)

## S4 method for signature 'MultivariateAnalysis'
get_eigenvalues(x)

## S4 method for signature 'PCOA'
get_eigenvalues(x)

## S4 method for signature 'MultivariateAnalysis'
get_inertia(x, margin = 1)

## S4 method for signature 'MultivariateAnalysis'
get_variance(x, digits = 2)
get_eigenvalues(x)

get_variance(x, ...)

get_distances(x, ...)

get_inertia(x, ...)

## S4 method for signature 'MultivariateAnalysis'
get_distances(x, margin = 1)

## S4 method for signature 'MultivariateAnalysis'
get_eigenvalues(x)

## S4 method for signature 'PCOA'
get_eigenvalues(x)

## S4 method for signature 'MultivariateAnalysis'
get_inertia(x, margin = 1)

## S4 method for signature 'MultivariateAnalysis'
get_variance(x, digits = 2)

Arguments

`x`	An object from which to get element(s) (a `CA`, `MCA` or `PCA` object).
`...`	Currently not used.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`digits`	An `integer` indicating the number of decimal places to be used.

Value

get_eigenvalues() returns a data.frame with the following columns: eigenvalues, variance (percentage of variance) and cumulative (cumulative percentage of variance).
get_variance() returns a numeric vector giving the amount of variance explained by each (principal) component.
get_distance()returns a numeric vector of squared distance to the centroid.
get_inertia() returns a numeric vector giving the inertia (weighted squared distance to the centroid).

Author(s)

N. Frerebeau

Extract Loadings

Description

Extract loadingsin principal components analysis.

Usage

## S4 method for signature 'PCA'
loadings(x, ...)
## S4 method for signature 'PCA'
loadings(x, ...)

Arguments

`x`	A `PCA` object.
`...`	Currently not used.

Value

Returns variable loadings (i.e. the coefficients of the linear combination of the original variables).

Note

loadings() is only implemented for consistency with stats::loadings().

Author(s)

N. Frerebeau

Multiple Correspondence Analysis

Description

Computes a multiple correspondence analysis.

Usage

mca(object, ...)

## S4 method for signature 'data.frame'
mca(object, rank = NULL, sup_row = NULL, sup_col = NULL, sup_quanti = NULL)

## S4 method for signature 'matrix'
mca(object, rank = NULL, sup_row = NULL, sup_col = NULL)
mca(object, ...)

## S4 method for signature 'data.frame'
mca(object, rank = NULL, sup_row = NULL, sup_col = NULL, sup_quanti = NULL)

## S4 method for signature 'matrix'
mca(object, rank = NULL, sup_row = NULL, sup_col = NULL)

Arguments

`object`	A $m \times p$ numeric `matrix` or a `data.frame`.
`...`	Currently not used.
`rank`	An `integer` value specifying the maximal number of components to be kept in the results. If `NULL` (the default), $min(m, p) - 1$ components will be returned.
`sup_row`	A `vector` specifying the indices of the supplementary rows.
`sup_col`	A `vector` specifying the indices of the supplementary categorical columns.
`sup_quanti`	A `vector` specifying the indices of the supplementary quantitative columns.

Value

A MCA object.

Author(s)

N. Frerebeau

References

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006.

Principal Components Analysis

Description

Computes a principal components analysis based on the singular value decomposition.

Usage

pca(object, ...)

## S4 method for signature 'data.frame'
pca(
  object,
  center = TRUE,
  scale = TRUE,
  rank = NULL,
  sup_row = NULL,
  sup_col = NULL,
  sup_quali = NULL,
  weight_row = NULL,
  weight_col = NULL
)

## S4 method for signature 'matrix'
pca(
  object,
  center = TRUE,
  scale = TRUE,
  rank = NULL,
  sup_row = NULL,
  sup_col = NULL,
  weight_row = NULL,
  weight_col = NULL
)
pca(object, ...)

## S4 method for signature 'data.frame'
pca(
  object,
  center = TRUE,
  scale = TRUE,
  rank = NULL,
  sup_row = NULL,
  sup_col = NULL,
  sup_quali = NULL,
  weight_row = NULL,
  weight_col = NULL
)

## S4 method for signature 'matrix'
pca(
  object,
  center = TRUE,
  scale = TRUE,
  rank = NULL,
  sup_row = NULL,
  sup_col = NULL,
  weight_row = NULL,
  weight_col = NULL
)

Arguments

`object`	A $m \times p$ numeric `matrix` or a `data.frame`.
`...`	Currently not used.
`center`	A `logical` scalar: should the variables be shifted to be zero centered?
`scale`	A `logical` scalar: should the variables be scaled to unit variance?
`rank`	An `integer` value specifying the maximal number of components to be kept in the results. If `NULL` (the default), $p - 1$ components will be returned.
`sup_row`	A `vector` specifying the indices of the supplementary rows.
`sup_col`	A `vector` specifying the indices of the supplementary columns.
`sup_quali`	A `vector` specifying the indices of the supplementary qualitative columns.
`weight_row`	A `numeric` vector specifying the active row (individual) weights. If `NULL` (the default), uniform weights are used. Row weights are internally normalized to sum 1
`weight_col`	A `numeric` vector specifying the active column (variable) weights. If `NULL` (the default), uniform weights (1) are used.

Value

A PCA object.

Author(s)

N. Frerebeau

References

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006.

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris)

## Get eigenvalues
get_eigenvalues(X)

## Get individual cos2
head(get_cos2(X, margin = 1))

## Get variable contributions
get_contributions(X, margin = 2)

## Get correlations between variables and dimensions
get_correlations(X)
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris)

## Get eigenvalues
get_eigenvalues(X)

## Get individual cos2
head(get_cos2(X, margin = 1))

## Get variable contributions
get_contributions(X, margin = 2)

## Get correlations between variables and dimensions
get_correlations(X)

Principal Coordinates Analysis

Description

Computes classical (metric) multidimensional scaling.

Usage

pcoa(object, ...)

## S4 method for signature 'dist'
pcoa(object, rank = 2)
pcoa(object, ...)

## S4 method for signature 'dist'
pcoa(object, rank = 2)

Arguments

`object`	A distance structure.
`...`	Currently not used.
`rank`	An `integer` value specifying the maximal number dimension of the space which the data are to be represented in.

Value

A PCOA object.

Author(s)

N. Frerebeau

References

Gower, J. C. (1966). Some Distance Properties of Latent Root and Vector Methods Used in Multivariate Analysis. Biometrika, 53(3‑4): 325-338. doi:10.1093/biomet/53.3-4.325.

Examples

## Load data
data("iris")

## Compute euclidean distances
d <- dist(iris[, 1:4], method = "euclidean")

## Compute principal coordinates analysis
X <- pcoa(d)

## Screeplot
screeplot(X)

## Plot results
plot(X, extra_quali = iris$Species)
## Load data
data("iris")

## Compute euclidean distances
d <- dist(iris[, 1:4], method = "euclidean")

## Compute principal coordinates analysis
X <- pcoa(d)

## Screeplot
screeplot(X)

## Plot results
plot(X, extra_quali = iris$Species)

Plot Coordinates

Description

Plot Coordinates

Usage

## S4 method for signature 'PCOA,missing'
plot(
  x,
  ...,
  axes = c(1, 2),
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  ann = graphics::par("ann"),
  frame.plot = TRUE,
  panel.first = NULL,
  panel.last = NULL
)
## S4 method for signature 'PCOA,missing'
plot(
  x,
  ...,
  axes = c(1, 2),
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  ann = graphics::par("ann"),
  frame.plot = TRUE,
  panel.first = NULL,
  panel.last = NULL
)

Arguments

`x`	An R object.
`...`	Further graphical parameters.
`axes`	A length-two `numeric` vector giving the dimensions to be plotted.
`labels`	A `logical` scalar: should labels be drawn? Labeling a large number of points can be computationally expensive and make the graph difficult to read. A selection of points to label can be provided using a `list` of two named elements, `filter` (a string specifying how to filter the labels to be drawn) and `n` (an integer specifying the number of labels to be drawn). See examples below.
`extra_quali`	An optional vector of qualitative data for aesthetics mapping.
`extra_quanti`	An optional vector of quantitative data for aesthetics mapping. If a single `character` string is passed, it must be one of "`observation`", "`mass`", "`sum`", "`contribution`" or "`cos2`" (see `augment()`).
`color`	The colors for lines and points (will be mapped to `extra_quanti` or `extra_quali`; if both are set, the latter has priority). Ignored if set to `FALSE`.
`fill`	The background colors for points (will be mapped to `extra_quanti` or `extra_quali`; if both are set, the latter has priority). Ignored if set to `FALSE`.
`symbol`	A vector of plotting characters or symbols (will be mapped to `extra_quali`). This can either be a single character or an integer code for one of a set of graphics symbols. If `symbol` is a named a named vector, then the symbols will be associated with their name within `extra_quali`. Ignored if set to `FALSE`.
`size`	A length-two `numeric` vector giving range of possible sizes (greater than 0; will be mapped to `extra_quanti`). Ignored if set to `FALSE`.
`xlim`	A length-two `numeric` vector giving the x limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`ylim`	A length-two `numeric` vector giving the y limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`main`	A `character` string giving a main title for the plot.
`sub`	A `character` string giving a subtitle for the plot.
`ann`	A `logical` scalar: should the default annotation (title and x and y axis labels) appear on the plot?
`frame.plot`	A `logical` scalar: should a box be drawn around the plot?
`panel.first`	An `expression` to be evaluated after the plot axes are set up but before any plotting takes place. This can be useful for drawing background grids.
`panel.last`	An `expression` to be evaluated after plotting has taken place but before the axes, title and box are added.

Author(s)

N. Frerebeau

Predict New Coordinates

Description

Predict the projection of new individuals/rows or variables/columns.

Usage

## S4 method for signature 'CA'
predict(object, newdata, margin = 1)

## S4 method for signature 'MCA'
predict(object, newdata, margin = 1)

## S4 method for signature 'PCA'
predict(object, newdata, margin = 1)
## S4 method for signature 'CA'
predict(object, newdata, margin = 1)

## S4 method for signature 'MCA'
predict(object, newdata, margin = 1)

## S4 method for signature 'PCA'
predict(object, newdata, margin = 1)

Arguments

`object`	A `CA` or `PCA` object.
`newdata`	An object of supplementary points coercible to a `matrix` for which to compute principal coordinates.
`margin`	A length-one `numeric` vector giving the subscript which the data will be predicted: `1` indicates individuals/rows (the default), `2` indicates variables/columns.

Value

A data.frame of coordinates.

Author(s)

N. Frerebeau

Examples

## Create a matrix
A <- matrix(data = sample(1:10, 100, TRUE), nrow = 10, ncol = 10)

## Compute correspondence analysis
X <- ca(A, sup_row = 8:10, sup_col = 7:10)

## Predict new row coordinates
Y <- matrix(data = sample(1:10, 120, TRUE), nrow = 20, ncol = 6)
predict(X, Y, margin = 1)

## Predict new column coordinates
Z <- matrix(data = sample(1:10, 140, TRUE), nrow = 7, ncol = 20)
predict(X, Z, margin = 2)
## Create a matrix
A <- matrix(data = sample(1:10, 100, TRUE), nrow = 10, ncol = 10)

## Compute correspondence analysis
X <- ca(A, sup_row = 8:10, sup_col = 7:10)

## Predict new row coordinates
Y <- matrix(data = sample(1:10, 120, TRUE), nrow = 20, ncol = 6)
predict(X, Y, margin = 1)

## Predict new column coordinates
Z <- matrix(data = sample(1:10, 140, TRUE), nrow = 7, ncol = 20)
predict(X, Z, margin = 2)

Scree Plot

Description

Plot eigenvalues (scree plot) or variances histogram.

Usage

## S4 method for signature 'MultivariateAnalysis'
screeplot(
  x,
  ...,
  eigenvalues = FALSE,
  cumulative = FALSE,
  labels = TRUE,
  limit = 10,
  col = "grey90",
  border = "grey10",
  col.cumulative = "red",
  lty.cumulative = "solid",
  lwd.cumulative = 2
)

## S4 method for signature 'PCOA'
screeplot(
  x,
  ...,
  labels = FALSE,
  limit = NULL,
  col = "grey90",
  border = "grey10"
)
## S4 method for signature 'MultivariateAnalysis'
screeplot(
  x,
  ...,
  eigenvalues = FALSE,
  cumulative = FALSE,
  labels = TRUE,
  limit = 10,
  col = "grey90",
  border = "grey10",
  col.cumulative = "red",
  lty.cumulative = "solid",
  lwd.cumulative = 2
)

## S4 method for signature 'PCOA'
screeplot(
  x,
  ...,
  labels = FALSE,
  limit = NULL,
  col = "grey90",
  border = "grey10"
)

Arguments

`x`	A `CA`, `MCA` or `PCA` object.
`...`	Extra parameters to be passed to `graphics::barplot()`.
`eigenvalues`	A `logical` scalar: should the eigenvalues be plotted instead of variance/inertia?
`cumulative`	A `logical` scalar: should the cumulative percentages of variance be plotted?
`labels`	A `logical` scalar: should text labels be drawn on top of bars?
`limit`	An `integer` specifying the number of top elements to be displayed.
`col`, `border`	A `character` string specifying the bars infilling and border colors.
`col.cumulative`	A specification for the line color.
`lty.cumulative`	A specification for the line type.
`lwd.cumulative`	A specification for the line width.

Value

screeplot() is called for its side-effects: it results in a graphic being displayed. Invisibly returns x.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Screeplot
screeplot(X)
screeplot(X, cumulative = TRUE)
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Screeplot
screeplot(X)
screeplot(X, cumulative = TRUE)

Extract Parts of an Object

Description

Operators acting on objects to extract parts.

Usage

## S4 method for signature 'CA,ANY,missing'
x[[i]]

## S4 method for signature 'PCA,ANY,missing'
x[[i]]
## S4 method for signature 'CA,ANY,missing'
x[[i]]

## S4 method for signature 'PCA,ANY,missing'
x[[i]]

Arguments

`x`	An object from which to extract element(s) or in which to replace element(s).
`i`	A `character` string specifying elements to extract. Any unambiguous substring can be given (see details).

Details

If i is "data", returns a list with the following elements:

data: A numeric matrix of raw data.
mean: A numeric vector giving the variables means (PCA).
sd: A numeric vector giving the variables standard deviations (PCA).

If i is "rows", returns a list with the following elements:

coord: A numeric matrix of rows/individuals coordinates.
cos2: A numeric matrix of rows/individuals squared cosine.
masses: A numeric vector giving the rows masses/individual weights.
sup: A logical vector specifying whether a point is a supplementary observation or not.

If i is "columns", returns a list with the following elements:

coord: A numeric matrix of columns/variables coordinates.
cor: A numeric matrix of correlation between variables and the dimensions (PCA).
cos2: A numeric matrix of columns/variables squared cosine.
masses: A numeric vector giving the columns masses/variable weights.
sup: A logical vector specifying whether a point is a supplementary observation or not.

If i is "eigenvalues", returns a numeric vector of eigenvalues.

Value

A list.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_row = 8:10, sup_col = 1)

## Get results for the individuals
X[["rows"]]
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_row = 8:10, sup_col = 1)

## Get results for the individuals
X[["rows"]]

Object Summaries

Description

Provides a summary of the results of a multivariate data analysis.

Usage

## S4 method for signature 'CA'
summary(object, ..., margin = 1, active = TRUE, sup = TRUE, rank = 3)

## S4 method for signature 'PCA'
summary(object, ..., margin = 1, active = TRUE, sup = TRUE, rank = 3)
## S4 method for signature 'CA'
summary(object, ..., margin = 1, active = TRUE, sup = TRUE, rank = 3)

## S4 method for signature 'PCA'
summary(object, ..., margin = 1, active = TRUE, sup = TRUE, rank = 3)

Arguments

`object`	A `CA`, `MCA` or `PCA` object.
`...`	Currently not used.
`margin`	A length-one `numeric` vector giving the subscript which the data will be summarized: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`active`	A `logical` scalar: should the active observations be summarized?
`sup`	A `logical` scalar: should the supplementary observations be summarized?
`rank`	An `integer` value specifying the maximal number of components to be kept in the results.

Author(s)

N. Frerebeau

Examples

## Data from Lebart et al. 2006, p. 170-172
data("colours")

## Compute correspondence analysis
X <- ca(colours)

## Rows summary
summary(X, margin = 1)

## Columns summary
summary(X, margin = 2)
## Data from Lebart et al. 2006, p. 170-172
data("colours")

## Compute correspondence analysis
X <- ca(colours)

## Rows summary
summary(X, margin = 1)

## Columns summary
summary(X, margin = 2)

Tidy Coordinates

Description

Tidy Coordinates

Usage

tidy(x, ...)

augment(x, ...)

## S4 method for signature 'MultivariateAnalysis'
augment(x, ..., margin = 1, axes = c(1, 2), principal = TRUE)

## S4 method for signature 'MultivariateAnalysis'
tidy(x, ..., margin = 1, principal = TRUE)
tidy(x, ...)

augment(x, ...)

## S4 method for signature 'MultivariateAnalysis'
augment(x, ..., margin = 1, axes = c(1, 2), principal = TRUE)

## S4 method for signature 'MultivariateAnalysis'
tidy(x, ..., margin = 1, principal = TRUE)

Arguments

`x`	A `CA`, `MCA` or `PCA` object.
`...`	Currently not used.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`axes`	A length-two `numeric` vector giving the dimensions for which to compute results.
`principal`	A `logical` scalar: should principal coordinates be returned? If `FALSE`, standard coordinates are returned.

Value

tidy() returns a long data.frame with the following columns:

label: Row/column names of the original data.
component: Component.
supplementary: Whether an observation is active or supplementary.
coordinate: Coordinates.
contribution: Contributions to the definition of the components.
cos2: $cos^2$ .

augment() returns a wide data.frame of the row/column coordinates along axes and the following columns:

label: Row/column names of the original data.
supplementary: Whether an observation is active or supplementary.
mass: Weight/mass of each observation.
sum: Sum of squared coordinates along axes.
contribution: Joint contributions to the definition of axes.
cos2: Joint $cos^2$ along axes.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_row = 5:10)

## Get row principal coordinates
head(get_coordinates(X, margin = 1, principal = TRUE))

## Get row standard coordinates
head(get_coordinates(X, margin = 1, principal = FALSE))

## Tidy principal coordinates
head(tidy(X, margin = 1))
head(tidy(X, margin = 2))

head(augment(X, margin = 1, axes = c(1, 2)))
head(augment(X, margin = 2, axes = c(1, 2)))
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_row = 5:10)

## Get row principal coordinates
head(get_coordinates(X, margin = 1, principal = TRUE))

## Get row standard coordinates
head(get_coordinates(X, margin = 1, principal = FALSE))

## Tidy principal coordinates
head(tidy(X, margin = 1))
head(tidy(X, margin = 2))

head(augment(X, margin = 1, axes = c(1, 2)))
head(augment(X, margin = 2, axes = c(1, 2)))

Visualize Contributions and cos2

Description

Plots contributions histogram and $cos^2$ scatterplot.

Usage

viz_contributions(x, ...)

viz_cos2(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_contributions(
  x,
  ...,
  margin = 2,
  axes = 1,
  sort = TRUE,
  decreasing = TRUE,
  limit = 10,
  horiz = FALSE,
  col = "grey90",
  border = "grey10"
)

## S4 method for signature 'MultivariateAnalysis'
viz_cos2(
  x,
  ...,
  margin = 2,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  sort = TRUE,
  decreasing = TRUE,
  limit = 10,
  horiz = FALSE,
  col = "grey90",
  border = "grey10"
)
viz_contributions(x, ...)

viz_cos2(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_contributions(
  x,
  ...,
  margin = 2,
  axes = 1,
  sort = TRUE,
  decreasing = TRUE,
  limit = 10,
  horiz = FALSE,
  col = "grey90",
  border = "grey10"
)

## S4 method for signature 'MultivariateAnalysis'
viz_cos2(
  x,
  ...,
  margin = 2,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  sort = TRUE,
  decreasing = TRUE,
  limit = 10,
  horiz = FALSE,
  col = "grey90",
  border = "grey10"
)

Arguments

`x`	A `CA`, `MCA` or `PCA` object.
`...`	Extra parameters to be passed to `graphics::barplot()`.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`axes`	A `numeric` vector giving the dimensions to be plotted.
`sort`	A `logical` scalar: should the data be sorted?
`decreasing`	A `logical` scalar: should the sort order be decreasing? Only used if `sort` is `TRUE`.
`limit`	An `integer` specifying the number of top elements to be displayed.
`horiz`	A `logical` scalar: should the bars be drawn horizontally with the first at the bottom?
`col`, `border`	A `character` string specifying the bars infilling and border colors.
`active`	A `logical` scalar: should the active observations be plotted?
`sup`	A `logical` scalar: should the supplementary observations be plotted?

Details

The red dashed line indicates the expected average contribution (variables with a contribution larger than this cutoff can be considered as important in contributing to the component).

Value

viz_contributions() and viz_cos2() are called for their side-effects: they result in a graphic being displayed. Invisibly return x.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Get row contributions
head(get_contributions(X, margin = 1))

## Plot contributions
viz_contributions(X, axes = 1)

## Plot cos2
viz_cos2(X)
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Get row contributions
head(get_contributions(X, margin = 1))

## Plot contributions
viz_contributions(X, axes = 1)

## Plot cos2
viz_cos2(X)

Visualize Individuals Factor Map

Description

Plots row/individual principal coordinates.

Usage

viz_individuals(x, ...)

viz_rows(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_rows(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'BootstrapCA'
viz_rows(x, ..., axes = c(1, 2), color = FALSE, fill = FALSE, symbol = FALSE)

## S4 method for signature 'PCA'
viz_individuals(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)
viz_individuals(x, ...)

viz_rows(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_rows(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'BootstrapCA'
viz_rows(x, ..., axes = c(1, 2), color = FALSE, fill = FALSE, symbol = FALSE)

## S4 method for signature 'PCA'
viz_individuals(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

Arguments

`x`	A `CA`, `MCA` or `PCA` object.
`...`	Further graphical parameters.
`axes`	A length-two `numeric` vector giving the dimensions to be plotted.
`active`	A `logical` scalar: should the active observations be plotted?
`sup`	A `logical` scalar: should the supplementary observations be plotted?
`labels`	A `logical` scalar: should labels be drawn? Labeling a large number of points can be computationally expensive and make the graph difficult to read. A selection of points to label can be provided using a `list` of two named elements, `filter` (a string specifying how to filter the labels to be drawn) and `n` (an integer specifying the number of labels to be drawn). See examples below.
`extra_quali`	An optional vector of qualitative data for aesthetics mapping.
`extra_quanti`	An optional vector of quantitative data for aesthetics mapping. If a single `character` string is passed, it must be one of "`observation`", "`mass`", "`sum`", "`contribution`" or "`cos2`" (see `augment()`).
`color`	The colors for lines and points (will be mapped to `extra_quanti` or `extra_quali`; if both are set, the latter has priority). Ignored if set to `FALSE`.
`fill`	The background colors for points (will be mapped to `extra_quanti` or `extra_quali`; if both are set, the latter has priority). Ignored if set to `FALSE`.
`symbol`	A vector of plotting characters or symbols (will be mapped to `extra_quali`). This can either be a single character or an integer code for one of a set of graphics symbols. If `symbol` is a named a named vector, then the symbols will be associated with their name within `extra_quali`. Ignored if set to `FALSE`.
`size`	A length-two `numeric` vector giving range of possible sizes (greater than 0; will be mapped to `extra_quanti`). Ignored if set to `FALSE`.
`xlim`	A length-two `numeric` vector giving the x limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`ylim`	A length-two `numeric` vector giving the y limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`main`	A `character` string giving a main title for the plot.
`sub`	A `character` string giving a subtitle for the plot.
`panel.first`	An `expression` to be evaluated after the plot axes are set up but before any plotting takes place. This can be useful for drawing background grids.
`panel.last`	An `expression` to be evaluated after plotting has taken place but before the axes, title and box are added.
`legend`	A `list` of additional arguments to be passed to `graphics::legend()`; names of the list are used as argument names. If `NULL`, no legend is displayed.

Value

⁠viz_*()⁠ is called for its side-effects: it results in a graphic being displayed. Invisibly returns x.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Plot individuals
viz_individuals(X, panel.last = graphics::grid())

## Labels of the 10 individuals with highest cos2
viz_individuals(X, labels = list(how = "cos2", n = 10))

## Plot variables
viz_variables(X, panel.last = graphics::grid())

## Graphical parameters
## Continuous values
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2))
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2),
                color = grDevices::hcl.colors(12, "RdPu"))

viz_variables(X, extra_quanti = "contribution",
              color = grDevices::hcl.colors(12, "BluGrn", rev = TRUE),
              size = c(0, 1))

## Discrete values
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23)
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23,
                fill = c("#004488", "#DDAA33", "#BB5566"),
                color = "black")

viz_variables(X, extra_quali = c("Petal", "Petal", "Sepal", "Sepal"),
              color = c("#EE7733", "#0077BB"),
              symbol = c(1, 3))
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Plot individuals
viz_individuals(X, panel.last = graphics::grid())

## Labels of the 10 individuals with highest cos2
viz_individuals(X, labels = list(how = "cos2", n = 10))

## Plot variables
viz_variables(X, panel.last = graphics::grid())

## Graphical parameters
## Continuous values
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2))
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2),
                color = grDevices::hcl.colors(12, "RdPu"))

viz_variables(X, extra_quanti = "contribution",
              color = grDevices::hcl.colors(12, "BluGrn", rev = TRUE),
              size = c(0, 1))

## Discrete values
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23)
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23,
                fill = c("#004488", "#DDAA33", "#BB5566"),
                color = "black")

viz_variables(X, extra_quali = c("Petal", "Petal", "Sepal", "Sepal"),
              color = c("#EE7733", "#0077BB"),
              symbol = c(1, 3))

Visualize Variables Factor Map

Description

Plots column/variable principal coordinates.

Usage

viz_variables(x, ...)

viz_columns(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_columns(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'MultivariateBootstrap'
viz_columns(
  x,
  ...,
  axes = c(1, 2),
  color = FALSE,
  fill = FALSE,
  symbol = FALSE
)

## S4 method for signature 'PCA'
viz_variables(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = list(filter = "contribution", n = 10),
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  symbol = NULL,
  size = 1,
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'CA'
viz_variables(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'BootstrapPCA'
viz_variables(
  x,
  ...,
  axes = c(1, 2),
  color = FALSE,
  fill = FALSE,
  symbol = FALSE
)
viz_variables(x, ...)

viz_columns(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_columns(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'MultivariateBootstrap'
viz_columns(
  x,
  ...,
  axes = c(1, 2),
  color = FALSE,
  fill = FALSE,
  symbol = FALSE
)

## S4 method for signature 'PCA'
viz_variables(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = list(filter = "contribution", n = 10),
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  symbol = NULL,
  size = 1,
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'CA'
viz_variables(
  x,
  ...,
  axes = c(1, 2),
  active = TRUE,
  sup = TRUE,
  labels = FALSE,
  extra_quali = NULL,
  extra_quanti = NULL,
  color = NULL,
  fill = FALSE,
  symbol = FALSE,
  size = c(1, 6),
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  panel.first = NULL,
  panel.last = NULL,
  legend = list(x = "topleft")
)

## S4 method for signature 'BootstrapPCA'
viz_variables(
  x,
  ...,
  axes = c(1, 2),
  color = FALSE,
  fill = FALSE,
  symbol = FALSE
)

Arguments

`x`	A `CA`, `MCA` or `PCA` object.
`...`	Further graphical parameters.
`axes`	A length-two `numeric` vector giving the dimensions to be plotted.
`active`	A `logical` scalar: should the active observations be plotted?
`sup`	A `logical` scalar: should the supplementary observations be plotted?
`labels`	A `logical` scalar: should labels be drawn? Labeling a large number of points can be computationally expensive and make the graph difficult to read. A selection of points to label can be provided using a `list` of two named elements, `filter` (a string specifying how to filter the labels to be drawn) and `n` (an integer specifying the number of labels to be drawn). See examples below.
`extra_quali`	An optional vector of qualitative data for aesthetics mapping.
`extra_quanti`	An optional vector of quantitative data for aesthetics mapping. If a single `character` string is passed, it must be one of "`observation`", "`mass`", "`sum`", "`contribution`" or "`cos2`" (see `augment()`).
`color`	The colors for lines and points (will be mapped to `extra_quanti` or `extra_quali`; if both are set, the latter has priority). Ignored if set to `FALSE`.
`fill`	The background colors for points (will be mapped to `extra_quanti` or `extra_quali`; if both are set, the latter has priority). Ignored if set to `FALSE`.
`symbol`	A vector of plotting characters or symbols (will be mapped to `extra_quali`). This can either be a single character or an integer code for one of a set of graphics symbols. If `symbol` is a named a named vector, then the symbols will be associated with their name within `extra_quali`. Ignored if set to `FALSE`.
`size`	A length-two `numeric` vector giving range of possible sizes (greater than 0; will be mapped to `extra_quanti`). Ignored if set to `FALSE`.
`xlim`	A length-two `numeric` vector giving the x limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`ylim`	A length-two `numeric` vector giving the y limits of the plot. The default value, `NULL`, indicates that the range of the finite values to be plotted should be used.
`main`	A `character` string giving a main title for the plot.
`sub`	A `character` string giving a subtitle for the plot.
`panel.first`	An `expression` to be evaluated after the plot axes are set up but before any plotting takes place. This can be useful for drawing background grids.
`panel.last`	An `expression` to be evaluated after plotting has taken place but before the axes, title and box are added.
`legend`	A `list` of additional arguments to be passed to `graphics::legend()`; names of the list are used as argument names. If `NULL`, no legend is displayed.

Value

⁠viz_*()⁠ is called for its side-effects: it results in a graphic being displayed. Invisibly returns x.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Plot individuals
viz_individuals(X, panel.last = graphics::grid())

## Labels of the 10 individuals with highest cos2
viz_individuals(X, labels = list(how = "cos2", n = 10))

## Plot variables
viz_variables(X, panel.last = graphics::grid())

## Graphical parameters
## Continuous values
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2))
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2),
                color = grDevices::hcl.colors(12, "RdPu"))

viz_variables(X, extra_quanti = "contribution",
              color = grDevices::hcl.colors(12, "BluGrn", rev = TRUE),
              size = c(0, 1))

## Discrete values
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23)
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23,
                fill = c("#004488", "#DDAA33", "#BB5566"),
                color = "black")

viz_variables(X, extra_quali = c("Petal", "Petal", "Sepal", "Sepal"),
              color = c("#EE7733", "#0077BB"),
              symbol = c(1, 3))
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE)

## Plot individuals
viz_individuals(X, panel.last = graphics::grid())

## Labels of the 10 individuals with highest cos2
viz_individuals(X, labels = list(how = "cos2", n = 10))

## Plot variables
viz_variables(X, panel.last = graphics::grid())

## Graphical parameters
## Continuous values
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2))
viz_individuals(X, extra_quanti = iris$Petal.Length, symbol = 16, size = c(1, 2),
                color = grDevices::hcl.colors(12, "RdPu"))

viz_variables(X, extra_quanti = "contribution",
              color = grDevices::hcl.colors(12, "BluGrn", rev = TRUE),
              size = c(0, 1))

## Discrete values
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23)
viz_individuals(X, extra_quali = iris$Species, symbol = 21:23,
                fill = c("#004488", "#DDAA33", "#BB5566"),
                color = "black")

viz_variables(X, extra_quali = c("Petal", "Petal", "Sepal", "Sepal"),
              color = c("#EE7733", "#0077BB"),
              symbol = c(1, 3))

Plot Envelopes

Description

Plot Envelopes

Usage

viz_hull(x, ...)

viz_confidence(x, ...)

viz_tolerance(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_tolerance(x, ..., margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'BootstrapCA'
viz_tolerance(x, ..., margin = 1, axes = c(1, 2), level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
viz_confidence(x, ..., margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'BootstrapCA'
viz_confidence(x, ..., margin = 1, axes = c(1, 2), level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
viz_hull(x, ..., margin = 1, axes = c(1, 2), group = NULL)

## S4 method for signature 'BootstrapCA'
viz_hull(x, ..., margin = 1, axes = c(1, 2))
viz_hull(x, ...)

viz_confidence(x, ...)

viz_tolerance(x, ...)

## S4 method for signature 'MultivariateAnalysis'
viz_tolerance(x, ..., margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'BootstrapCA'
viz_tolerance(x, ..., margin = 1, axes = c(1, 2), level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
viz_confidence(x, ..., margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'BootstrapCA'
viz_confidence(x, ..., margin = 1, axes = c(1, 2), level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
viz_hull(x, ..., margin = 1, axes = c(1, 2), group = NULL)

## S4 method for signature 'BootstrapCA'
viz_hull(x, ..., margin = 1, axes = c(1, 2))

Arguments

`x`	An object from which to wrap observations (a `CA`, `MCA` or `PCA` object).
`...`	Further graphical parameters to be passed to `graphics::polygon()`.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`axes`	A length-two `numeric` vector giving the dimensions for which to compute results.
`group`	A vector specifying the group an observation belongs to.
`level`	A `numeric` vector specifying the confidence/tolerance level.

Value

⁠viz_*()⁠is called for its side-effects: it results in a graphic being displayed. Invisibly returns x.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_quali = "Species")

## Plot with convex hulls
col <- c("#004488", "#DDAA33", "#BB5566")
viz_rows(X, extra_quali = iris$Species, color = col)
viz_hull(X, group = iris$Species, border = col)

## Plot with tolerance ellipses
col <- c("#004488", "#DDAA33", "#BB5566")
viz_rows(X, extra_quali = iris$Species, color = col)
viz_tolerance(X, group = iris$Species, border = col)
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_quali = "Species")

## Plot with convex hulls
col <- c("#004488", "#DDAA33", "#BB5566")
viz_rows(X, extra_quali = iris$Species, color = col)
viz_hull(X, group = iris$Species, border = col)

## Plot with tolerance ellipses
col <- c("#004488", "#DDAA33", "#BB5566")
viz_rows(X, extra_quali = iris$Species, color = col)
viz_tolerance(X, group = iris$Species, border = col)

Wrap Observations

Description

wrap_hull() computes convex hull of a set of observations.
wrap_confidence() computes a confidence ellipse.
wrap_tolerance() computes a tolerance ellipse.

Usage

wrap_hull(x, ...)

wrap_confidence(x, ...)

wrap_tolerance(x, ...)

## S4 method for signature 'MultivariateAnalysis'
wrap_confidence(x, margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
wrap_tolerance(x, margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
wrap_hull(x, margin = 1, axes = c(1, 2), group = NULL)
wrap_hull(x, ...)

wrap_confidence(x, ...)

wrap_tolerance(x, ...)

## S4 method for signature 'MultivariateAnalysis'
wrap_confidence(x, margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
wrap_tolerance(x, margin = 1, axes = c(1, 2), group = NULL, level = 0.95)

## S4 method for signature 'MultivariateAnalysis'
wrap_hull(x, margin = 1, axes = c(1, 2), group = NULL)

Arguments

`x`	An object from which to wrap observations (a `CA`, `MCA` or `PCA` object).
`...`	Currently not used.
`margin`	A length-one `numeric` vector giving the subscript which the data will be returned: `1` indicates individuals/rows (the default), `2` indicates variables/columns.
`axes`	A length-two `numeric` vector giving the dimensions for which to compute results.
`group`	A vector specifying the group an observation belongs to.
`level`	A `numeric` vector specifying the confidence/tolerance level.

Value

⁠wrap_*()⁠ returns a data.frame of envelope x and y coordinates.

An extra column named group is added specifying the group an observation belongs to.

Author(s)

N. Frerebeau

Examples

## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_quali = "Species")

## Confidence ellipse coordinates
conf <- wrap_confidence(X, margin = 1, group = "Species", level = c(0.68, 0.95))

## Tolerance ellipse coordinates
conf <- wrap_confidence(X, margin = 1, group = "Species", level = 0.95)

## Convex hull coordinates
hulls <- wrap_hull(X, margin = 1, group = "Species")
## Load data
data("iris")

## Compute principal components analysis
X <- pca(iris, scale = TRUE, sup_quali = "Species")

## Confidence ellipse coordinates
conf <- wrap_confidence(X, margin = 1, group = "Species", level = c(0.68, 0.95))

## Tolerance ellipse coordinates
conf <- wrap_confidence(X, margin = 1, group = "Species", level = 0.95)

## Convex hull coordinates
hulls <- wrap_hull(X, margin = 1, group = "Species")

Package 'dimensio'

Help Index

Benthos

Description

Usage

Format

Source

See Also

Biplot

Description

Usage

Arguments

Details

Value

PCA Biplots

CA Biplots

Author(s)

References

See Also

Examples

Partial Bootstrap Analysis

Description

Usage

Arguments

Value

Author(s)

References

Examples

Burt Table

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Correspondence Analysis

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Complete Disjunctive Table

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Colours

Description

Usage

Format

Source

See Also

Countries

Description

Usage

Format

Source

See Also

Dimnames of an Object

Description

Usage

Arguments

Author(s)

See Also

Get Contributions

Description

Usage

Arguments

Value

Author(s)

See Also

Get Coordinates

Description