eigenvalue: Extract and visualize the eigenvalues/variances of dimensions

Description

Eigenvalues correspond to the amount of the variation explained by each principal component (PC).

get_eig(): Extract the eigenvalues/variances of the principal dimensions
fviz_eig(): Plot the eigenvalues/variances against the number of dimensions
get_eigenvalue(): an alias of get_eig()
fviz_screeplot(): an alias of fviz_eig()

These functions support the results of Principal Component Analysis (PCA), Correspondence Analysis (CA), Multiple Correspondence Analysis (MCA), Factor Analysis of Mixed Data (FAMD), Multiple Factor Analysis (MFA) and Hierarchical Multiple Factor Analysis (HMFA) functions. fviz_eig() validates ncp, parallel.iter, and parallel.seed before plotting, accepting integer-like numeric values while still rejecting fractional inputs.

Recent versions of FactoMineR::PCA() may retain only the number of eigenvalues requested through its ncp argument. When the stored eigenvalues do not account for the result's recorded total inertia, fviz_eig() warns that the scree plot is incomplete. Refit the PCA with a sufficiently large ncp to plot the complete spectrum. get_eig() continues to return the eigenvalues stored in the object.

Usage

get_eig(X)
get_eigenvalue(X)
fviz_eig(
  X,
  choice = c("variance", "eigenvalue"),
  geom = c("bar", "line"),
  barfill = "steelblue",
  barcolor = "steelblue",
  linecolor = "black",
  ncp = 10,
  addlabels = FALSE,
  hjust = 0,
  main = NULL,
  xlab = NULL,
  ylab = NULL,
  ggtheme = theme_minimal(),
  parallel = FALSE,
  parallel.color = "red",
  parallel.lty = "dashed",
  parallel.iter = 100,
  parallel.seed = NULL,
  ...
)
fviz_screeplot(...)

Value

get_eig() (or get_eigenvalue()): returns a data.frame containing 3 columns: the eigenvalues, the percentage of variance and the cumulative percentage of variance retained by each dimension.
fviz_eig() (or fviz_screeplot()): returns a ggplot2

Arguments

X: an object of class PCA, CA, MCA, FAMD, MFA, or HMFA [FactoMineR]; prcomp or princomp [stats]; factoextra_pca; dudi, pca, coa, acm, between, or within [ade4]; ca or mjca [ca]; correspondence [MASS]; or expoOutput [ExPosition].
choice: a text specifying the data to be plotted. Allowed values are "variance" or "eigenvalue".
geom: a text specifying the geometry to be used for the graph. Allowed values are "bar" for barplot, "line" for lineplot or c("bar", "line") to use both types.
barfill: fill color for bar plot.
barcolor: outline color for bar plot.
linecolor: color for line plot (when geom contains "line").
ncp: a single positive integer specifying the number of dimensions to be shown. Integer-like numeric values are accepted.
addlabels: logical value. If TRUE, labels are added at the top of bars or points showing the information retained by each dimension.
hjust: horizontal adjustment of the labels.
main, xlab, ylab: plot main and axis titles.
ggtheme: function, ggplot2 theme name. The default is set by each function's ggtheme argument; see the function usage for the actual default. Set ggtheme = NULL to skip applying a ggpubr theme, so the plot keeps ggplot2 default theme or the theme set globally via theme_set(). Allowed values include ggplot2 official themes: theme_gray(), theme_bw(), theme_minimal(), theme_classic(), theme_void(), ....
parallel: logical value. If TRUE, adds a Horn parallel-analysis threshold curve. Each point is the 95th percentile of the corresponding ordered eigenvalue from independently simulated reference data. Components whose eigenvalues exceed their component-specific thresholds are retained by the parallel-analysis rule. Correlation PCA uses standardized reference data; covariance PCA uses reconstructed marginal scales. This is available only when choice = "eigenvalue" and X is a sufficiently complete prcomp or princomp object. Mean centering is required; prcomp also requires retained scores. Custom scaling and incomplete covariance decompositions are rejected when their reference distribution cannot be reconstructed. Default is FALSE.
parallel.color: color of the parallel-analysis threshold curve. Default is "red".
parallel.lty: line type for the parallel-analysis curve. Default is "dashed".
parallel.iter: a single positive integer giving the number of iterations for parallel analysis simulation. Integer-like numeric values are accepted. Default is 100.
parallel.seed: NULL or a single non-negative integer seed for reproducible parallel analysis simulation. If NULL (default), the current RNG stream is used. Integer-like numeric values are accepted.
...: optional arguments to be passed to the function ggpar.

Author

Alboukadel Kassambara alboukadel.kassambara@gmail.com

References

https://www.datanovia.com/learn/

Examples

Run this code

# Principal Component Analysis
# ++++++++++++++++++++++++++
data(iris)
res.pca <- prcomp(iris[, -5],  scale = TRUE)

# Extract eigenvalues/variances
get_eig(res.pca)

# Default plot
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 85))
  
# Scree plot - Eigenvalues
fviz_eig(res.pca, choice = "eigenvalue", addlabels=TRUE)

# Use only bar  or line plot: geom = "bar" or geom = "line"
fviz_eig(res.pca, geom="line")

# Parallel analysis (Horn's method) to determine the number of components
# Retain components whose eigenvalues exceed their component-specific points
fviz_eig(res.pca, choice = "eigenvalue", parallel = TRUE,
         addlabels = TRUE, parallel.color = "red",
         parallel.iter = 10, parallel.seed = 123)

if (FALSE) {         
# Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(housetasks)
res.ca <- CA(housetasks, graph = FALSE)
get_eig(res.ca)
fviz_eig(res.ca, linecolor = "#FC4E07",
   barcolor = "#00AFBB", barfill = "#00AFBB")

# Multiple Correspondence Analysis
# +++++++++++++++++++++++++++++++++
library(FactoMineR)
data(poison)
res.mca <- MCA(poison, quanti.sup = 1:2, 
              quali.sup = 3:4, graph=FALSE)
get_eig(res.mca)
fviz_eig(res.mca, linecolor = "#FC4E07",
   barcolor = "#2E9FDF", barfill = "#2E9FDF")
}

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