Non-linear Iterative Partial Least Squares (NIPALS) algorithm

This function performs NIPALS algorithm, i.e. a principal component analysis of a data table that can contain missing values.

Usage

nipals(df, nf = 2, rec = FALSE, niter = 100, tol = 1e-09)
# S3 method for class 'nipals'
scatter(x, xax = 1, yax = 2, clab.row = 0.75, clab.col
= 1, posieig = "top", sub = NULL, ...)
# S3 method for class 'nipals'
print(x, ...)

Arguments

df: a data frame that can contain missing values
nf: an integer, the number of axes to keep
rec: a logical that specify if the functions must perform the reconstitution of the data using the nf axes
niter: an integer, the maximum number of iterations
tol: a real, the tolerance used in the iterative algorithm
x: an object of class nipals
xax: the column number for the x-axis
yax: the column number for the y-axis
clab.row: a character size for the rows
clab.col: a character size for the columns
posieig: if "top" the eigenvalues bar plot is upside, if "bottom" it is downside, if "none" no plot
sub: a string of characters to be inserted as legend
...: further arguments passed to or from other methods

Details

Data are scaled (mean 0 and variance 1) prior to the analysis.

Value

Returns a list of classes nipals:

tab: the scaled data frame
eig: the pseudoeigenvalues
rank: the rank of the analyzed matrice
nf: the number of factors
c1: the column normed scores
co: the column coordinates
li: the row coordinates
call: the call function
nb: the number of iterations for each axis
rec: a data frame obtained by the reconstitution of the scaled data using the nf axes

References

Wold, H. (1966) Estimation of principal components and related models by iterative least squares. In P. Krishnaiah, editors.Multivariate Analysis, Academic Press, 391–420.

Wold, S., Esbensen, K. and Geladi, P. (1987) Principal component analysis Chemometrics and Intelligent Laboratory Systems, 2, 37–52.

Author

Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

data(doubs)
## nipals is equivalent to dudi.pca when there are no NA
acp1 <- dudi.pca(doubs$env, scannf = FALSE, nf = 2)
nip1 <- nipals(doubs$env)


if(adegraphicsLoaded()) {
  if(requireNamespace("lattice", quietly = TRUE)) {
    g1 <- s1d.barchart(acp1$eig, psub.text = "dudi.pca", p1d.horizontal = FALSE, plot = FALSE)
    g2 <- s1d.barchart(nip1$eig, psub.text = "nipals", p1d.horizontal = FALSE, plot = FALSE)
    g3 <- lattice::xyplot(nip1$c1[, 1] ~ acp1$c1[, 1], main = "col scores", xlab = "dudi.pca", 
      ylab = "nipals")
    g4 <- lattice::xyplot(nip1$li[, 1] ~ acp1$li[, 1], main = "row scores", xlab = "dudi.pca", 
      ylab = "nipals")
    G <- ADEgS(list(g1, g2, g3, g4), layout = c(2, 2))
  }
  
} else {
  par(mfrow = c(2, 2))
  barplot(acp1$eig, main = "dudi.pca")
  barplot(nip1$eig, main = "nipals")
  plot(acp1$c1[, 1], nip1$c1[, 1], main = "col scores", xlab = "dudi.pca", ylab = "nipals")
  plot(acp1$li[, 1], nip1$li[, 1], main = "row scores", xlab = "dudi.pca", ylab = "nipals")
}


if (FALSE) { # \dontrun{
## with NAs:
doubs$env[1, 1] <- NA
nip2 <- nipals(doubs$env)
cor(nip1$li, nip2$li)
nip1$eig
nip2$eig
} # }