pcomp: Principal Components Analysis.

In SciViews: SciViews - Main package

Description

Perform a principal components analysis on a matrix or data frame and return a pcomp object.

Usage

pcomp(x, ...)

## S3 method for class 'formula'
pcomp(formula, data = NULL, subset, na.action,
  method = c("svd", "eigen"), ...)

## Default S3 method:
pcomp(x, method = c("svd", "eigen"), scores = TRUE,
  center = TRUE, scale = TRUE, tol = NULL, covmat = NULL,
  subset = rep(TRUE, nrow(as.matrix(x))), ...)

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

## S3 method for class 'pcomp'
summary(object, loadings = TRUE, cutoff = 0.1, ...)

## S3 method for class 'summary.pcomp'
print(x, digits = 3, loadings = x$print.loadings,
  cutoff = x$cutoff, ...)

## S3 method for class 'pcomp'
plot(x, which = c("screeplot", "loadings", "correlations",
  "scores"), choices = 1L:2L, col = par("col"), bar.col = "gray",
  circle.col = "gray", ar.length = 0.1, pos = NULL, labels = NULL,
  cex = par("cex"), main = paste(deparse(substitute(x)), which, sep =
  " - "), xlab, ylab, ...)

## S3 method for class 'pcomp'
screeplot(x, npcs = min(10, length(x$sdev)),
  type = c("barplot", "lines"), col = "cornsilk",
  main = deparse(substitute(x)), ...)

## S3 method for class 'pcomp'
points(x, choices = 1L:2L, type = "p", pch = par("pch"),
  col = par("col"), bg = par("bg"), cex = par("cex"), ...)

## S3 method for class 'pcomp'
lines(x, choices = 1L:2L, groups, type = c("p", "e"),
  col = par("col"), border = par("fg"), level = 0.9, ...)

## S3 method for class 'pcomp'
text(x, choices = 1L:2L, labels = NULL, col = par("col"),
  cex = par("cex"), pos = NULL, ...)

## S3 method for class 'pcomp'
biplot(x, choices = 1L:2L, scale = 1, pc.biplot = FALSE,
  ...)

## S3 method for class 'pcomp'
pairs(x, choices = 1L:3L, type = c("loadings",
  "correlations"), col = par("col"), circle.col = "gray",
  ar.col = par("col"), ar.length = 0.05, pos = NULL,
  ar.cex = par("cex"), cex = par("cex"), ...)

## S3 method for class 'pcomp'
predict(object, newdata, dim = length(object$sdev), ...)

## S3 method for class 'pcomp'
correlation(x, newvars, dim = length(x$sdev), ...)

scores(x, ...)

## S3 method for class 'pcomp'
scores(x, labels = NULL, dim = length(x$sdev), ...)

Arguments

x	A matrix or data frame with numeric data.
...	Arguments passed to or from other methods. If 'xis a formula one might specifyscale =,tol =orcovmat ='.
formula	A formula with no response variable, referring only to numeric variables.
data	An optional data frame (or similar: see model.frame()) containing the variables in the formula formula =. By default the variables are taken from environment(formula).
subset	An optional vector used to select rows (observations) of the data matrix x.
na.action	A function which indicates what should happen when the data contain NAs. The default is set by the na.action = setting of options(), and is na.fail() if that is not set. The 'factory-fresh' default is na.omit().
method	Either "svd" (using prcomp()), "eigen" (using princomp()), or an abbreviation.
scores	A logical value indicating whether the score on each principal component should be calculated.
center	A logical value indicating whether the variables should be shifted to be zero centered. Alternately, a vector of length equal the number of columns of x can be supplied. The value is passed to scale =. Note that this argument is ignored for method = "eigen" and the dataset is always centered in this case.
scale	A logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place. The default is TRUE, which in general, is advisable. Alternatively, a vector of length equal the number of columns of x can be supplied. The value is passed to scale().
tol	Only when method = "svd". A value indicating the magnitude below which components should be omitted. (Components are omitted if their standard deviations are less than or equal to tol times the standard deviation of the first component.) With the default null setting, no components are omitted. Other settings for tol = could be tol = 0 or tol = sqrt(.Machine$double.eps), which would omit essentially constant components.
covmat	A covariance matrix, or a covariance list as returned by cov.wt() (and cov.mve() or cov.mcd() from package MASS). If supplied, this is used rather than the covariance matrix of x.
object	A 'pcomp' object.
loadings	Do we also summarize the loadings?
cutoff	The cutoff value below which loadings are replaced by white spaces in the table. That way, larger values are easier to spot and to read in large tables.
digits	The number of digits to print.
which	The graph to plot.
choices	Which principal axes to plot. For 2D graphs, specify two integers.
col	The color to use in graphs.
bar.col	The color of bars in the screeplot.
circle.col	The color for the circle in the loadings or correlations plots.
ar.length	The length of the arrows in the loadings and correlations plots.
pos	The position of text relative to arrows in loadings and correlation plots.
labels	The labels to write. If NULL default values are computed.
cex	The factor of expansion for text (labels) in the graphs.
main	The title of the graph.
xlab	The label of the x-axis.
ylab	The label of the y-axis.
npcs	The number of principal components to represent in the screeplot.
type	The type of screeplot ("barplot" or "lines") or pairs plot ("loadings" or "correlations").
pch	The type of symbol to use.
bg	The background color for symbols.
groups	A grouping factor.
border	The color of the border.
level	The probability level to use to draw the ellipse.
pc.biplot	Do we create a Gabriel's biplot (see biplot())?
ar.col	Color of arrows.
ar.cex	Expansion factor for terxt on arrows.
newdata	New individuals with observations for the same variables as those used for calculating the PCA. You can then plot these additional individuals in the scores plot.
dim	The number of principal components to keep.
newvars	New variables with observations for same individuals as those used for mcalculating the PCA. Correlation with PCs is calculated. You can then plot these additional variables in the correlation plot.

Details

pcomp() is a generic function with "formula" and "default" methods. It is essentially a wrapper around prcomp() and princomp() to provide a coherent interface and object for both methods.

A 'pcomp' object is created. It inherits from 'pca' (as in labdsv package, but not compatible with the 'pca' object of package ade4) and of 'princomp'.

For more information on calculation done, refer to prcomp() for method = "svd" or princomp() for method = "eigen".

Value

A c("pcomp", "pca", "princomp") object.

Note

The signs of the columns of the loadings and scores are arbitrary, and so may differ between functions for PCA, and even between different builds of R.

Author(s)

Philippe Grosjean [e-mail], but the core code is indeed in package stats.

See Also

vectorplot(), prcomp(), princomp(), loadings(), Correlation()

Examples

# We will analyze mtcars without the Mercedes data (rows 8:14)
data(mtcars)
cars.pca <- pcomp(~ mpg + cyl + disp + hp + drat + wt + qsec, data = mtcars,
  subset = -(8:14))
cars.pca
summary(cars.pca)
screeplot(cars.pca)

# Loadings are extracted and plotted like this
(cars.ldg <- loadings(cars.pca))
plot(cars.pca, which = "loadings") # Equivalent to vectorplot(cars.ldg)

# Similarly, correlations of variables with PCs are extracted and plotted
(cars.cor <- Correlation(cars.pca))
plot(cars.pca, which = "correlations") # Equivalent to vectorplot(cars.cor)
# One can add supplementary variables on this graph
lines(Correlation(cars.pca,
  newvars = mtcars[-(8:14), c("vs", "am", "gear", "carb")]))

# Plot the scores
plot(cars.pca, which = "scores", cex = 0.8) # Similar to plot(scores(x)[, 1:2])
# Add supplementary individuals to this plot (labels), also points() or lines()
text(predict(cars.pca, newdata = mtcars[8:14, ]), col = "gray", cex = 0.8)

# Pairs plot for 3 PCs
iris.pca <- pcomp(iris[, -5])
pairs(iris.pca, col = (2:4)[iris$Species])

Example output

Call:
pcomp(formula = ~mpg + cyl + disp + hp + drat + wt + qsec, data = mtcars, 
    subset = -(8:14))

Variances:
       PC1        PC2        PC3        PC4        PC5        PC6        PC7 
5.13759552 1.21698212 0.28325478 0.15620899 0.12409321 0.05604916 0.02581622 

 7  variables and  25 observations.
Importance of components (eigenvalues):
                         PC1   PC2    PC3    PC4    PC5     PC6     PC7
Variance               5.138 1.217 0.2833 0.1562 0.1241 0.05605 0.02582
Proportion of Variance 0.734 0.174 0.0405 0.0223 0.0177 0.00801 0.00369
Cumulative Proportion  0.734 0.908 0.9483 0.9706 0.9883 0.99631 1.00000

Loadings (eigenvectors, rotation matrix):
     PC1    PC2    PC3    PC4    PC5    PC6    PC7   
mpg  -0.415        -0.107  0.754 -0.353  0.318  0.144
cyl   0.425        -0.165  0.447  0.289 -0.485  0.521
disp  0.423 -0.110  0.234  0.465  0.103        -0.726
hp    0.385  0.349  0.106        -0.817 -0.203       
drat -0.320  0.505  0.736         0.208 -0.222       
wt    0.400 -0.262  0.499                0.590  0.416
qsec -0.240 -0.733  0.323        -0.267 -0.475       

Loadings:
     PC1    PC2    PC3    PC4    PC5    PC6    PC7   
mpg  -0.415        -0.107  0.754 -0.353  0.318  0.144
cyl   0.425        -0.165  0.447  0.289 -0.485  0.521
disp  0.423 -0.110  0.234  0.465  0.103        -0.726
hp    0.385  0.349  0.106        -0.817 -0.203       
drat -0.320  0.505  0.736         0.208 -0.222       
wt    0.400 -0.262  0.499                0.590  0.416
qsec -0.240 -0.733  0.323        -0.267 -0.475       

                 PC1   PC2   PC3   PC4   PC5   PC6   PC7
SS loadings    1.000 1.000 1.000 1.000 1.000 1.000 1.000
Proportion Var 0.143 0.143 0.143 0.143 0.143 0.143 0.143
Cumulative Var 0.143 0.286 0.429 0.571 0.714 0.857 1.000
Matrix of PCA variables and components correlation:
     PC1    PC2    PC3    PC4    PC5    PC6    PC7   
mpg  -0.940  0.055 -0.057  0.298 -0.124  0.075  0.023
cyl   0.963  0.062 -0.088  0.177  0.102 -0.115  0.084
disp  0.960 -0.122  0.124  0.184  0.036 -0.003 -0.117
hp    0.873  0.385  0.056 -0.039 -0.288 -0.048  0.005
drat -0.726  0.557  0.392  0.030  0.073 -0.053  0.009
wt    0.906 -0.289  0.266 -0.006  0.004  0.140  0.067
qsec -0.544 -0.808  0.172  0.010 -0.094 -0.112  0.010
Warning message:
In isTRUE(!as.numeric(labels)) : NAs introduced by coercion

SciViews documentation built on Nov. 17, 2019, 1:06 a.m.