mdatools (version 0.7.0)

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 Q 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.

Qlim

statistical limit for Q residuals.

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 Q residuals vs. Hotelling T2 values), calculate confidence limits for Q 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:

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 Q vs. T2 residuals plot.

Most of the methods for plotting data are also available for PCA results (pcares) objects. Also check pca.mvreplace, which replaces missing values in a data matrix with approximated using iterative PCA decomposition.

Examples

library(mdatools)
### Examples for PCA class

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

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))