selkaiser: Heuristic selection of the dimension of a PCA model with the...

In mlesnoff/rnirs: Dimension reduction, Regression and Discrimination for Chemometrics

Heuristic selection of the dimension of a PCA model with the Guttman-Kaiser rule

Description

The function helps selecting the dimension (i.e. nb. components) of a PCA model using the method firstly proposed by Guttman 1954 and Kaiser 1960.

The input matrix X is centered internally to the function. The eigenvalues are compared to the mean eigenvalue (= sum(eigs) / p for a matrix with p columns). If X is scaled and using the denominator n (not n - 1) for the variance and covariance calculations, sum(eigs) / p = 1.

If argument ci = TRUE, the eigenvalues are replaced by the lower limit of their 95pct confidence interval, calculated by back-transformation after assuming that var(log(eig) = 2 / n where n is the number of observations (see Karlis et al. 2003 p.647).

Usage

selkaiser(X, ncomp, algo = NULL,
    ci = FALSE, alpha = 1,
    plot = TRUE,
    xlab = "Nb. components", ylab = NULL,
    ...)

Arguments

X	A n x p matrix or data frame of variables.
ncomp	The maximal number of PCA scores (= components = latent variables) to be calculated.
algo	A function (algorithm) implementing a PCA. Default to NULL: if n < p, pca_eigenk is used; in the other case, pca_eigen is used.
ci	Logical. If TRUE, the eigenvalues are replaced by an estimate of the lower limit of their 95pct confidence interval. Default to FALSE.
alpha	A scalar multiplying the mean eigenvalue used for comparisons. Default to alpha = 1.
plot	Logical. If TRUE (default), the results are plotted.
xlab	Label for the x-axis of the plot.
ylab	Label for the y-axis of the plot.
...	Optionnal arguments to pass in the function defined in algo.

Value

A list of several items, see the examples. Output opt is the selected number of components.

References

Bro, R., Smilde, A.K., 2014. Principal component analysis. Anal. Methods 6, 2812-2831. https://doi.org/10.1039/C3AY41907J

Cangelosi, R., Goriely, A., 2007. Component retention in principal component analysis with application to cDNA microarray data. Biology Direct 2, 2. https://doi.org/10.1186/1745-6150-2-2

Guttman, L., 1954. Some necessary conditions for common-factor analysis. Psychometrika 19, 149–161. https://doi.org/10.1007/BF02289162

Karlis, D., Saporta, G., Spinakis, A., 2003. A Simple Rule for the Selection of Principal Components. Communications in Statistics - Theory and Methods 32, 643–666. https://doi.org/10.1081/STA-120018556

Kaiser, H.F., 1960. The application of electronic computers to factor analysis. Educational and Psychological Measurement 20, 141–151.

Examples

data(datoctane)
X <- datoctane$X
## removing outliers
zX <- X[-c(25:26, 36:39), ]
n <- nrow(zX)
plotsp(zX)

ncomp <- 30
selkaiser(zX, ncomp = ncomp)
xvar <- apply(zX, 2, var) * (n - 1) / n
selkaiser(scale(zX, scale = xvar), ncomp = ncomp)

mlesnoff/rnirs documentation built on April 24, 2023, 4:17 a.m.