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Principal Component Analysis

dudi.pca.Rd

dudi.pca performs a principal component analysis of a data frame and returns the results as objects of class pca and dudi.

Usage

dudi.pca(df, row.w = rep(1, nrow(df))/nrow(df), 
    col.w = rep(1, ncol(df)), center = TRUE, scale = TRUE, 
    scannf = TRUE, nf = 2)

Arguments

df

a data frame with n rows (individuals) and p columns (numeric variables)

row.w

an optional row weights (by default, uniform row weights)

col.w

an optional column weights (by default, unit column weights)

center

a logical or numeric value, centring option
if TRUE, centring by the mean
if FALSE no centring
if a numeric vector, its length must be equal to the number of columns of the data frame df and gives the decentring

scale

a logical value indicating whether the column vectors should be normed for the row.w weighting

scannf

a logical value indicating whether the screeplot should be displayed

nf

if scannf FALSE, an integer indicating the number of kept axes

Value

Returns a list of classes pca and dudi (see dudi) containing the used information for computing the principal component analysis :

tab

the data frame to be analyzed depending of the transformation arguments (center and scale)

cw

the column weights

lw

the row weights

eig

the eigenvalues

rank

the rank of the analyzed matrice

nf

the number of kept factors

c1

the column normed scores i.e. the principal axes

l1

the row normed scores

co

the column coordinates

li

the row coordinates i.e. the principal components

call

the call function

cent

the p vector containing the means for variables (Note that if center = F, the vector contains p 0)

norm

the p vector containing the standard deviations for variables i.e. the root of the sum of squares deviations of the values from their means divided by n (Note that if norm = F, the vector contains p 1)

See also

prcomp, princomp in the mva library

Author

Daniel Chessel
Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr

Examples

data(deug)
deug.dudi <- dudi.pca(deug$tab, center = deug$cent, scale = FALSE, scan = FALSE)
deug.dudi1 <- dudi.pca(deug$tab, center = TRUE, scale = TRUE, scan = FALSE)

if(adegraphicsLoaded()) {
  g1 <- s.class(deug.dudi$li, deug$result, plot = FALSE)
  g2 <- s.arrow(deug.dudi$c1, lab = names(deug$tab), plot = FALSE)
  g3 <- s.class(deug.dudi1$li, deug$result, plot = FALSE)
  g4 <- s.corcircle(deug.dudi1$co, lab = names(deug$tab), full = FALSE, plot = FALSE)
  G1 <- rbindADEg(cbindADEg(g1, g2, plot = FALSE), cbindADEg(g3, g4, plot = FALSE), plot = TRUE)
  
  G2 <- s1d.hist(deug.dudi$tab, breaks = seq(-45, 35, by = 5), type = "density", xlim = c(-40, 40), 
    right = FALSE, ylim = c(0, 0.1), porigin.lwd = 2)
    
} else {
  par(mfrow = c(2, 2))
  s.class(deug.dudi$li, deug$result, cpoint = 1)
  s.arrow(deug.dudi$c1, lab = names(deug$tab))
  s.class(deug.dudi1$li, deug$result, cpoint = 1)
  s.corcircle(deug.dudi1$co, lab = names(deug$tab), full = FALSE, box = TRUE)
  par(mfrow = c(1, 1))

  # for interpretations
  par(mfrow = c(3, 3))
  par(mar = c(2.1, 2.1, 2.1, 1.1))
  for(i in 1:9) {
    hist(deug.dudi$tab[,i], xlim = c(-40, 40), breaks = seq(-45, 35, by = 5), 
      prob = TRUE, right = FALSE, main = names(deug$tab)[i], xlab = "", ylim = c(0, 0.10))
  abline(v = 0, lwd = 3)
  }
  par(mfrow = c(1, 1))
}