Non-linear Iterative Partial Least Squares (NIPALS) algorithm

Description

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

Usage

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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

Author(s)

Stephane Dray stephane.dray@univ-lyon1.fr

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.

See Also

dudi.pca

Examples

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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", quiet = TRUE)) {
    g1 <- s1d.barchart(acp1$eig, psub.text = "dudi.pca", p1d.hori = F, plot = F)
    g2 <- s1d.barchart(nip1$eig, psub.text = "nipals", p1d.hori = F, plot = F)
    g3 <- xyplot(nip1$c1[, 1] ~ acp1$c1[, 1], main = "col scores", xlab = "dudi.pca", 
      ylab = "nipals")
    g4 <- 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")
}

## Not run: 
## with NAs:
doubs$env[1, 1] <- NA
nip2 <- nipals(doubs$env)
cor(nip1$li, nip2$li)
nip1$eig
nip2$eig

## End(Not run)

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