mdatools (version 0.5.3)

pca: Principal Component Analysis

Description

pca is used to build and explore a principal component analysis (PCA) model.

Usage

pca(x, ncomp = 15, center = T, scale = F, cv = NULL, x.test = NULL, 
   alpha = 0.05, method = 'svd', info = '')

Arguments

x

a numerical matrix with calibration data.

ncomp

maximum number of components to calculate.

center

logical, do mean centering of data or not.

scale

logical, do sdandardization of data or not.

cv

number of segments for random cross-validation (1 for full cross-validation).

x.test

a numerical matrix with test data.

alpha

significance level for calculating limit for Q2 residuals.

method

method to compute principal components.

info

a short text line with model description.

Value

• Returns an object of pca class with following fields:
• ncomp
  number of components included to the model.
• ncomp.selected
  selected (optimal) number of components.
• loadings
  matrix with loading values (nvar x ncomp).
• eigenvals
  vector with eigenvalues for all existent components.
• expvar
  vector with explained variance for each component (in percent).
• cumexpvar
  vector with cumulative explained variance for each component (in percent).
• T2lim
  statistical limit for T2 distance.
• Q2lim
  statistical limit for Q2 distance.
• info
  information about the model, provided by user when build the model.
• calres
  an object of class pcares with PCA results for a calibration data.
• testres
  an object of class pcares with PCA results for a test data, if it was provided.
• cvres
  an object of class pcares with PCA results for cross-validation, if this option was chosen.

Details

So far only SVD (Singular Value Decompisition) method is available, more coming soon.

By default pca uses number of components (ncomp) as a minimum of number of objects - 1, number of variables and default or provided value. Besides that, there is also a parameter for selecting an optimal number of components (ncomp.selected). The optimal number of components is used to build a residuals plot (with Q2 residuals vs. Hotelling T2 values), calculate confidence limits for Q2 residuals, as well as for SIMCA classification.

If data contains missing values (NA) the pca will use an iterative algorithm to fit the values with most probable ones. The algorithm is implemented in a function pca.mvreplace. The same center and scale options will be used. You can also do this step manually before calling pca and play with extra options.

See Also

Methods for pca objects: ll{ plot.pca makes an overview of PCA model with four plots. summary.pca shows some statistics for the model. selectCompNum.pca set number of optimal components in the model predict.pca applies PCA model to a new data. plotScores.pca shows scores plot. plotLoadings.pca shows loadings plot. plotVariance.pca shows explained variance plot. plotCumVariance.pca shows cumulative explained variance plot. plotResiduals.pca shows Q2 vs. T2 residuals plot. } Most of the methods for plotting data are also available for PCA results (pcares) objects.

Other methods implemented in pca: ll{ pca.mvreplace replaces missing values in a data matrix with approximated using iterative PCA decomposition. }

Examples

### Examples for PCA class

## 1. Make PCA model for People data with autoscaling
## and full cross-validation

library(mdatools)

data(people)
model = pca(people, scale = TRUE, cv = 1, info = 'Simple PCA model')
model = selectCompNum(model, 4)
summary(model)
plot(model, show.labels = TRUE)

## 2. Add missing values, make a new model and show plots
peoplemv = people
peoplemv[2, 7] = NA
peoplemv[6, 2] = NA
peoplemv[10, 4] = NA
peoplemv[22, 12] = NA

modelmv = pca(peoplemv, scale = TRUE, info = 'Model with missing values')
modelmv = selectCompNum(modelmv, 4)
summary(modelmv)
plot(modelmv, show.labels = TRUE)

## 3. Show scores and loadings plots for the model
par(mfrow = c(2, 2))
plotScores(model, comp = c(1, 3), show.labels = TRUE)
plotScores(model, comp = 2, type = 'h', show.labels = TRUE)
plotLoadings(model, comp = c(1, 3), show.labels = TRUE)
plotLoadings(model, comp = c(1, 2), type = 'h', show.labels = TRUE)
par(mfrow = c(1, 1))

## 4. Show residuals and variance plots for the model
par(mfrow = c(2, 2))
plotVariance(model, type = 'h')
plotCumVariance(model, show.labels = TRUE, legend.position = 'bottomright')
plotResiduals(model, show.labels = TRUE)
plotResiduals(model, ncomp = 2, show.labels = TRUE)
par(mfrow = c(1, 1))